Home

ASKI User Manual - Ruhr

Contents

1. If INVERSION GRID CELLS SPECIFIC the following line must contain the number of cells nce11 which should be taken followed by nce11 blocks of lines each defining an inversion grid cell In case of PARAMETERS ALL these blocks consist of a single line line containing an inversion grid cell index In case of PARAMETERS SPECIFIC these blocks consist of two lines one line containing an inversion grid cell index and an additional second line of the form nparam pmtrization 1 param 1 pmtrization n param n defining the parameters to be used for this specific inversion grid cell 36 CHAPTER 2 FILES 2 7 3 Data Samples Block line DATA SAMPLES line of form PATHS value where value is either ALL all paths for a given set of event and station indices are used or SPECIFIC a specific definition of paths as a series of event and station index pairs follows below If PATHS ALL the next two lines are of form nev iev 1 iev n and nstat istat istat n defining the set of event and station indices which form by all combinations the used paths line of form COMPONENTS value where value is either ALL for all paths the same components are used or SPECIFIC only allowed if PATHS SPECIFIC for each path a specific set of components may be defined If COMPONENTS ALL the next line is of form ncomp comp 1 comp
2. ECART INVGRID FILE NODES TRT A File name relative to MAIN PATH INVERSION ITERATION STEP PATH of nodes co ordinates file to be used for definition of tet4 type cells in case of ECART INVGRID USE NODES COMMON False 22 CHAPTER 1 BASIC STEPS ECART INVGRID FILE NODES HEXS8 File name relative to MAIN PATH INVERSION ITERATION STEP PATH of nodes co ordinates file to be used for definition of hex8 type cells in case of ECART INVGRID USE NODES COMMON False ECART INVGRID FILE CELLS TET4 4 File name relative to MAIN PATH INVERSION ITERATION STEP PATH of cell con nectivity file for definition of tet4 type cells When using module cubit 2ASKIecartInversionGrid you should set ECART INVGRID FILE CELLS TETA4 cell connectivity tet4 ECART INVGRID FILE CELLS HEXS8 File name relative to MAIN PATH INVERSION ITERATION STEP PATH of cell con nectivity file for definition of hex8 type cells When using module cubit 2ASKIecartInversionGrid you should set ECART INVGRID FILE CELLS HEX8 cell connectivity hex8 ECART INVGRID FILE NEIGHBOURS File name relative to MAIN PATH INVERSION ITERATION STEP PATH of cell neigh bours file If not present this file will be created when first using the inversion grid If present its c
3. For each inversion grid cell Q C IR which contains wavefield points x x the weights U1 w5 are computed such that K x dx X wiK xi 3 1 Qe i 1 There are several types of integration weights supported indicated by dummy variable int w_ type of subroutine createIntegrationWeights 3 1 0 Compute Average no integration In case of intw type 0 function createIntegrationWeights sets 1 l Wi 1 1 Ne Ne in each inversion grid cell Q This way the summation 577 w K x S07 K xf yields the average kernel value in Qe This type of integration weights which are actually no integration weights may be used to perform some sort of interpolation of kernel values onto the inversion grid e g in order to compare kernel values from different methods which use different sets of wavefield points 39 40 CHAPTER 3 PROGRAMS SCRIPTS AND MODULES 3 1 1 Scattered Data Integration In case of intw type 1 4 a method by David Levin Lev99 is apllied to a stan dardized inversion grid cell Q For different shapes of inversion grid cells different types of standard cells are used which are referred to below For each inversion grid cell Q C IR containing wavefield points x4 Xn a transformation T Qe Q is used to transform cell into the standard cell QS and to compute the respective transformed wavefield points x T x contained in Q5 Then Lev99
4. Florian Schumacher 2013 How to use this manual Only chapter Guide page 7 is intended to be read through which for this reason is held as compact as possible This chapter may itself be regarded as the manual with the appending chapters only containing more specific detail on processes or objects which chapter Guide refers to In other words just start reading the respective section of chapter Guide which you are inter ested in and whenever you feel the need for more detail follow the respective references This way we try to focus the user on necessary information and successfully guide through the lot of details contained in this document When you conduct a specific ASKI operation for the first time we recommend you to first fully read through the respective guiding list and the referred basic steps before you start running any programs This way you will get an impression of the repuirements for your operation All chapters appending chapter Guide are not intended to be read through section by section but may well serve the user as a reference Contents L a L R RES QR Time Domain Sensitivity Kernels Full Waveform Inversion Classical Waveform Sensitivity Kernels 1 2 Basic Steps 1 1 1 3 Installing ASKT 1 2 Create Main Parameter File Iteration Step Parameter Files llle 1 4 Create Directory Environment 2 2 ee ee ees ba Sete ws Ste 1 6 Prepare
5. is applied to points x x7 and volume 22 to compute integration weights wp w3 such that i K x dx xc x Ir x dx Y we J K xj 3 2 i l i 1 whereby 7 1 denotes the Jacobian of the inverse transformation T J Jr 1 x and the desired weights compute as w w J The method of computing such integration weights w w as presented in Lev99 is explained in the following nc The Method of Scattered Data Integration follows a composite rule strategy for building the integration weights For subsets of the volume of interest it constructs integration formulae which are as local and as stable as possible and are exact for polyinomials p of a certain fixed degree m It is assumed that the integrals of these polynomials p IL over the subsets are easily computable In notation of Lev99 the integration weights A for a function f on domain 2 C R which is given on a set lr LT C Q are constructed as K Ape AI Lee where Q is subdivided into K disjoint subsets p For each g the N weights AQ are calcu lated as follows We choose a basis pia of the space II of all polynomials in IR with maximum total de gree m where J S a is the dimension of space Ilm AQ are then defined as the components a A of vector DTE E D E e where D 2Diag n 2 zi n llz ew ll Fij p t 1 lt i lt N 1 lt j lt J and c contains the integrals of t
6. 8 1 Nodes Coordinates Files These files contain a collection of points in space given in Cartesian X Y Z coordinates They must be text files and have the following format The first line contains a single integer value indicating the number of lines to come i e the number of points Each following line contains 3 floating point numbers separated by white space defining Carte sian X Y Z coordinates of a point 2 8 2 Cell Connectivity Files These files contain the definition of cells based on points as defined in the nodes coordinates files They must be text files and have the following format 2 8 ECARTINVERSIONGRID FILES 37 The first line contains a single integer value indicating the number of lines to come i e the number of cells Each following line contains n integer numbers separated by white space n 4 in case of tet4 type cells n 8 in case of hex8 type cells which define the control nodes of the cell and correspond to the point indices in the respective nodes coordinates file whereby the lowest point index is 1 corresponding to the second line first point in the nodes coordinates file The order of the point indices in a line is assumed to correspond to the vtk cell conventions In case one of the cell connectivity files not existing or their first line containing value 0 no cells of the respective type will be created 2 8 3 Cell Neighbours File The terminology lines below refers t
7. COORDS FOR VTK Logical value to indicate whether to use local inversion grid coordinates for vtk geometry i e no rotation by SCART INVGRID ROT and no shift by SCART INVGRID CX SCART_ NVGRID CY SCART INVGRID ZMAX cuboid centered in X Y 0 and ZMAX 0 Example USE LOCAL INVGRID COORDS FOR VTR false SCALE VTK COORDS VTK COORDS SCALING FACTOR Scale vtk geometry coordinates by factor VTK COORDS SCALING FACTOR real number if SCALE VTK COORDS true This may be helpful if coordinate values e g in me ters get so large that they cause problems when plotting in paraview Example SCALE VTK COORDS false VTK COORDS SCALING FACTOR 1 0 1 7 2 ecartInversionGrid WARNING EXPERIMENTAL FEATURE so far this type of inversion grid works for tetra hedral cells only since support for hexahedreal cells is not completed throughout However even for tetrahedra the automatic detection of neighbours did not work properly in some test cases So if you intend to use this inversion grid please have a look at the grid and all neigh bours neighbours only required for model smoothing in case of solving the Kernel system of equations You can do that by using binary program invgrid2vtk along with option nb Call invgrid2vtk h for further details on how to use it An External CARTesian inversion grid is defined by several text files c
8. Documentation License Version 1 3 or any later version published by the Free Software Foundation with no Invariant Sections no Front Cover Texts and no Back Cover Texts A copy of the license is included in the section entitled GNU Free Documentation License If you have Invariant Sections Front Cover Texts and Back Cover Texts replace the with Texts line with this with the Invariant Sections being LIST THEIR TITLES with the Front Cover Texts being LIST and with the Back Cover Texts being LIST 52 CHAPTER 3 PROGRAMS SCRIPTS AND MODULES If you have Invariant Sections without Cover Texts or some other combination of the three merge those two alternatives to suit the situation If your document contains nontrivial examples of program code we recommend releasing these examples in parallel under your choice of free software license such as the GNU General Public License to permit their use in free software Bibliography Lev99 D Levin Stable integration rules with scattered integration points Journal of Com putational and Applied Mathematics 112 181 187 1999 Sch13 Florian Schumacher Using SPECFEM3D_Cartesian 2 1 for ASKI Analysis of Sen sitivity and Kernel Inversion version 0 3 2013 53
9. In the following we describe how data samples and model parameters are defined in this soft ware package and how you can choose specific subsets to be used 1 13 INITIATE BASIC REQUIREMENTS 25 1 12 1 Definition of Data Samples As the sensitivities are calculated in frequency domain the data live in frequency domain too A data sample is uniquely characterized by a seismic source a component of a seismic receiver and a frequency as well as if it is real or imaginary part of the complex spectral values Refer to I 5 page 16 for details on data in ASKI 1 12 2 Definition of Model Parameters A model parameter is uniquely characterized by a parameter name mus be a valid param eter name of the model parametrization as defined by MODEL PARAMETRIZATION 2 1 1 page Bop and an inversion grid cell index in valid range 1 12 3 Choosing a Set of Data Samples and Model Parameters Create a text file as described in section 2 7 page B5 1 13 Initiate Basic Requirements Run binary initBasics initBasics h will print a help message how to use it It first checks if all parameters needed are present in the parameter files and then creates all basic requirements for ASKI operations It reads in required files like event list and station list files the wavefield points and the kernel reference model Furthermore it creates the inversion grid possibly storing some inversion grid files depen dent on the type of
10. Y coordinate second Cartesian coordinate CZ Cartesian Z coordinate third Cartesian coordinate N same as CX S same as CX E same as CY W same as CY UP same as CZ DOWN same as CZ 1 6 PREPARE MEASURED DATA 17 Spherical receivers CX Cartesian X coordinate with X axis through equator and 0 meridian CY Cartesian Y coordinate with Y axis through equator and 90 E meridian CZ Cartesian Z coordinate with Z axis through north pole N local north S local south E local east W local west UP local up DOWN local down Frequency Discretization In ASKI frequencies are given by a frequency step Af Hz and by a set of integer valued frequency indices For specific frequency index i the corresponding frequency f Hz computes as f Af E g Af 10 Hz and frequency indices 2 3 5 7 10 define the set of discrete frequencies 20 0 30 0 50 0 70 0 100 0 Hz 1 6 Prepare Measured Data In the future we plan to have a binary program createMeasuredData which converts time domain data to the special frequency domain form required by ASKI It is planned to supporte measured data given in some basic data formats like Seismic Unix and time series given as textfiles per trace For now you must prepare measured data files on your own as required by ASKI see sec tions 1 5 page 16 and D H page 34 1 7 Define an Inversion Grid There are different types
11. file for your specific program opera tion are described 29 30 CHAPTER 2 FILES FORWARD METHOD GEMIN SPECFEM3D SPECFEMS3D Cartesian SPECFEM3D GLOBE For details on the methods and references to their documentation refer to section 1 10 MODEL PARAMETRIZATION isoLame isotropic Lame parameters p A u isoVelocity isotropic seismic velocities p Up Us Nothing else supported yet MAIN PATH INVERSION All subpaths for filenames are considered relative to this main path This directory is thought to contain all your relevant output and temporary data Example MAIN PATH INVERSION scratch inversions Aegeanl CURRENT ITERATION STEP Example CURRENT ITERATION STEP 3 ITERATION STEP PATH Relative to main path defining name of subdirectory of MAIN PATH INVERSION which contains all relevant meta data of an inversion step A three digit integer CURRENT TERATION STEP and will be appended to ITERATION STEP PATH ie 001 002 defining the first second iteration step directory Example ITERATION STEP PATH iteration step PARFILE ITERATION STEP File name of iteration step specific parameter file relative to MAIN PATH INVERSION TERATION STEP PATHExample PARFILE ITERATION STEP iter parfile PATH MEASURED DATA PATH EVENT FILTER PATH STA
12. in the course of inverting one dataset e g starting with a 1D method continuing with a 3D method then it may make sense to create a different directory structure for each method and using the final model of one method as the starting model for the next method Choose a model parametrization by setting MODEL PARAMETRIZATION in the main parameter file to a value of your choice which is supported by your forward method Before Each Iteration Step including the first one e Set CURRENT ITERATION STEP in your main parameter file to the correct value When continuing your inversion with a different method you may also keep the current iteration step index in order for you not to get confused and leave subdirectories of your MAIN PATH INVERSION empty or delete them after creation if they are not needed e g an inversion with one method could start with iteration step 4 and respective subdi rectory if you have already conducted 3 iteration steps with other methods e Define the inversion grid of the current iteration 1 7 page 17 13 e Set all parameters in the specific iteration step parameter file to correct values page 15 including the correct reference to your inversion grid Refer to the documenta tion of your forward method on how to set filenames FILE WAVEFIELD POINTS and FILE KERN
13. the values living on the inverison grid cells 26 CHAPTER 1 BASIC STEPS Use binary computeKernels computeKernels h will print a help message how to use it It makes sense to only compute kernel files for those paths that you are going to use defined by your data model space file You can define the set of paths for which sensitivities should be computed in two ways way compute a kernel for only one path defined by eventID and station name using options evid and stname way 2 input a data and model space file as defined by page 24p by option dmspace defining all paths for which kernels should be computed optionally define range of path index by ipathl ipath2 1 15 Transform to Time Domain Sensitivity Kernels The time kernels are computed from the standard frequency domain kernels which were com puted path wise by applying an inverse Fourier transform The transforation is done for specific data components e g N DOWN CY where first the spectra for the standard component CX CY CZ are rotated and afterwards the respective event filter and station component filter are applied before the actual Fourier transform takes place Use binary spec2timeKernels spec2timeKernels h will print a help message how to use it It makes sense to only compute kernel files for those paths that you are going to use defined by your data model space file You can define the set of paths for which the time domain kerne
14. underscors network code 6 character network code lat latitude in degrees 90 lt lat lt 90 S or first coordinate in wavefield points inversion grid frame C read the manual on inversion grid definitions 1 7 lon longitude in degrees O lt lon lt 360 S or second coordinate in wavefield points inversion grid frame C read L 7 elevation altitude of station S or third coordinate in wavefield points inversion grid frame C read 2 4 Measured Data Files All measured data files are expected to be in the directory PATH_MEASURED_DATA as defined in the main parameter file One measured data file contains all data values for one specific receiver component and a spe cific event Its filename is by convention data EVENTID STATIONNAME COMP The files are text files containing 1 column of MEASURED_DATA_NUMBER_OF_FREQ com plex numbers which can be understood by FORTRAN read command Line i contains measured data values for the i frequency as defined by vector of indices MEASURED_DATA_INDEX_OF_FREQ and frequency step MEASURED_DATA_FREQUENCY_ STEP In particular this means that all measured data files must contain the same frequency dis cretization given by parameters MEASURED_DATA_INDEX_OF_FREQ MEASURED_DATA_ FREQUENCY STEP of the main parameter file 2 5 Synthetic Data Files Al
15. 02 2007 2008 Free Software Foundation Inc lt http fsf org gt Everyone is permitted to copy and distribute verbatim copies of this license document but changing it is not allowed Preamble The purpose of this License is to make a manual textbook or other functional and useful doc ument free in the sense of freedom to assure everyone the effective freedom to copy and redistribute it with or without modifying it either commercially or noncommercially Secon darily this License preserves for the author and publisher a way to get credit for their work while not being considered responsible for modifications made by others This License is a kind of copyleft which means that derivative works of the document must themselves be free in the same sense It complements the GNU General Public License which is a copyleft license designed for free software We have designed this License in order to use it for manuals for free software because free software needs free documentation a free program should come with manuals providing the same freedoms that the software does But this License is not limited to software manuals it can be used for any textual work regardless of subject matter or whether it is published as a printed book We recommend this License principally for works whose purpose is instruction or reference 1 APPLICABILITY AND DEFINITIONS This License applies to any manual or other work in any medium that
16. Analysis of S ensitivity and Kernel Inversion displacement nm p b o b ASKI User Manual ASKI version 0 3 2013 Florian Schumacher Wolfgang Friederich Ruhr Universit t Bochum Germany UP_vs kernel 2e 15 2e 15 measured synthetic current time o 2 Copyright 2013 Florian Schumacher Permission is granted to copy distribute and or modify this document under the terms of the GNU Free Documentation License Version 1 3 or any later version published by the Free Software Foundation with no Invariant Sections no Front Cover Texts and no Back Cover Texts A copy of the license is included in the section entitled GNU Free Documentation License This documentation was written in the hope that it will be useful to the user but it cannot be assured that it is accurate in every respect or complete in any sense Please do not hesitate to improve this documentation by incorporating your experiences with ASKI and your personal experience of getting used to it When you have developed new ASKI components or have modified existing once please extend modify this document accoringly Furthermore my moderate experience with BIEXmay well give rise to improving the document style hence the readability of the manual as a whole as well as the coding style of the particular tex files The LTEXsource files and all related components of this document are available via http
17. EL REFERENCE MODEL as the handling of these file are method depen dent e Dependent on your method and model parametrization take care about communicat ing the current model inverted in the previous iteration to your forward method page 23 Before the first iteration however you need to define some starting model 1 8 page 23 Conducting An Iteration Step e Compute forward wavefields and Green tensors w r t the current model by your method Refer to the respective documentation of your method After that you may prepare the synthetic data in the way ASKI expects it see sec tions I 5 page 16 and 2 5 page 34 Refer to the documentation of your method on how to do it e Setfilename FILE INTEGRATION WEIGHTS in your main parameter file can be any name will be created as well as TYPE INTEGRATION WEIGHTS gt page 24 e Initiate basic requirements for all programs and scripts gt page 251 e Define data and model space whereby the paths are mainly important for now 1 12 page 24 e Compute sensitivity kernels for your specific set of paths and your set of model parame ters gt page 25 If desired you may have a look at your kernels page 26 e Choose a specific data and model space You may well play around with different subsets of data or smoothing next step in the course of inverting for different model
18. Measured Data 1 7 Define an Inversion Grid 1 7 1 1 7 2 1 7 3 scartInversionGrid ecartInversionGrid 2 2 Specftem3dInversionGrid xkse e es 9 oo xo ya 1 8 Define a Starting Model 1 9 Export Inverted Model Low ooh eB bohm ecbox iude adore ie ade a ee ee ee kaa EP dex d RW RE Lag eee ee eee an T 1 12 2 Definition of Model Parameters llle vex Eee Tn 1 15 Transform to Time Domain Sensitivity Kernels less T Tm Files 2 1 Parameter Files 2 1 1 Main Parameter File 12 15 15 15 15 15 16 17 17 18 20 22 23 23 23 24 24 25 25 25 25 25 26 26 26 21 2 2 Parameter File for Specific Iteration Step 22 Event list Filej o ona 2 3 Station List Fel 0 0 0000 0000 4 2 4 Measured Data Files 2 5 synthetic Data Files a uc ruego Use arx woe 260 Vi Piles e aco Rus beue WE YN QR XC ONUS X EN 2 7 1 Header Block llle 2 7 Model Parameters Block 2 7 3 DataSamplesBlock 2 8 ecartlInversionGridHles 2 8 1 Nodes Coordinates Files 2 8 2 Cell Connectivity Files a llle 2 8 3 Cell Neighbours File o sx oe Ros 3 Programs Scripts and Modules 3 1 Integration Weights 2 uo o oo Rom a 3 1 0 Compute Average no integration rrr no
19. SION GRID 21 Every type of integration weights is supported by this type of inversion grid except weights of type 6 external integration weights Figure 1 2 Example of an external Cartesian inversion grid created by Cubit The nodes and cell files e g produced by Cubit are referred to in a parameter file a tem plate of which is file template ecartInversionGrid_parfile_template In the following the particular parameters are explained An example inversion grid of this type is displayed in figure 1 2 page 21 ECART INVGRID USE NODES COMMON Logical value to indicate whether to use one common nodes coordinates file for all cell types only use parameter ECART INVGRID FILE NODES below or to use an individual nodes coordinates file for each cell type use parameters files ECART INVGRID FILE NODES TET4 ECART INVGRID FILE NODES HEXS below When using module cubit 2ASKIecartInversionGrid you should set ECART INVGRID USE NODES COMMON True ECART INVGRID FILE NODES COMMON File name relative to MAIN PATH INVERSION ITERATION STEP PATH of nodes co ordinates file to be commonly used for definition of cells of all types in case of ECART_ NVGRID USE NODES COMMON True When using module cubit 2ASKIecartInversionGrid you should set ECART INVGRID FILE NODES COMMON node coordinates
20. TION FILTER Paths where ASKI finds files related to the measured data files These paths can be every where e g close to where you have stored processed your time domain data or in directory MAIN PATH INVERSION etc The naming convention of files in these directories is FILE MEASURED DATA data EVENTID STATIONNAME COMP FILE EVENT FILTER filter EVENTID FILE STATION FILTER filter STATIONNAME COMP where filters are dependet on component and STATIONNAME and EVENTID are defined in FILE STATION LISTandFILE EVENT LIST file and COMP is a valid component supported by module componentTransformation Example 2 1 PARAMETER FILES 31 PATH MEASURED DATA mydata your name of inversion ASKI data PATH EVENT FILTER mydata your name of inversion ASKI event filter PATH STATION FILTER mydata your name of inversion ASKI station filter FILE EVENT LIST Absolute filename where ASKI finds a text file defining a set of events in the required format 2 2 Example FILE EVENT LIST mydata your name of inversion ASKI events FILE STATION LIST Absolute filename where ASKI finds a text file defining a set of stations in the required format 2 3 Example FILE STATION LIST mydata your name of inversion ASKI stations MEASURED DATA FREQUENC
21. Y STEP MEASURED DATA NUMBER OF FREQ MEASURED _ DATA INDEX OF FREQ Discretized frequency window of measured data same expected in event filter station filter given by a frequency step FREQUENCY STEP Hz and a vector of frequency indices INDEX OF FREO of length NUMBER OF FREO where for specific frequency index the corre sponding frequency f Hz computes to f i FREQUENCY STEP Example MEASURED FREQUENCY STEP 10 MEASURED NUMBER OF FREO 5 MEASURED INDEX OF FREQ 2 357 10 which corresponds to the 5 frequencies 20 30 50 70 100 Hz DEFAULT VTK FILE FORMAT Either BINARY or ASCII defining the default type of vtk files which will be produced in the course of running the programs 2 1 2 Parameter File for Specific Iteration Step Here shortly all keywords required in a parameter file for a specific iteration step i e MAIN PATH INVERSION ITERATION STEP PATH PARFILE ITERATION STEP are described ITERATION STEP NUMBER OF FREQ ITERATION STEP INDEX OF FREOQ Frequency discretization of this iteration step must be a subset of global frequency discretiza tion for this inversion defined as defined by D 1 1 TERATION STEP NUMBER OF FREQ lt MEASURED DATA NUMBER OF FREQ and vector TERATION STEP INDEX OF FREQ oflength ITERATION STEP NUMBER OF FREQ 32 CHAPTER 2 FILES m
22. ailers of that edition to the public It is requested but not required that you contact the authors of the Document well before redistributing any large number of copies to give them a chance to provide you with an updated version of the Document 4 MODIFICATIONS You may copy and distribute a Modified Version of the Document under the conditions of sections 2 and 3 above provided that you release the Modified Version under precisely this License with the Modified Version filling the role of the Document thus licensing distribution and modification of the Modified Version to whoever possesses a copy of it In addition you must do these things in the Modified Version A Use in the Title Page and on the covers if any a title distinct from that of the Document and from those of previous versions which should if there were any be listed in the History section of the Document You may use the same title as a previous version if the original publisher of that version gives permission 48 O CHAPTER 3 PROGRAMS SCRIPTS AND MODULES List on the Title Page as authors one or more persons or entities responsible for au thorship of the modifications in the Modified Version together with at least five of the principal authors of the Document all of its principal authors if it has fewer than five unless they release you from this requirement State on the Title page the name of the publisher of the Modified Version as
23. al relation Ad Js Am K In order to build a linear system the model update Am is assumed to be constant throughout small scattering volumes Q where Q U j2 These volumes constitute the cells of the volumetric inversion grid and the sensitivity matrix contains entries of preintegrated kernels fo As J The sensitivity kernels K are computed from forward wavefields produced on a set of points in space which is dependent on the particular forward method This set of points is refered to as wavefield points The wavefields are written to file by the respective forward method which may require very large discspace Providing methods for constructing integration rules for arbitrary point sets contained in arbitrary volumes ASKI computes integration weights for integration of functions on the wavefield points over the volumetric cells of the inversion grid Thereby the inversion grid takes care of the localization of wavefield points inside the inversion grid cells and if requested the transformation of cells to a hexahedral or tetrahedral standard cell for the computation of the integration weights Hence some combinations of 7 8 CHAPTER 0 GUIDE wavefield points 1 e forward methods integration weight types and inversion grid types are not possible The preintegrated kernel values are also written to files which may be flexibly read in for arbi trary subsets of data by the binary programs conducting any sensitivity analysi
24. al rights of the com pilation s users beyond what the individual works permit When the Document is included in 50 CHAPTER 3 PROGRAMS SCRIPTS AND MODULES an aggregate this License does not apply to the other works in the aggregate which are not themselves derivative works of the Document If the Cover Text requirement of section 3 is applicable to these copies of the Document then if the Document is less than one half of the entire aggregate the Document s Cover Texts may be placed on covers that bracket the Document within the aggregate or the electronic equivalent of covers if the Document is in electronic form Otherwise they must appear on printed covers that bracket the whole aggregate 8 TRANSLATION Translation is considered a kind of modification so you may distribute translations of the Doc ument under the terms of section 4 Replacing Invariant Sections with translations requires special permission from their copyright holders but you may include translations of some or all Invariant Sections in addition to the original versions of these Invariant Sections You may include a translation of this License and all the license notices in the Document and any War ranty Disclaimers provided that you also include the original English version of this License and the original versions of those notices and disclaimers In case of a disagreement between the translation and the original version of this License or a notice or disclaimer
25. an example of such a server A Massive Multiauthor Collaboration or MMC contained in the site means any set of copyrightable works thus published on the MMC site CC BY SA means the Creative Commons Attribution Share Alike 3 0 license published by Creative Commons Corporation a not for profit corporation with a principal place of business in San Francisco California as well as future copyleft versions of that license published by that same organization Incorporate means to publish or republish a Document in whole or in part as part of another Document An MMC is eligible for relicensing if it is licensed under this License and if all works that were first published under this License somewhere other than this MMC and subsequently incorporated in whole or in part into the MMC 1 had no cover texts or invariant sections and 2 were thus incorporated prior to November 1 2008 The operator of an MMC Site may republish an MMC contained in the site under CC BY SA on the same site at any time before August 1 2009 provided the MMC is eligible for relicensing ADDENDUM How to use this License for your documents To use this License in a document you have written include a copy of the License in the docu ment and put the following copyright and license notices just after the title page Copyright YEAR YOUR NAME Permission is granted to copy distribute and or modify this document under the terms of the GNU Free
26. and a passage of up to 25 words as a Back Cover Text to the end of the list of Cover Texts in the Modified Version Only one passage of Front Cover Text and one of Back Cover Text may be added by or through arrangements made by any one entity If the Document already includes a cover text for the same cover previously added by you or by arrangement made by the same entity you are acting on behalf of you may not add another but you may replace the old one on explicit permission from the previous publisher that added the old one The author s and publisher s of the Document do not by this License give permission to use their names for publicity for or to assert or imply endorsement of any Modified Version 5 COMBINING DOCUMENTS You may combine the Document with other documents released under this License under the terms defined in section 4 above for modified versions provided that you include in the combi nation all of the Invariant Sections of all of the original documents unmodified and list them all as Invariant Sections of your combined work in its license notice and that you preserve all their Warranty Disclaimers The combined work need only contain one copy of this License and multiple identical Invariant Sections may be replaced with a single copy If there are multiple Invariant Sections with the same name but different contents make the title of each such section unique by adding at the end of it in parentheses the name o
27. contains a notice placed by the copyright holder saying it can be distributed under the terms of this License Such a notice grants a world wide royalty free license unlimited in duration to use that work under the conditions stated herein The Document below refers to any such manual or work Any member of the public is a licensee and is addressed as you You accept the license if you copy modify or distribute the work in a way requiring permission under copyright law A Modified Version of the Document means any work containing the Document or a portion of it either copied verbatim or with modifications and or translated into another language A Secondary Section is a named appendix or a front matter section of the Document that deals exclusively with the relationship of the publishers or authors of the Document to the Doc ument s overall subject or to related matters and contains nothing that could fall directly within that overall subject Thus if the Document is in part a textbook of mathematics a Secondary 45 46 CHAPTER 3 PROGRAMS SCRIPTS AND MODULES Section may not explain any mathematics The relationship could be a matter of historical con nection with the subject or with related matters or of legal commercial philosophical ethical or political position regarding them The Invariant Sections are certain Secondary Sections whose titles are designated as being those of Invariant Sections in the not
28. ction Entitled XYZ according to this definition The Document may include Warranty Disclaimers next to the notice which states that this Li cense applies to the Document These Warranty Disclaimers are considered to be included by reference in this License but only as regards disclaiming warranties any other implication that these Warranty Disclaimers may have is void and has no effect on the meaning of this License 2 VERBATIM COPYING You may copy and distribute the Document in any medium either commercially or noncom mercially provided that this License the copyright notices and the license notice saying this 3 1 INTEGRATION WEIGHTS 47 License applies to the Document are reproduced in all copies and that you add no other con ditions whatsoever to those of this License You may not use technical measures to obstruct or control the reading or further copying of the copies you make or distribute However you may accept compensation in exchange for copies If you distribute a large enough number of copies you must also follow the conditions in section 3 You may also lend copies under the same conditions stated above and you may publicly display copies 3 COPYING IN QUANTITY If you publish printed copies or copies in media that commonly have printed covers of the Document numbering more than 100 and the Document s license notice requires Cover Texts you must enclose the copies in covers that carry clearly and l
29. eceipt of a copy of some or all of the same material does not give you any rights to use it 10 FUTURE REVISIONS OF THIS LICENSE The Free Software Foundation may publish new revised versions of the GNU Free Documenta tion License from time to time Such new versions will be similar in spirit to the present version but may differ in detail to address new problems or concerns See http www gnu org copyleft Each version of the License is given a distinguishing version number If the Document speci fies that a particular numbered version of this License or any later version applies to it you 3 1 INTEGRATION WEIGHTS 51 have the option of following the terms and conditions either of that specified version or of any later version that has been published not as a draft by the Free Software Foundation If the Document does not specify a version number of this License you may choose any version ever published not as a draft by the Free Software Foundation If the Document specifies that a proxy can decide which future versions of this License can be used that proxy s public statement of acceptance of a version permanently authorizes you to choose that version for the Document 11 RELICENSING Massive Multiauthor Collaboration Site or MMC Site means any World Wide Web server that publishes copyrightable works and also provides prominent facilities for anybody to edit those works A public wiki that anybody can edit is
30. egibly all these Cover Texts Front Cover Texts on the front cover and Back Cover Texts on the back cover Both covers must also clearly and legibly identify you as the publisher of these copies The front cover must present the full title with all words of the title equally prominent and visible You may add other material on the covers in addition Copying with changes limited to the covers as long as they preserve the title of the Document and satisfy these conditions can be treated as verbatim copying in other respects If the required texts for either cover are too voluminous to fit legibly you should put the first ones listed as many as fit reasonably on the actual cover and continue the rest onto adjacent pages If you publish or distribute Opaque copies of the Document numbering more than 100 you must either include a machine readable Transparent copy along with each Opaque copy or state in or with each Opaque copy a computer network location from which the general network using public has access to download using public standard network protocols a complete Transparent copy of the Document free of added material If you use the latter option you must take reasonably prudent steps when you begin distribution of Opaque copies in quantity to ensure that this Transparent copy will remain thus accessible at the stated location until at least one year after the last time you distribute an Opaque copy directly or through your agents or ret
31. elSystem h will print a help message how to use it 28 CHAPTER 1 BASIC STEPS Chapter 2 Files This chapter collects documentation on file formats involved in ASKI 2 1 Parameter Files Parameter files are simple text files The following type of lines are ignored e comment lines i e lines STARTING with an arbitrary number of blanks followed by a character e empty lines and lines containing blanks only 669 e lines not containing any character How to specify one parameter e valid lines have the form keyword value blanks leading or following keyword TED or value are ignored e in a valid line all characters in front of without leading and appending blanks are interpreted as the keyword allowing for blank characters within the keyword e g for lines key word value the string key word is used as the keyword e all characters behind without leading and appending blanks are interpreted as the value string from which the value is read which in particular means that TT comments at the end of a line such as keyword value comment are not allowed By convention specify paths i e directory names which will be concatenated with a filename of a file in that directory always ending on T and specify filenames always without leading ep 2 1 1 Main Parameter File Here shortly all keywords required in the main parameter
32. ep of a full waveform inver sion e Define the inversion grid page 17 which controls the spacial volumetric dis cretization resolution of the computed sensitivity kernels In case of just computing time kernels to look at it is not crucial to regard this resolution as the resolution of some inverted model as no inversion will be conducted on the inversion grid e Set all parameters in the specific iteration step parameter file to correct values page 15 including the correct reference to the inversion grid Set ITERATION STEP NUMBER OF FREQ and ITERATION STEP INDEX OF FREO to the same values as the MEASURED DATA NUMBER OF FREQ and MEASURED DATA INDEX OF FREQ in the main parameter file Refer to the documentation of your forward method on how to set filenames FILE WAVEFIELD POINTSandFILE KERNEL REFERENCE MODEL as the handling of these file are method dependent e Dependent on your method and model parametrization define your background model with respect to which the kernels will be computed If you have some inverted model file use I 9 page 23 For defining a starting model see 1 8 page 23 Computing Standard Frequency Domain Sensitivity Kernels e Compute forward wavefields and Green tensors w r t the current model by your method Refer to the respective documentation of your method After that you may prepare the s
33. es NEN a oh oe GNU Free Documentation License CONTENTS Chapter 0 Guide This chapter is intended to guide you dependent on what you want to do through all necessary steps to achieve your goals If you don t know about ASKI yet we recommend you to quickly read through the next section which explains some basic terminology in ASKI and the concepts it is based on The sections below address possible operations you can conduct with ASKI For every op eration we only refer to the necessary basic steps by which are described in chapter 1 page 15 Make sure to read through a complete item before hastily doing anything Good Luck What is ASKI ASKI is a modularized software package which offers analysis tools of seismic data and a full waveform inversion concept based on waveform sensitivity kernels derived from Born scattering theory Instead of using time dependent values of ground motion i e samples of a time series of seis mic data ASKI uses freqency dependent complex values of ground motion at a certain re ceiver excited by a certain seismic source This mainly has reasons of computational feasibil ity and does not mean any draw back e g in the sense that no time windowing is possible etc since ASKI aims at taking into account all available information contained in a waveform Using sensitivity kernels K change in a data sample Ad is connected to model uptdates Am by an integr
34. ev99 polynomial degree 1 2 Scattered Data Integration as in Lev99 polynomial degree 2 i e approximation order 3 3 Scattered Data Integration as in Lev99 polynomial degree 3 i e approximation order 4 4 for each cell compute the highest possible order of Scattered Data lintegration inte gration after Lev99 trying types 3 2 1 in that order until computation was successful 5 average of function values multiplied with volume of box i e linear integration 6 external integration weights to be used along with a suitable inversion grid e g of type specfem3dInversionGrid see section page 22 A detailed description of some of the integration weights especially the weights after Lev99 can be found in section B 1 page 39 1 12 Create a Data and Model Space In order to choose a set of data samples which to invert and a set of model parameters which to invert for you need to define a data space and a model space Essentially if you have m data samples the space in which the data live is just R analogously for n model parameters the model lives in IR You only need to define which data sample model parameter refers to which dimension i e entry in vector of the data space model space The m x n sensitivity kernel matrix will then connect a vector of model updates from model space in IR to your specific data vector from R
35. f the original author or publisher of that section if known or else a unique number Make the same adjustment to the section titles in the list of Invariant Sections in the license notice of the combined work In the combination you must combine any sections Entitled History in the various original documents forming one section Entitled History likewise combine any sections Entitled Acknowledgements and any sections Entitled Dedications You must delete all sections Entitled Endorsements 6 COLLECTIONS OF DOCUMENTS You may make a collection consisting of the Document and other documents released under this License and replace the individual copies of this License in the various documents with a single copy that is included in the collection provided that you follow the rules of this License for verbatim copying of each of the documents in all other respects You may extract a single document from such a collection and distribute it individually under this License provided you insert a copy of this License into the extracted document and follow this License in all other respects regarding verbatim copying of that document 7 AGGREGATION WITH INDEPENDENT WORKS A compilation of the Document or its derivatives with other separate and independent docu ments or works in or on a volume of a storage or distribution medium is called an aggregate if the copyright resulting from the compilation is not used to limit the leg
36. function createIntegrationWeights sets 1 wi vo Qe 49 Locis Ne in each inversion grid cell Q where vol Q4 denotes the volume of inversion grid cell Q which is expected to be provided by module inversionGrid for every cell This way the summation 5 77 w K x vol Q 1 5 77 K xf yields the average ker nel value in Q multiplied with the volume of Qe This somehow approximates the generalization of the trapezoidal rule to 3 dimensions in which the integral of a function f over some tetrahedron 7 which is defined by 4 incoplanar points ti t4 is computed by vol T 1 5 f ti 3 1 3 External Integration Weights In case of intw type 6 function createIntegrationWeights does not actually compute any integration weights Instead it calls function transformToStandardCelliInversionGri 3 1 INTEGRATION WEIGHTS 43 of module inversionGrid with dummy variable type standard cell set to value 1 which requests the routine to return the total integration weights in variable jacobian instead the jacobian values These returned values are then stored as the integration weights This functionality must be supported by the type of inversion grid At the moment only inversion grids of type specfem3dInversionGrid support external type integration weights 44 CHAPTER 3 PROGRAMS SCRIPTS AND MODULES GNU Free Documentation License Version 1 3 3 November 2008 Copyright c 2000 2001 20
37. grid localizes the wavefield points inside it and computes the integration weights which are written to file Once those files exist initBasics and all other programs will always read the integration weights and possibly part of the inversion grid from file regardless of what the parameter files say So if at some you point want to use different inte gration weights or a different inversion grid you will have to either delete the respective file s andrerun initBasics orruninitBasics recr in order to recreate them Also a lot of vtk files with statistics are produced having base filename FILEBASE BASIC STATS as defined in the parameter file of the current iteration step Those files mainly re gard the inversion grid the wavefield points and the integration weights whereby the respec tive filenames are extended by something with vtk It is highly recommended to call initBasics recr in order to assure that all those vtk files are produced and to ac tually have a look at them before continuing any ASKI operation 1 14 Compute Standard Sensitivity Kernels The kernels are computed by combining green tensor and forward wavefield for a given path and by integration over all inverison grid cells Le there is one sensitivity kernel file for a specific path This file contains sensitivity values of the three Cartesian receiver components CX CY CZ for all model parameters of your model parametrization with
38. he p over Ep i e c fp pi n r exp r h is a fast increasing weight function which gives the localizing properties of the weights is approxi mately the diameter of subsets E and x is some center of Ex This composite local approach of calculating global integration weights involves K solutions of a full linear system of order J 3 1 INTEGRATION WEIGHTS 4 Application to Hexahedral Inversion Grid Cells For inversion grid cells of general hexahedral shape the 3 dimensional cube x Q9 71 1 y l lt a y z lt 1 Z is used as the standard cell For every such inversion grid cell Q module inversionGridis expected to provide its transformed wavefield points x7 x and their corresponding values of Jacobian 7 In the context of Scattered Data Integration the inversion domain Q Q 1 1 is subdi vided into K nj subcubes E of edge length h 2 n4 n max 1 is chosen in such a way that there should be at least J or all otherwise integration points within as otherwise the damping by matrix D might cause numerical instabilities by making matrix E DE close to singular As z the center of the respective subcube is chosen The desired weights wf w are then given by w Aj 1 X i nc Application to Tetrahedral Inversion Grid Cells For inversion grid cells of general tetrahedral shape the 3 dimensional simplex with corners 0 1 0 0 0 l 0 1 0 0 0 0 1 is used as
39. hoose 1 2 y 2 27 zy xz y yz 27 Scattered Data Integration Order 3 intw_type 3 In the context of this subsection 3 1 1 m 3 is used as the degree of polynomials which are integrated in an exact way and of course d 3 The space II of all polynomials in IR of 3 m 6 maximum total degree m 3 has dimension J a SUL Jom 20 As a basis of 3 2 2 2 2 ig 2 25 58 22 2 3 Ia we choose 4 1 2 y Z 2 Y 2 MP YZ 27 07 x y 272 mU pue de Y3 yz y2 2 Scattered Data Integration Optimal Order In case of intw type 4 function createIntegrationWeights tries to seperately find for each inversion grid cell the highest possible order of Scattered Data Integration Starting with highest order m 3 it continues to recompute Scattered Data Integration weights of order m 2 and m 1 until the computation was successful If the computation for order m 1 fails the integration weights of that cell will be marked erroneous the computation of the weights is not successfull in that case As the success of the Scattered Data Integration method is strongly dependent on the specific set of points x a since matrix E p r must have full rank the strategy of choosing the highest possible degree of integration for each cell tries to take all locally availabe informa tion of inversion grid and wavefield points into account 3 1 2 Linear first order Integration Incaseof intw type 5
40. ice that says that the Document is released under this License If a section does not fit the above definition of Secondary then it is not allowed to be designated as Invariant The Document may contain zero Invariant Sections If the Document does not identify any Invariant Sections then there are none The Cover Texts are certain short passages of text that are listed as Front Cover Texts or Back Cover Texts in the notice that says that the Document is released under this License A Front Cover Text may be at most 5 words and a Back Cover Text may be at most 25 words A Transparent copy of the Document means a machine readable copy represented in a format whose specification is available to the general public that is suitable for revising the document straightforwardly with generic text editors or for images composed of pixels generic paint programs or for drawings some widely available drawing editor and that is suitable for input to text formatters or for automatic translation to a variety of formats suitable for input to text formatters A copy made in an otherwise Transparent file format whose markup or absence of markup has been arranged to thwart or discourage subsequent modification by readers is not Transparent An image format is not Transparent if used for any substantial amount of text A copy that is not Transparent is called Opaque Examples of suitable formats for Transparent copies include plain ASCII without ma
41. l synthetic data files are expected to be in the directory PATH SYNTHETIC DATA as de fined in the parameter file of the current iteration step One synthetic data file contains the complete synthetic data values for one specific path i e a specific source receiver combination Its filename is by convention synthetics EVENTID STATIONNAME The files are text files containing ITERATION STEP NUMBER OF FREQ lines and 3 columns of complex numbers which can be understood by FORTRAN read command Line i contains synthetic data values for the i frequency as defined by vector of indices TERATION STEP INDEX OF FREOandfrequency stepMEASURED DATA FREQUENCY STEP The 3 complex numbers on a line refer to the 3 Cartesian components CX CY CX 2 6 Vtk Files For visualization of basic objects of the inversion such as the inversion grid the wavefield points the integration weights etc as well as some inversion results and models we use the 2 7 DATA AND MODEL SPACE FILE 35 vtk file format General information on this file format may be found under PUT HERE General info about the two types of vtk files invgridVtk wavefield points Vtk files Some basic content description about some special vtk files 2 7 Data and Model Space File Files in which a data and model space is defined have the following form Also have a look at example template files ctemplate data model space info temp
42. late The blocks described in the subsections below should be put into a file one after another The header block must come first then the data space block and model parameter block The order of the latter two is arbitrary both orders are allowed however if the model parameters block is defined first an additional check for empty kernel file names will be done in the processing of the data samples block 2 7 Header Block line 1 currently ignored file format version specification possible header comment line 2 must either contain ASCII or BINARY currently ignored possible form definition like ASCII mixed ASCII BINARY similar to in vtk At the moment this file must be a formatted text file 2 7 30 Model Parameters Block line MODEL PARAMETERS this defines that the definition of the model parameters starts here line INVERSION GRID CELLS value where value is either ALL all inversion grid cells are taken or SPECIFIC specific definition of set of invgrid cells following below line PARAMETERS value where value is either ALL all inversion grid cells are taken or SPECIFIC specific definition of model parameters for each invgrid cell following below Only allowed if INVERSION GRID CELLS SPECIFIC If PARAMETERS ALL lne nparam pmtrization 1 param 1 pmtrization n param n defines the parametrization used for all inversion grid cells
43. length of the time series you want to deal with define the fre quency discretization of the spectral kernels that will be produced first This must be done by MEASURED DATA FREQUENCY STEP MEASURED DATA NUMBER OF FREQ and MEASURED DATA INDEX OF FREO In general for the pure kernel computation you do not need any measured data So here you do not need to prepare data in the ASKI required form e Set PATH EVENT FILTER and PATH STATION FILTER in your main parameter file The transformation of the standard frequency domain sensitivity kernels to the time domain always requires event filters i e source time functions and station filters i e receiver responses Even if you do not want to apply those values you need to artifi cially create the required files in pahts PATH EVENT FILTER and PATH STATION 10 CHAPTER 0 GUIDE FILTER and may set the spectral filter values to the real value 1 R i e 1 0 C for all frequencies e Set FORWARD METHOD in your main parameter file to the value of your choice e Choose a model parametrization by setting MODEL PARAMETRIZATION in the main parameter file to a value of your choice which is supported by your forward method e Set CURRENT ITERATION STEP in your main parameter file to value 1 as you are technically starting to conduct the first and only iteration st
44. locks of layers the vectors SCART_INVGRID_NLAY integer values and SCART_INVGRID_THICKNESS real val ues both of length SCART_INVGRID_NREF_BLOCKS define the Z direction refinement of each block whereby SCART_INVGRID_NLAY i defines the number of layers in block i and SCART_INVGRID_THICKNESS i defines the thickness of all layers contained in block i Hence the overall Z direction coverage of the inversion grid is defined by SCART_INVGRID_ ZMAX which is the coordinate of the top of the first layer in the first refinement block and SCART INVGRID ZMAX SUM i THICKNESS i NLAY i coordinate of the bottom of the last layer in last refinement block Example SCART INVGRID NREF BLOCKS 3 SCART INVGRID NLAY 4 5 2 SCART INVGRID THICKNESS 5 0 10 0 20 0 SCART INVGRID NX Vector of length SCART INVGRID NREF BLOCKS of integer values defining number of inversion grid cells in X direction one value for each refinement block Example SCART INVGRID NX 20 10 6 SCART INVGRID NY Vector of length SCART INVGRID NREF BLOCKS of integer values defining number of inversion grid cells in Y direction one value for each refinement block 20 CHAPTER 1 BASIC STEPS Example SCART INVGRID NX 30 15 9 USE LOCAL INVGRID
45. ls should be computed in two ways way transform a kernel for only one path defined by eventID and station name using options evid and stname way 2 input a data and model space file as defined by page 24 by option dmspace defining all paths for which kernels should be transformed optionally define range of path index by ipathl ipath2 1 16 Plot Standard Sensitivity Kernels One way to plot a specific sensitivity Kernel in frequency domain i e the sensitivity spectra for a specific path is to procuce vtk files with binary kernel2vtk kernel2vtk h will print a help message how to use it Please note that the output vt k files one for every frequency might get large dependent on the resolution of the inversion grid since the geometry information of the inversion grid cells is contained in each vtk file 1 17 Plot Time Sensitivity Kernels One way to plot a specific sensitivity Kernel in time domain is to procuce vtk files with binary timeKernel2vtk timeKernel2vtk h will print a help message how to use it Please note that the output vtk files one for every time step might get large dependent on the resolution of the inversion grid since the geometry information of the inversion grid cells is contained in each vtk file 1 18 SOLVE KERNEL SYSTEM 27 1 18 Solve Kernel System Call binary solveKernelSystem to set up the kerne matrix read in synthetic and real data add smoothing if required solveKern
46. n defining the component indices for all paths line of form FREQUENCIES value where value is either ALL for all paths the same frequency indices are used or SPECIFIC only allowed if PATHS SPECIFIC for each path a specific set of frequency indices may be defined If FREQUENCIES ALL the next line is of form nfreq ifreq_l ifreq_n defining the frequency indices for all paths line of form IMRE value where value is either ALL for all paths the same set of imagi nary real parts are used or SPECIFIC only allowed if PATHS SPECIFIC for each path a specific set of imaginary real parts may be defined If IMRE ALL the next line is of form nimre imre 1 imre n defining imaginary i e imre i im or real parts imre i re for all paths If PATHS SPECIFIC the following line must contain the number npaths of paths which should be used followed by npahts blocks of lines each defining the path and the data samples for that path These blocks constist of at least one line containing the event station index pair iev istat For each keyword COMPONENTS FREQUENCIES and IMRE if SPECIFIC one line is added to such a block of lines in the same form as the line following keyword ALL see above defining the specific components frequencies or set of imaginary real parts for each of the specific paths 2 8 ecartInversionGrid Files 2
47. n etc Tech nically you will be conducting an incomplete first iteration step of a full waveform inversion using all the program infrastructure which is also used for a full waveform inversion In addition to ASKI I I page I5 you will need software to solve the forward problem I 10 page 23 Preliminary Considerations e Create a main parameter file e g in the parent directory of your specific inversion direc tory or where you collect main parameter files for all your inversion projects or analyses page I5 You will need this file as an input argument to almost all program s scripts Set MAIN PATH INVERSION to a correct value The directory does not need to exist yet if not then it will be created Set ITERATION STEP PATH and PARFILE ITERATION STEP to desired values or leave the default values if present All other parameters can be adjusted later e Create a directory structure for only one iteration step 1 4 page 15 e Even if you do not have any measured data it might still be beneficial for you to make yourself roughly familiar with the from of data used in ASKI 1 5 page I6 In your main parameter file set the following values Set FILE EVENT LIST and FILE STATION LIST to define the sources and receivers which are involved in the paths that you would like to compute the kernels for Dependent on the
48. o the case of this file not being binary but a text file In case of this file being binary the file content is expected value by value as on the rows of the text file It will be opened by FORTRAN code with attribute access stream i e expecting the values as a simple byte stream and expects integer values of kind 4 The first line contains the total number of inversion grid cells nce11 The next nce11 lines one for each cell in order of the cell index are of the form nnb icell 1 icell nnb whereby nnb is the number of neighbours of the respective cell must be 0 if no neighbours followed by nnb cell indices icell 1 icell nnb defining the neighbour cells if there are any neighbours 38 CHAPTER 2 FILES Chapter 3 Programs Scripts and Modules This chapter collects some scripts binary programs or modular program components contained in the ASKI package for which some more detail on arguments and basic functionality is required by expert users It is not refered to any code here 3 1 Integration Weights The ASKI module integrationWeights computes integration weights for the set of wavefield points in order to integrate the kernels over the inversion grid As we need to calculate the integrals of the kernels over each inversion grid cell separately the integration weights are computed for each cell in such a way that weighting the summation of the kernel values yields the desired integral value
49. o the given documentation on any details regarding the interaction of the forward codes with ASKI Gemini II Gemini is not yet fully supported in this release version For some test cases waveform kernels were successfully computed using Gemini in Cartesian as well as spherical set ting We hope to provide the Gemini interface for ASKI soon SPECFEM3D Cartesian The Cartesian spectral element code SPECFEM3D Cartesian is supported by ASKI cf Sch13 24 CHAPTER 1 BASIC STEPS SPECFEM3D GLOBE The global spectral element code SPECFEM3D GLOBE is not yet fully supported in this release version For some test cases waveform kernels were successfully computed using SPECFEM3D_ GLOBE We hope to provide the SPECFEM3D GLOBE interface for ASKI soon 1 11 Choose Integration Weights In order to numerically integrate the sensitivity kernels which are computed on the wavefield points over the inversion grid cells by a weightet summation of values there are different types of integration weights provided following different rules of integration The integer values of the type have the following meaning 0 all weights are the same weight 1 number of points in box Le no integration just building the average sensitivity value e g convenient for comparison of sensitivities computed with different methods on different forward grids 1 Scattered Data Integration as in L
50. ocumentation of your SPECFEM3D forward method 1 10 page 23 on how to define an inversion grid of type specfem3dInversionGrid 1 8 Define a Starting Model There are two possibilities to define an earth model for the forward wave propagation in your first iteration On the one hand you may use any standard earth model provided by the forward method you are using if appropriate If this is not possible or the models provided do not meet your needs you may use binary createStartmodelkKim along with the inversion grid of your first iteration which you should have already defined to produce an inverted model file containing some simple model on this inversion grid createStartmodelKim h will print a help message how to use the program Afterwards you may export the produced model file to your forward method as explained in section I 9 page 23 1 9 Export Inverted Model The binary program exportKim exports an inverted model file kim stands for K ernel T nverted M odel along with the respective inversion grid specifications to a text file which may be used to communicate such a model to a forward method or postprocess the model values in any way exportKim h will print a help message how to use it Template files of starting model descriptions may be found in template 1 10 Solving the Forward Problem In the following all wave propagation codes which are supported by ASKI are listed Refer t
51. of ASKI inversion grids suitable for different geometries forward methods hence applications All inversion grids are defined by setting parameters TYPE_INVERSION_GRID and PARFILE_ NVERSION_GRID in the parameter file of the current iteration step In the following we present the supported inversion grid types and explain the particular pa rameters in the respective inversion grid parameter file 18 CHAPTER 1 BASIC STEPS 1 7 1 scartInversionGrid A Simple CARTesian inversion grid covers a Cartesian cuboid which can be shifted to a cer tain location in Cartesian space and may be rotated about the local vertical axis Its cells are distributed in layers Each layer has a certain thickness and a regularly distributed number of inversion grid cells along each lateral direction of the cuboid Please consult the documentation of your forward method 1 10 page 23 if it supports inver sion grids of type scart InversionGrid All coordinates e g of events and stations or wavefield points are interpreted by this type of inversion grid as X first coordinate Y second coordinate Z third coordinate Their units e g meters or kilometers are not assumed by the inversion grid and are essentially defined by the wavefield points hence they might be method dependent and must be overall consistend Every type of integration weights is supported by this type of inversion grid except weights of type 6 ex
52. ontaining the definintion of nodes i e essentially the corner points or rather the control nodes of the inversion grid cells and the definition of cells by refering to the nodes At the moment 4 node tetrahedral cells are fully supported and 8 node hexahedral cells are partly supported Those files may be produced by any meshing tool In case you are interested to export meshes your own way section page 36 defines the required file formats ASKI provides the python module cubit2ASKIecartInversionGrid py which can be used with the meshing software Cubit in a python script by first importing the module import cubit2ASKIecartInversionGrid and at the very end of your meshing process calling cubit cmd compress all cubit2ASKIecartInversionGrid export2ASKI EXPORT_PATH whereby you may replace EXPORT_PATH by some location where the output files will be written Please consult the documentation of your forward method I 10 page 23 if it supports inver sion grids of type ecart InversionGrid All coordinates e g of events and stations or wavefield points are interpreted by this type of inversion grid as X first coordinate Y second coordinate Z third coordinate Their units e g meters or kilometers are not assumed by the inversion grid and are essentially defined by the wavefield points hence they might be method dependent and must be overall consistend 1 7 DEFINE AN INVER
53. ontent defines the neighbour structure of the inversion grid cells If however the inversion grid is to be recreated e g when calling initBasics recr see section I 13 page 25 this file is recreated ECART INVGRID FILE NEIGHBOURS IS BINARY Logical value to indicate whether ECART INVGRID FILE NEIGHBOURS should be binary or not SCALE VTK COORDS VTK COORDS SCALING FACTOR Scale vtk geometry coordinates by factor VTK COORDS SCALING FACTOR real number if SCALE VTK COORDS true This may be helpful if coordinate values e g in me ters get so large that they cause problems when plotting in paraview Example SCALE VTK COORDS false VTK COORDS SCALING FACTOR 1 0 1 7 3 specfem3dInversionGrid An inversion grid of type specfem3dInversionGrid is method dependent and is to be used with METHOD SPECFEM3D only Whole spectral elements are used as inversion grid cells and all GLL points inside such an element as the wavefield points All information re garding the element geometry including information on neighbour cells and the values of the 1 8 DEFINE A STARTING MODEL 23 jacobian for every wavefield point contained in an element are read from files which are pro duced by SPECFEM3D methods Every type of integration weights is supported by this type of inversion grid including weights of type 6 external integration weights Please refer to the d
54. r any section Entitled Acknowledgements or Dedications Preserve the Title of the section and preserve in the section all the substance and tone of each of the contributor acknowledgements and or dedications given therein Preserve all the Invariant Sections of the Document unaltered in their text and in their titles Section numbers or the equivalent are not considered part of the section titles Delete any section Entitled Endorsements Such a section may not be included in the Modified Version Do not retitle any existing section to be Entitled Endorsements or to conflict in title with any Invariant Section Preserve any Warranty Disclaimers If the Modified Version includes new front matter sections or appendices that qualify as Sec ondary Sections and contain no material copied from the Document you may at your option designate some or all of these sections as invariant To do this add their titles to the list of Invariant Sections in the Modified Version s license notice These titles must be distinct from any other section titles 3 1 INTEGRATION WEIGHTS 49 You may add a section Entitled Endorsements provided it contains nothing but endorsements of your Modified Version by various parties for example statements of peer review or that the text has been approved by an organization as the authoritative definition of a standard You may add a passage of up to five words as a Front Cover Text
55. rkup Tex info input format LaTeX input format SGML or XML using a publicly available DTD and standard conforming simple HTML PostScript or PDF designed for human modification Ex amples of transparent image formats include PNG XCF and JPG Opaque formats include proprietary formats that can be read and edited only by proprietary word processors SGML or XML for which the DTD and or processing tools are not generally available and the machine generated HTML PostScript or PDF produced by some word processors for output purposes only The Title Page means for a printed book the title page itself plus such following pages as are needed to hold legibly the material this License requires to appear in the title page For works in formats which do not have any title page as such Title Page means the text near the most prominent appearance of the work s title preceding the beginning of the body of the text The publisher means any person or entity that distributes copies of the Document to the public A section Entitled XYZ means a named subunit of the Document whose title either is pre cisely XYZ or contains XYZ in parentheses following text that translates XYZ in another lan guage Here XYZ stands for a specific section name mentioned below such as Acknowledgements Dedications Endorsements or History To Preserve the Title of such a section when you modify the Document means that it remains a se
56. rm Sensitivity Ker nels Iterative inversion scheme which uses waveform sensitivity kernels to gain model updates form data residua In addition to ASKI I I page I5 you will need software to solve the forward problem E10 page 23 Before The First Iteration Step Create a main parameter file e g in the parent directory of your specific inversion di rectory or where you collect main parameter files for all your inversion projects gt page I5 You will need this file as an input argument to almost all programs scripts Set MAIN PATH INVERSION to a correct value The directory does not need to exist yet if not then it will be created Set ITERATION STEP PATH and PARFILE ITERATION STEP to desired values or leave the default values if present All other parameters can be adjusted later Create a directory structure for the expected number of iteration steps of your inversion gt L4 page I5 Make yourself familiar with the from of data used in ASKI 1 5 page 16 Set PATH MEASURED DATA PATH EVENT FILTER PATH STATION FILTER FILE EVENT LIST and FILE STATION LIST as wellas MEASURED DATA FREQUENCY STEP MEASURED DATA NUMBER OF FREQ andMEASURED DATA NDEX OF FREO in your main parameter file before preparing your data in the required iom page Set FORWARD METHOD in your main parameter file to the value of your choice If you want to use different methods
57. s e Finally compute the inverted model by solving the kernel system page 27 14 CHAPTER 0 GUIDE Chapter 1 Basic Steps In general in this chapter we provide only basic information For more detail on specific steps or objects we always refer to the respective sections below in this document 1 1 Installing ASKI e Download here http www rub de ASKI e Unpack tar ball somewhere e Follow the directions in file ASKI 0 3 README 1 2 Create Main Parameter File The simplest way to create a specific main parameter file for your operation is to modify adjust a copy of the template file ctemplate main parfile template Refer to the commented documentation in main parfile template or to sections 2 1 page 29 and page 9 1 3 Iteration Step Parameter Files Having created a directory environment for your operation as described in section I 4 page 15 there should automatically have been created template parameter files in each directory of an iteration step having filenames as defined by parameter PARFILE ITERATION STEP in the main parameter file Refer to the commented documentation in those template files or to sections page 29 and 2 1 2 pageB 1 1 4 Create Directory Environment Call python script create ASKI dir py USAGE please give 2 arguments 1 main parmeter file of inversion 2 number of iteration steps 15 16 CHAPTER 1 BASIC STEPS EXAMPLE crea
58. s or an interation step in the iterative full waveform inversion Those tools work on the sensitivity matrix which in the FWI is used in a linear system of equations which relates a data residuum Ad to a model update Am After updating the model wavefields may be computed with respect to the new model which again may be improved in the same way possibly using higher frequencies and smaller scatteres Any details on ASKI and the theory behind may be found in the near future in respective journal publications Time Domain Sensitivity Kernels This section describes how to compute time domain waveform sensitivity kernels for a specific set of sources receivers with respect to a certain background earth model as an operation seper ate of any other ASKI operations The kernels in time domain are much more intuitive to look at for human beings than the standard frequency domain sensitivity kernels You may as well compute time domain sensitivity kernels from the kernels produced in any iteration step of a full waveform inversion page 12 For this purpose apply the steps Transforming to Time Domain Sensitivity Kernels below after you computed the standard kernels in you iteration step as the time domain waveform kernels are produced by an inverse Fourier transform from the standard frequency domain waveform sensitivity kernels on which ASKI is based Please do not get confused by the general terminology of inversion and iteratio
59. separated values eventid 13 character name e g 2006 10 2977 or 061113 141238 should not con tain whitespace origintime characters of form yyyymmdd_hhmmss_nnnnnnnnn or yyyymmdd hhmmss i e with or without nano seconds e g 20130320 170012 or 20130320 170002 718000000 lat latitude in degrees 90 lt lat lt 90 S or first coordinate in wavefield points inversion grid frame C read the section on inversion grid definitions 1 7 lon longitude in degrees O lt lon lt 360 S or second coordinate in wavefield points inversion grid frame C read I 7 depth source depth in km S or third coordinate in wavefield points inversion grid frame C read 1 7 typ source type 0 force 1 moment tensor 1 not specified mag factor on source mechanism mom frce either 3 values force vector or 6 values moment tensor 2 3 Station List File Please find the template station list file template file station list template e first line contains single character C or S defining the coordinate system C artesian or S pherical with respect to which the given event coordinates lat lon are interpreted 34 CHAPTER 2 FILES e each following non empty line of the file is interpreted as a definition of one station and must contain the following space separated values ec 551 station name 5 character name which should neither contain whitespace nor
60. te ASKI dir py main_parfile_Aegeanl 10 Put your main parameter file see 1 2 page 15 as the first and the expected number of iteration steps as the second argument You can always recall this script at any later time with a larger number of iteration steps AII existing directories will not be affected only additional non existing objects will be created Recalling this script with a smaller number of steps will not delete anything 1 5 Datain ASKI One certain data sample in ASKI is characterized by a seismic source a component of a seismic receiver and a frequency as well as if it is real or imaginary part of the complex spectral values It has the value of displacement of the ground in the unit of meters Events and Receivers The events file page 33 and stations file page 33 constitute a collection of all events stations which will be involved in any way in your ASKI operation All programs scripts will refer to a specific event station by its event ID station name Receiver Components All programs scripts will refer to a specific receiver component by the following abbreviatory names Dependent on the coordinate system in which the receivers are defined Cartesian or spheri cal which is defined by the first line of the station list file the supported names of receiver components may have a different meaning Cartesian receivers CX Cartesian X coordinate first Cartesian coordinate CY Cartesian
61. ternal integration weights Figure 1 1 Example of a simple Cartesian inversion grid The shape of the cuboid as well as the distribution of inversion grid cells are defined via a paramter file a template of which is file template scartInversionGrid_parfile_ template In the following the particular parameters are explained with the example values always refering to the inversion grid as displayed in figure I 1 page I8 SCART INVGRID CX X coordinate of center of cuboid real number Example SCART INVGRID CX 50 0 SCART INVGRID CY Y coordinate of center of cuboid real number Example SCART INVGRID CY 30 0 SCART INVGRID ZMAX Maximum Z coordinate of cuboid real number i e Z coordinate of the surface of the inver sion grid 1 7 DEFINE AN INVERSION GRID 19 Example SCART INVGRID ZMAX 0 0 SCART INVGRID WX Width of cuboid in X direction real number Example SCART INVGRID WX 100 0 SCART INVGRID WY Width of cuboid in Y direction real number Example SCART INVGRID WY 150 0 SCART INVGRID ROT Angle in degrees of anti clockwise rotation about the local Z axis through the lateral center of the cuboid real number Example SCART INVGRID ROT 60 0 SCART INVGRID NREF BLOCKS SCART INVGRID NLAY SCART INVGRID THICKNESS For an arbitrary number of SCART INVGRID NREF BLOCKS b
62. the original version will prevail If a section in the Document is Entitled Acknowledgements Dedications or History the requirement section 4 to Preserve its Title section 1 will typically require changing the actual title 9 TERMINATION You may not copy modify sublicense or distribute the Document except as expressly provided under this License Any attempt otherwise to copy modify sublicense or distribute it is void and will automatically terminate your rights under this License However if you cease all violation of this License then your license from a particular copyright holder is reinstated a provisionally unless and until the copyright holder explicitly and finally terminates your license and b permanently if the copyright holder fails to notify you of the violation by some reasonable means prior to 60 days after the cessation Moreover your license from a particular copyright holder is reinstated permanently if the copy right holder notifies you of the violation by some reasonable means this is the first time you have received notice of violation of this License for any work from that copyright holder and you cure the violation prior to 30 days after your receipt of the notice Termination of your rights under this section does not terminate the licenses of parties who have received copies or rights from you under this License If your rights have been terminated and not permanently reinstated r
63. the publisher Preserve all the copyright notices of the Document Add an appropriate copyright notice for your modifications adjacent to the other copyright notices Include immediately after the copyright notices a license notice giving the public per mission to use the Modified Version under the terms of this License in the form shown in the Addendum below Preserve in that license notice the full lists of Invariant Sections and required Cover Texts given in the Document s license notice Include an unaltered copy of this License Preserve the section Entitled History Preserve its Title and add to it an item stating at least the title year new authors and publisher of the Modified Version as given on the Title Page If there is no section Entitled History in the Document create one stating the title year authors and publisher of the Document as given on its Title Page then add an item describing the Modified Version as stated in the previous sentence Preserve the network location if any given in the Document for public access to a Trans parent copy of the Document and likewise the network locations given in the Document for previous versions it was based on These may be placed in the History section You may omit a network location for a work that was published at least four years before the Document itself or if the original publisher of the version it refers to gives permission Fo
64. the standard cell QS For every such inversion grid cell Q module inversionGrid is expected to provide its transformed wavefield points x x7 and their corresponding val ues of Jacobian In the context of Scattered Data Integration here the inversion domain QS is not subdivided into any true subsets Ej It is always K 1 and E Q mainly because a subdivision of the standard tetrahedron is not trivial compared with e g the cube 1 1 considering that the integrals of the base polynomials must be computed over all subsets Fg As z the barycenter 0 25 0 25 0 25 of the standard simplex is chosen and h 1 The desired weights wj w are then given by w Aj 1 i ne Scattered Data Integration Order 1 intw type 1 In the context of this subsection 3 1 1 m 1 is used as the degree of polynomials which are integrated in an exact way and of course d 3 The space II of all polynomials in IR of maximum total degree m 1 has dimension J il x 4 As a basis of II m 1 we choose 1 55 y Ek 42 CHAPTER 3 PROGRAMS SCRIPTS AND MODULES Scattered Data Integration Order 2 intw type 2 In the context of this subsection 3 1 1 m 2 is used as the degree of polynomials which are integrated in an exact way and of course d 3 The space II of all polynomials in IR of P E A 10 As a basis of maximum total degree m 2 has dimension J E 9 II we c
65. tively small output like models coefficients etc NO wavefields kernels etc relative to MAIN PATH INVERSION ITERATION STEP PATH Be sure the path ends on T PATH KERNEL DISPLACEMENTS Subdirectory of current iteration step path MAIN PATH INVERSION ITERATION STEP PATH which contains the kernel displacement files Be sure the path ends on T 2 2 EVENT LIST FILE 33 PATH KERNEL GREEN TENSORS Subdirectory of current iteration step path MAIN PATH INVERSION ITERATION STEP PATH which contains the kernel green tensor files Be sure the path ends on T PATH SENSITIVITY KERNELS Subdirectory of current iteration step path MAIN PATH INVERSION ITERATION STEP PATH which contains the velocity kernel files Be sure the path ends on T PATH SYNTHETIC DATA Subdirectory of current iteration step path MAIN PATH INVERSION ITERATION STEP PATH which contains the files with synthetic data Be sure the path ends on T 2 2 Event List File Please find the template event list file template file event list template e first line contains single character C or S defining the coordinate system C artesian or S pherical with respect to which the given event coordinates lat lon are interpreted e each following non empty line of the file is interpreted as a definition of one event and must contain the following space
66. ust only contain indices contained in MEASURED DATA INDEX OF FREQ All indices here are assumed in accordance with the global frequency step MEASURED DATA FREQUENCY STEP TYPE INVERSION GRID PARFILE INVERSION GRID Type of inversion grid as supported cf and corresponding filename of parameter file defining this inversion grid relative to MAIN PATH INVERSION ITERATION STEP PATH TYPE INTEGRATION WEIGHTS Type of integration weights integer number cf for supported values FILE INTEGRATION WEIGHTS Filename of the integration weights file which will be created and used relative to MAIN PATH INVERSION FILE WAVEFIELD POINTS Filename of the wavefield points file relative to MAIN PATH INVERSION which is in gen eral created by the method you are using Just refer here to this file FILE KERNEL REFERENCE MODEL Dependent on the method you are using these filenames may be handled individually Please refer to the respective documentation of the methods for recommendations how to use these parameters or which naming to choose FILEBASE BASIC STATS Base filename of vtk stats output files related to inversion grid wavefield points integra tion weights events stations relative to MAIN PATH INVERSION ITERATION STEP PATH PATH OUTPUT FILES Folder relative to which some sensitivity analysis and inversion programs write their output rela
67. ynthetic data in the way ASKI expects it see sec tions 1 5 page and 2 5 page 34 Refer to the documentation of your method on how to do it e Setfilename FILE INTEGRATION WEIGHTS in your main parameter file can be any name will be created as well as TYPE INTEGRATION WEIGHTS gt page R4 e Initiate basic requirements for all programs and scripts gt page 251 e If you have many paths you may define a data and model space concentrating on defining paths page 24 If you have only one path or just a few it possible and propably also convenient to just continue to the computation of the kernels e Compute the standard frequency domain sensitivity kernels for your specific set of paths or the one or few paths one after another and your set of model parameters 1 14 page If desired you may have a look at the standard frequency domain kernels page 26 11 Transforming to Time Domain Sensitivity Kernels e Transform the standard frequency domain waveform kernels to time domain 1 15 page 26 Note that the transformation always requires event filters 1 e source time functions and station filters 1 e receiver responses which in case they are not required may artificially all have real value 1 R i e 1 0 C for all frequencies e Plot the time kernels gt page 26 12 CHAPTER 0 GUIDE Full Waveform Inversion Classical Wavefo

Download Pdf Manuals

Related Search

Related Contents

Universidade Federal do Rio de Janeiro Escola Politécnica  Samsung BM-501S User's Manual  Brother 885-X36 Sewing Machine User Manual  OL_TM16DOLB INSTRUCTIONS    

Copyright © All rights reserved. Failed to retrieve file