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1. BCE Ltd BSDSolver 4 2 Water Level Technique As previously outlined it is recommended that the user implement the WLT on the PPD source wave estimates The implementation of the WLT is a fast and simple approach if there is minimal source wave variation within the seismogram 4 2 1 WLT Theoretical Background A standard frequency domain methodology in estimating the reflection series 4 is the water level technique WLT 2 If the measurement noise term in 1 is ignored then the Z transform of 1 is given as t S t u t Z z S z P z 9 where z denotes the Z transform of the reflection series The WLT can be described by considering 9 representing the Z transform by the Fourier transform i e z e and rearranging terms as follows wo 202 10 S 0 where Y denotes the Fourier transform of the reflection series u t Theoretically for a known source wave one could simply implement 10 and calculate P w The reflection series 4g is then estimated by taking the inverse Fourier transform of Unfortunately due to inaccuracies in the specification of the source wave the bandlimited nature of the source wave and additive measurement noise the implementation of 10 is highly unstable and inaccurate To mitigate that 10 is modified by multiplying the numerator and denominator by the complex conjugate of S denoted as q and then by introducing an additive scalar value2. COMMERCIALLY CONFIDENTIAL BCE Ltd BSDSolver Figure 32 Main graphical interface in View Seismogram software Option oooooonnncncncccnnnnnnnnnnnos 28 Figure 33 Filtered seismic trace in View Seismic in software option View Seismogram 29 Figure 34 Overlaying unfiltered seismic trace onto filtered seismic trace illustrated in Figure 31 A RT 29 Figure 35 Display of spectrum of seismic time series illustrated in Figure 30 eee 30 Figure 36 Dominant frequency window 45Hz to 60Hz for frequency spectrum shown in Figure e aie aa ase eee eect le oa ae E wpe seid eae ete serge ate Geen eet ces eect cates eae nck 30 Figure 37 Seismogram with poorly defined first break ococccccccccnnnnnononnnonnnnnnnnnnncnnnnnnnnnnnnos 31 Figure 38 Time window magnification of first break shown in Figure 3d ooooooonnnnnncocincnnnnnnnnnn 32 Figure 39 Seismogram with front end decay applied oocccccccoooonnnnnnnnnnnnonnnonnnnnnnnnnnnnnnannnnnss 32 Figure 40 Pile miu aloe DO N oni 33 Figure 41 Filtered 30 to 100 Hz bandpass seismic trace profile with peak particle accelerations Prada dado 34 Figure 42 Filtered 30 to 100Hz bandpass seismic trace profile illustrating trend lines with corresponding interval velocity estimate S auseneen a a a 35 Fievre 43 Chart Editine Dialogue BOX coincidir ET 36 Fisarc 44C hart Printing Dialogue DO ia a E ie E 36 BSDSolver User s Manual OBaziw Consulting Engineers Ltd 111
3. Te oe To 50 A oe To oe To 50 a a a a a a a a a a a O a a a a a a y a C a 3 O mM qn C O a a q a a mS a mS O a a ao a qn a Ci a mS a mS a a q O q q a ao a a mS a a mS a mS a a ao q O a ao q a a a a mS a a a a mS a mS a a qn a q q a a a q a a qn a m a a mo a a qn a mS a a q qn a C a q a qn qn a mo a mS a a a a q a qn m C a a a m a a a a a q a qn m C a AR 2a a a a moe a a qn a a O a a a a a y a m C a 32 O yn 32 Ci O a a qn Ci a mS a mS O a q q qn a a a a a a y a O a a ao y a a a mS a mS a mS a qn a ao O a a ao qn qn a mo a mS a a a a a a mS a a q qn a C a a a q a qn qn a mS a a C a a a a a a ao a q C a q a qn a a a a a a a qn a a q y a a C a a a a mS a mS a a ao q C a AR 2a a a a 0 a a a a a a O a a a a a a a a C a 3 O yn a Ci O a a q Ci a a a mS qn a ao m qn qn a mS
4. a a a q a qn qn qn a mS a mS a a ao y a q a a a mo a mS a a a y a a qn C a a mo a mS a a ao Po a a ate a a a a a a J oie 0 2 0 lt lt Friction sleeve lt Pore pressure sensor ial seismic 19X1 Tr cone sensor configuration EEE 0 tg ggg ss ta a tg tata ag ts ta ats EE tll rll lariat OOOO OOOO OOOO OOOO NOS a CA RICE IE AAN A A A OA AAA Pate eee ea Te eT TT TT TTT CA Par ae AE ANA A AA AA AAA AAA AA a ACA PEI A ANA A A AA AA AAA a CA SERIA AAA A AO AA AAA AAA A a CA ARARNAR AAA CA ARAARA CN Bearing pressure measurement at cone tip in a SCPT investigation with ing a hen conduct te containing stone columns Ing Source Waves w f overlapp LON O Figure 24 Illustrat latlon SI remed 20 Baziw Consulting Engineers Ltd BSDSolver User s Manual COMMERCIALLY CONFIDENTIAL BCE Ltd BSDSolver MY PPD Results ER lo ue pa BC C Sp 3 E ol DF Hz 54 5 ms 0 0988 AMS Error 0 003975 Time ms 51 735 30 Time ms v pz a E T 100 120 Time ms Figure 25 BSDSolver algorithm output after processing the noisy seismograms illustrated in Figures 15 and 16 with a 200 Hz low pass filter applied and a MCFL parameter setting of 2 7T BSDSolver User s Manual Baziw Consulting Engineers Ltd 21 COMMERCIALLY CONFIDENTIAL
5. 1 M A Selecting software option Blind Seismic S Samora z Na 4 1 Blind Seismic Deconvolution Deconvolution opens the user interface as shown in Figure 5 As previously outlined in Section 2 1 the PPD algorithm is designed to process two closely spaced seismograms simultaneously utilizing multi threading and making use of standard dual core processor technology This is done to reduce the solution space for estimating the source wave BSDSolver User s Manual Minimum Reflection Coefficent Time Offset ms E ke Set AO to Masimum 25 Maximum Cost Function Length n T Source Wave Parameters Bandwidth Minimum Hz 140 Mas Length ni T J 2 5 Max Peak n T 12 First Break Specification e In Phase C Out of Phase eo Masimum Hz Maxinum A elate Ratio 0 9 OL Close MM Abort OF e Begin Processing 1 h Y fife r at i PO me en Figure 5 Blind Seismic Deconvolution user interface Baziw Consulting Engineers Ltd 8 COMMERCIALLY CONFIDENTIAL BCE Ltd BSDSolver 4 1 1 Specifying Seismic Time Series and Filter Parameters Input Seismic Time 1 Series The seismogram files are inputted by Lookin Noisy Data e eE selecting button ERE which opens the file Emma SS input dialog window shown in Figure 6 In emei Gascmasencstowmsnve lorcozoo Eomndsnmogan 251 Oa this window the user is instructed to input E E E aig the two seismograms to be processed If the
6. COMMERCIALLY CONFIDENTIAL BCE Ltd BSDSolver 1 0 Introduction 1 1 What is BSDSolver BSDSolver is a program that facilitates the implementation of the Principle Phase Decomposition PPD technique 1 2 amp 3 It uses a seismic deconvolution algorithm which allows for the estimation of the source wave and reflection series Seismic deconvolution is one of the most widely researched and implemented seismic signal processing tools The primary goal of seismic deconvolution is to remove the characteristics of the source wave from the recorded seismic time series so that one is ideally left with only the reflection coefficients These coefficients identify and quantify the impedance mismatches between different geological layers which are of great interest to the geophysicist A very challenging and yet common seismic deconvolution problem is where the source wave is unknown and has the potential for time variation This is referred to as blind seismic deconvolution BSD the situation where we have one known measured seismogram with additive noise and two unknowns source wave and reflection coefficients PPD is designed to solve blind seismic deconvolution problems BSDSolver includes the following features Configurable for either geophones or accelerometers Extensive frequency spectrum analysis Bandpass high pass low pass and notch frequency digital filters Vertical seismic profile display with trend line
7. Consulting Engineers Ltd 17 COMMERCIALLY CONFIDENTIAL BCE Ltd BSDSolver The bottom chart illustrated in Figures 19 and 21 is similar to that of the top chart but in this case the complete seismogram is displayed unnormalized and the estimated seismogram calculated by convolving the estimated reflection series with the estimated source wave is derived over the complete length of the recorded seismogram The estimated source wave and reflection series have been scaled by the windowed seismogram normalization factor by selecting button The scaling of the estimated source wave and reflection series can be undone by selecting button as is shown in Figure 22 The user should note that the signs of the reflection coefficients are assigned based upon the estimated first break sign of the estimated source wave For example the estimated source wave of Figure 19 has a negative first break resulting in a negative sign for the first reflection coefficient The estimated source wave estimated reflection series and residual seismogram can be sae by selecting the appropriate radio button SW RC and SR respectively and pressing button mms user is then instructed to specify the file name and directory as is illustrated in Figure 23 The source wave estimate illustrated in Figures 19 and 21 is then utilized to deconvolve the source wave from the seismogram by implementing the water level technique WLT so that the complete reflection s
8. El residTest1 E resull Ext El resul25wt1 bt El resul25we2 bt Ea iiij gt 3 My Network File name BerlageSw2_5T Result Em Use May 22 2010 y Placez Save as type k Figure 23 Saving the estimated source wave reflection series and residual seismogram The user can reprocess the previously outlined data set with a larger MCFL value setting if they have some insight into the testing environment For example Figure 24 illustrates a downhole seismic testing DST investigation within a remediation site where there are stone columns present In this situation it would not be expected that there would be more than 3 direct wave and two reflections to 4 overlapping source waves If the user does not have insight into the seismic testing environment a larger MCFL value setting can be specified if there is a short duration seismogram and based upon results like those outlined in Figures 19 21 and 22 In these figures it is evident that the last reflection coefficient occurs at the end of the seismograms and we are processing relatively short duration seismogram therefore applying a larger MCFL value makes intuitive sense The major advantage of increasing the MCFL value is that more accurate results are obtained due to the fact that a greater portion of the seismogram is utilized when calculating the cost function The disadvantage 1s that significantly greater processing time is required The previously estimated seismo
9. Scalar e Automatic Frequency Filter Specification e Normalize Input Output The WLT Scalar corresponds to the water level WL Ain 11 In the BSDSolver program the user specified WLT Scalar value is scaled by the maximum power of the seismogram prior to inputting into 11 The default value of the WL is 0 0002 In general terms the setting of the WL is a trial and error approach and depends upon the measurement noise level and the accuracy of the estimated source wave A higher WL value is required if the seismogram to be processed has increasing measurement noise and decreasing source wave accuracy The estimated reflection coefficient amplitudes are highly affected by the value of the WL and whether a frequency filter had been applied to the seismogram prior to implementing the WLT A higher WL value and application of a frequency filter e g 200 Hz Low Pass will result in a significant decrease in the resolution of the reflection series This results in a more bell shaped reflection series energy is spread out whereby the peak values are reduced due to energy spreading In other words a high WL value has the same effect as a frequency filter smoothing and spreading of energy of the reflection series As previously stated as A 0 the resulting estimated reflection coefficients approach Dirac delta functions and if measurement noise is present the reflection series become significantly indiscernible e g white noise When A gt
10. at the specified time index If it is desired to decay from the start of the trace to the Initial Delay Time then check box Front End Decay must be checked This is most likely the case as the purpose of signal decay is to clearly define the first break when it is not apparent Figures 37 and 38 illustrate a filtered 200 Hz low pass seismogram data where there is a poorly defined first break The Signal Decay option was implemented on the seismogram with the Initial Time Delay set to 13 ms and the Decay Factor to the default value of 0 5 ms The Initial Time Delay of 13 ms was selected due to the fact that the seismogram appears to have a smooth decay until this time reference Figure 39 illustrates the output after applying signal decay by pressing button MRJ Selecting button undoes the previously applied signal decay and button ar ES facilitates the user in saving the filtered and front end decayed seismogram for further processing with the BSD and WLT software options Al Seismic Data EN m Filet m Ovenlay M FFT 28 803 26 300 AJO Alt ehlbto where t gt to to inal decay time and h decay factor Initial Decay Time me 20 Decay Factor 1m 05 if Front End Decay y Ea Data File CUOBSIPPOASE Mmultichannel 20102 57 DataillataWlolsy DataisecondSeismogram 2 57 Depth 6m war 20 TC 0_01 txt i E T pz a E T SO 60 F 0 480 100 110 120 130 140 150 160 170 180 180 200 Time ms Figure 37 S
11. estimation Display of peak particle accelerations velocities and displacements Implementation of the PPD technique for source wave and reflection series estimation Implementation of the water level technique for reflection series estimation based on an inputted PPD estimated source wave Extensive chart editing plotting and exporting functions V V Y VVVV WV 1 2 Organization of user s manual The purpose of this manual is to instruct users of BSDSolver in the use of the program by explaining the mathematical background and the program structure taking the user step by step through the program menus and specifying the use of interactive graphics and I O routines BSDSolver User s Manual OBaziw Consulting Engineers Ltd 1 COMMERCIALLY CONFIDENTIAL BCE Ltd BSDSolver 2 0 PPD Mathematical Background PPD is an analysis technique that facilitates blind seismic deconvolution allowing for the estimation of the source wave and reflection series In seismology the most important seismic model is in general terms written as 1 z t S t L t v t 1 where z t the measured seismogram S t the seismic wave which is a superposition of earth and instrument responses u t the reflectivity of the earth which consists of all primary reflections as well as all surface and internal multiples v t the additive noise generally taken to be white with a Gaussian pdf x denotes the convolution operat
12. features consists of filtering the seismic trace overlaying the unfiltered trace onto the filtered trace displaying the smoothed Fourier transform of either the unfiltered or filtered seismic time series and applying an exponential decay The user is strongly encouraged to implement the View Seismic software option so that the appropriate source wave bandwidth 1 e fmin and fmax and frequency filters can be selected prior to implementing BSD and the WLT Upon selecting the View Seismogram option a file input dialog box appears e g Figure 6 where the user 1s requested to specify the seismic file to process Figure 32 illustrates the graphical output which appears once the appropriate seismic file has been selected At the top of Figure 32 there are the checkboxes of Filter Overlay and FFT as well as the numeric values of the time and amplitude at the current location of the graphical crosshair If the Filter check box is selected the user interface illustrated in Figure 7 appears E Seismic Data El Filter Overlay FFT 19 377 ie 2 550 Atty Aft ehilt to where t gt to to intial decay time and h decay factor Initial Decay Time me 2 0 Decay Factor 1 mej 0 5 le Front End Decay x BB Data File CUOBSPPO E Multichannel 201012 57 Data DataiMoisy DatalsecondSei mogram 2 5T Depth 6m war 10 TC 0_01 txt S E T pz a z T oo g 100 110 120 130 140 150 160 170 180 180 200 Time ms Figure 32 Main g
13. ji E reies user desires to process only one seismogram Ms then the same file should be selected twice SB resis PE B resul45W1 Ext The PPD algorithm requires that the 5 sccondsesnogan 21 Depth em Ne nosse seismograms are preprocessed so that the amp a signal to noise ratio of the user specified bs Files of type seismograms is increased and ideally that the measurement noise is removed without Figure 6 File input dialog box distorting the seismogram containing only overlapping source waves User interface button HE allows the user to Boo select a range of digital frequency filters High Pass Frequency Hz 20 bandpass notch low pass and high pass Figure 7 illustrates the user interface which appears when button is selected Low Pass Frequency Hz 1240 The appropriate filter is selected by opening the tab for that particular filter checking the Enabled check box and entering the following data e for the Bandpass Filter the High Pass Frequency and Low Pass Frequency e for the Notch Filter the Notch Frequency e for the Low Pass Filter the Low Pass Frequency e for the High Pass Filter the High Pass Frequency Once the desired digital frequency filters have been enabled and corresponding parameters specified the user selects button MA to save the entered data Figure 7 Filter Parameter Specification user interface In addition the following must be done e Enter the Minimum Reflection Coeffic
14. wave 1s reduced For example in a typical downhole seismic investigation the receivers are offset by 1 m This m offset is equivalent to a 10 ms source time offset for a medium velocity of 100 m s It is therefore very likely that two source waves offset by 10 ms are identical By processing two seismic traces simultaneously the PPD algorithm determines the top source wave estimates where the weighted RMS difference between the estimated seismograms and the true seismograms over time window t source wave arrival time to to T ma are minimized The weight of the cost function is then defined as the absolute sum difference between the source wave parameters 1 e fofiser h and the time location T of the maximum peak of the source wave weight abs f fy abs T T abs h h ADS tiren topcer2 8 The minimum and maximum source wave attenuation values are automatically estimated within the PPD algorithm based on the user specified minimum fmin and maximum fmax dominant frequency window of the source Minimum attenuation value The exponential decay is defined as X X Y If the amplitude of the AMT has decayed to 0 05 5 of the maximum value AMTuax then 0 05 e or hAt 3 Since it can be assumed that the maximum source length is 2 57 and that it will take at least 0 25T to reach AMTvyax from to as is the case with every sine wave the time for the source wave to decay to 5 of AMT way 1s therefo
15. BSDSolver 2 0 User s Reference Manual SLE SUB SURFACE DIAGNOSTICS Wi BsDSolver File Seismic Signal Analysis Utilities Help q EZ 2 EL E LI 60 Time ms Source Wave Seismogram Reflection Coefficients Baziw Consulting Engineers Ltd 2080 2010 No part of this document may be reproduced stored in a retrieval system or transmitted in any form or by any means electronic mechanical photocopying or otherwise without the prior written permission of Baziw Consulting Engineers Ltd Although every precaution has been taken in the preparation of this manual we assume no responsibility for any errors or omissions nor do we assume liability for damages resulting from the use of the information contained in this book BCE Ltd BSDSolver Table of Contents ADs oooO A e O E E E E E l LI Wiari Bo DS0R er M pee NEE l 1 2 Orrann or user o mandl eren EE EEE EEEE l 2 0 PPD Mathematical Background ccccccconoonncncnnnnnnnnnnocnnnnnnnnnnnnnnnonnncnnnnnnonnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnos 2 AP on scene oeevene 7 4U DEIS Sinal Analy SiS cesos eran opi a aE nacio 8 Adi Bund Seismic ACCOM VOL siesena E EEE eni ES 8 4 1 1 Specifying Seismic Time Series and Filter Parameters oooccccccccncoonncnnnnnnnnnnnnnannnnnnnnnnnnnnnnnnos 9 41 2 Spec ING police Wave Paramoters acirsancsendacasoamanaeahanesimentaenmedenacaswactaeatesstmesanenaeanarmnesteaanes 10 4 1 3 Blind Seismic Deconvolution Impl
16. Data File CUOBSPPD EMutichannel 201 002 57 DataiData Moisy DatalsecondSejismogram 2 57 Depth Em War 10 To O04 txt Amplitude m s 2 000 3 000 4 000 5 000 6 000 Frequency Hz aa 20 418 7 0 236 Aft A t e lt to where t gt to to intial decay time and h decay factor Initial Decay Time me 2 0 Decay Factor 1 mz 0 5 W Front End Decay y al BB Data File T WOBS BSDSolvert2_ST DataiDataiNoisy Datalsecondseismogram 2 57 Depth Gm var 10 To 007 tet Amplitude m s 50 55 Frequency Hz Figure 36 Dominant frequency window 45Hz to 60Hz for frequency spectrum shown in Figure 35 BSDSolver User s Manual OBaziw Consulting Engineers Ltd 30 COMMERCIALLY CONFIDENTIAL BCE Ltd BSDSolver When implementing the PPD algorithm it is important that the seismogram has an unambiguous first break or source wave arrival time t The Signal Decay option in View Seismogram facilitates the user in defining clear first breaks when they do not exist due to excessive measurement noise The technique implemented to do this relies upon the application of an exponential decay that is applied to the selected time series data after a user specified time the so called Initial Time Delay The option therefore requires that the user specifies this Initial Time Delay ms and the Decay Factor 1 ms which has a default value of 0 5 ms As the Decay Factor 1s increased there is a sharper decay of the time series data
17. LLY CONFIDENTIAL BCE Ltd BSDSolver 9 0 Utilities As illustrated in Figure 30 the Utilities menu option consists of the following sub menus e Sensor Type to specify the sensor used to record the seismic data i e accelerometer or geophone e View Seismogram to view a seismogram file and its corresponding frequency spectrum so that the appropriate type of digital frequency filters can be ascertained e VSP to display Vertical Seismic Profiles VSPs and corresponding trend lines for downhole seismic investigations Wl BSDSolver File Seismic Signal Analysis MENES o Sensor Type View Seismogram q T 5 T 50 60 70 Time ms Source Wave Selsmograrn eee Refection Coefficients Figure 30 Utilities software options 5 1 Sensor Type The Sensor Type dialogue box 1s illustrated in Figure 31 The user selects either an Accelerometer output proportional to particle acceleration or Geophone output proportional to particle velocity The user should specify the type of data to be processed prior to proceeding with the analysis options provided A Seismic Sensor Specification A El Sensor Type Specification i Geophone Figure 31 Sensor Type dialog box BSDSolver User s Manual OBaziw Consulting Engineers Ltd 27 COMMERCIALLY CONFIDENTIAL BCE Ltd BSDSolver 5 2 View Seismogram The View Seismogram software option allows the user to analyze a seismic file on an individual basis Analysis
18. and thus provided greater accuracy and uniqueness in the source wave and reflection series estimation Amplitude 0 gt 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 55 90 95 100 Figure 8 PPD cost function time window Unless a residual wave is analyzed the first arriving source wave has typically the largest amplitude The user can specify this a priori within the PPD algorithm by setting RO reflection coefficient of first arriving source wave to the maximum value in the reflection series within time length fo source wave arrival time to tr MCFL This is implemented by enabling check box Set RO to Maximum default setting 4 1 2 Specifying Source Wave Parameters As outlined in Figure 5 the Source Wave Parameters required for user input are Bandwidth Maximum possible length of the source wave Tmax Maximum possible time location of the maximum peak of the source wave Tan Maximum Relative Ratio MRR First Break Specification FBS BSDSolver User s Manual Baziw Consulting Engineers Ltd 10 COMMERCIALLY CONFIDENTIAL BCE Ltd BSDSolver These input parameters allow the user to provide a priori information of the source wave to be estimated Input Bandwidth represents the source wave dominant frequency window The user is required to specify the Minimum fmin and Maximum fmax dominant frequencies of the frequency window It should be noted that the larger the source wave bandwidth the greater time is requi
19. ci v Acceleration velocity Displacement 120 140 160 180 200 220 240 260 280 300 320 340 360 380 400 420 440 Time ms M Legend f v O ee Figure 41 Filtered 30 to 100 Hz bandpass seismic trace profile with peak particle accelerations PPA displayed The trend lines illustrated in Figure 42 are specified by pressing the middle mouse button or lt shift gt right mouse button or lt shift gt left mouse button to identify individual points of interest The BSDSolver program then automatically draws a line between the points specified and provides a velocity estimate Pressing options lt Ctrl gt left mouse button or lt Ctrl gt right mouse button will delete the previously specified trend line Double clicking the middle mouse button will delete all the specified trend lines To obtain accurate interval arrival times utilizing the trend line specification it is mandatory that the investigator select the appropriate time index at the exact depth of the probe from which the seismic data was recorded Alternatively if check box Enable Closest Depth is enabled the BSDSolver software relates back to the closest data depth when specifying trend lines BSDSolver User s Manual OBaziw Consulting Engineers Ltd 34 COMMERCIALLY CONFIDENTIAL BCE Ltd BSDSolver Wi Seismic Profile ale a R Normalize Y Enable Closest Depth 0 639 13 311 C WOBS SCPT4SC1 Systems Training SC1 RAY Test DataMleftSCPT 22 C
20. cnnnnnnnnnnnnnnnnnnnnnncnnnnncnnnccnnnnnnnnnnnnnos 9 Figure 6 PPD Cost tuncuon Ume WINDOW sens icoutmsssnanovsionaenosndanerarendatnesonanteoneedeeasaaaameeeesnontasens 10 Figure 9 Source waye input parameter rice 11 Figure 10 Berlage wave with superimposed 55 HZ SINUSO LO occcccnnnncncnnnnnnnnnoninonnnnnnncccnnnnnnnnnnnnos 12 Figure 11 Seismogram 1 reflection coefficients ooooooonnnnncnnnnccnnnnnnnnnnnnnnnnnnnnnnonncnnncccnnnnnnnnnnnnos 13 Figure 13 Seismogram 2 reflection coefficients ooooooononnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnananonocnnncncnnnnnnnnnnnnos 13 Figure 12 The output after convolving Berlage wave of Figure 10 with reflection coefficients Mustrated eE o e T E E E olaa tapo ribetes 13 Figure 14 The output after convolving Berlage wave of Figure 10 with reflection coefficients UREE USSE 1 AT SBD E E o A A 13 Figure 15 Seismogram of Figure 12 with additive Gauss Markov measurement noise 14 Figure 16 Seismogram of Figurel4 with additive Gauss Markov measurement noise 14 Figure 17 Specifying a 200 Low Pass Filter ooooooonnnnnnnnnnccnnnnnnnnnnonononononnncnnncnncncccnnnnnnnnnnnos 15 Figure 18 BSDSolver Parameter Settings c c c ccccscscssscsesesssssessesesescsessesscscavevevsvsvstsesssesssseees 15 Figure 19 BSDSolver algorithm output after processing the noisy seismograms illustrated in Figures 15 and 16 with a 200 Hz low pass filter applied oooooooncccnnnnncnnn
21. e wave normalized estimated reflection series and normalized estimated seismogram from time span ty to tp MCFL for the low pass filtered data file shown in Figure 15 Also illustrated is the normalized true low pass filtered seismogram and the error residual between the estimated seismogram calculated by convolving the estimated reflection series with the estimated source wave and the true filtered and normalized seismogram between time span time span t to tot MCFL It should be noted that in the top chart display the first break value t and subsequent first arriving reflection coefficient are set arbitrarily at a reference of time 10 ms In the bottom chart of Figure 19 the estimated reflection series and seismogram have shifted to the true fo value BSDSolver User s Manual Baziw Consulting Engineers Ltd 15 COMMERCIALLY CONFIDENTIAL BCE Ltd BSDSolver Displayed in the top panel above the top chart in Figure 19 is the estimated source wave dominant frequency DF Hz 56 1 attenuation h 1 ms 0 1054 and RMS error residual between the true seismogram and estimated seismogram RMS Error 0 004335 Selecting button Giles within the top panel located above the top chart will result in the chart editing user interface illustrated in Figure 20 Section 6 0 outlines the chart formatting editing and printing capabilities of the BSDSolver program The user can enable and disable the display of a desired series by checking and u
22. ed by moving back in time from fo until the first zero crossing is reached Once the Seismic Time and Filter Parameters and the Source Wave Parameters have been specified the user selects push button Begin Processing 4 1 3 Blind Seismic Deconvolution Implementation The implementation of the PPD algorithm is demonstrated by considering the analysis of two challenging synthetic seismograms The seismograms are challenging due to the fact that there are five closely spaced reflection coefficients with dipoles in a high measurement noise environment The first seismogram was generated by convolving the Berlage wave illustrated in Figure 10 with the reflection coefficients outlined in Figure 11 to give the output illustrated in Figure 12 The second seismogram is generated by convolving the Berlage wave of Figure 10 with the reflection series illustrated in Figure 13 The resulting seismogram is shown in Figure 14 Table I outlines the reflection series parameters of arrival time and amplitude for seismograms and 2 Amplitude m s2 o 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 50 55 30 95 100 Time ms Figure 10 Berlage wave with superimposed 55 Hz sinusoid BSDSolver User s Manual Baziw Consulting Engineers Ltd 12 COMMERCIALLY CONFIDENTIAL BCE Ltd BSDSolver LY Lo E a E XI 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 116 120 Time ms Figure 11 Seismogram I reflection coefficie
23. eft mouse click or lt CTRL gt left mouse click After specifying the files to be displayed the Filter Parameter Specification user interface 1 e Figure 7 appears facilitating the user applying the digital frequency filters to the selected seismic data files Once the seismic data files and frequency filters are specified a VSP appears as 1s illustrated in Figure 41 The magnifying glass icons shown in Figure 41 allow the user to scale the seismic amplitudes in 10 increments The legend can be added and removed from the display by checking and un checking the Legend check box respectively The buttons EA and allow the user to automatically display and remove all the inputted data files from the graphical chart respectively The user can display acceleration velocity or displacement profiles by pressing the right mouse button and selecting the desired particle motion as shown in Figure 41 When the traces are not normalized the peak particle accelerations PPA velocities PPV or displacements PPD are displayed In this mode the seismic amplitudes are scaled relative to the maximum amplitude within the seismic profile BSDSolver User s Manual OBaziw Consulting Engineers Ltd 33 COMMERCIALLY CONFIDENTIAL BCE Ltd BSDSolver A Seismic Profile ajal El paa M Normalize V Enable Closest Depth 295 844 14 194 C JOBSSSCPT4SC1 Systems Training SC1 RAW Test Data left SCPT 22 Chartwell WestfieldS4_0L14_07_2008 11 16 19 a_SC1 a
24. eismogram with poorly defined first break BSDSolver User s Manual OBaziw Consulting Engineers Ltd 31 COMMERCIALLY CONFIDENTIAL BCE Ltd BSDSolver D Seismic Data E Fite M Overlay FFT 30 112 27 200 Alt A t e lt to where t gt to to intial decay time and h decay factor Initial Decay Time ma 20 Decay Factor 1m 0 5 e Front End Decay v Data File CAJOBSPPO WEMultichannel 201012 ST DataDataiNoisy DataisecandSeismagram 2 5T Depth 6m ar 20 TC 0_01 txt N E di D 3 a E 9 10 11 12 13 14 15 16 17 18 18 20 21 22 23 24 25 26 27 26 29 30 Time ms Figure 38 Time window magnification of first break shown in Figure 34 A Seismic Data ea B M Fiter Overlay FFT 16 602 27 700 A t Alt ht to Where t gt to to inital decay time and h decay factor Initial Decay Time ma 13 Decay Factor 1 ma 0 4 W Front End Decay y al Data File CWJOBS PPD VvE Multichannel 2010 2_5T DataDataiNoisy DatatsecondSeismogram 2 57 Depth 6m var 20 TC 0_01 txt Amplitude m s2 bo 8 4 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 20 29 30 Time ms Figure 39 Seismogram with front end decay applied BSDSolver User s Manual OBaziw Consulting Engineers Ltd 32 COMMERCIALLY CONFIDENTIAL BCE Ltd BSDSolver 5 3 VSP Specify Seismic Profile Data The VSP software option allows the user to plot filtered seismic traces or estimated reflection seri
25. ementation ccccccnnnnnocnnnnnnncnnnononcnnnnnnnononononnnnnnnnnnnnnnnnnnos 12 A Water level ec ares E tone aaratines baron bi isos 22 4 2 1 WLT Theoretical Background vero 20sssseanceacesutasa esnncsanndesssanssananannsebevavesesscanedbaevanesanenencaebes sine 22 a Ea a a E E y o E AE E E A S 23 IOE Sea a dos teens sees ansaseesnateasvanience 21 A a I 5 II 27 de VENAS CSN MN E N E EA E A E A E E 28 DIN P a O III 33 6 0 Chart Formatting Exporting and Printing ooooccnnnnncnonnnocnnnnnnnnnnnnnnnnnnnnnnnnnonononnnnnnnnnnnnononaninnnncnnnnns 36 T PDM AAA e E e e En 37 Ni PP A E E AT PO E E E E EE 38 BSDSolver User s Manual OBaziw Consulting Engineers Ltd i COMMERCIALLY CONFIDENTIAL BCE Ltd BSDSolver List of Figures Figure Finite difference source wave with superimposed 140 Hz sinusoid and exponential aL e he a Ha ire ena T ks epee ee Po OO OOO E Unt enn A 3 Figure 2 Illustrating the concept behind parameters Tmax and Nmax e0ooooooccccnnnnnnnnnonccnnnnnnononanininonss 4 Figure 3 Main Menu in BSDSOlVer sicsacasoeetccsdadoedescveudesarenlazsasdoadcenesescios naaa ERr 7 Figure 4 Seismic Signal Analysis Software Options ccccccccccccccccccceeaeeeseeeeeeeeceeceeeeeeeeeeeeeeaaaaas 8 Figure 5 Blind Seismic Deconvolution user interface ooooonnnnnnncnncnnnnnnnononononnononononnncnnnocnnnnnnnnnnnnnos 8 Freire Oo lia AAA e E O II A 9 Figure 7 Filter Parameter Specification user interface oooooonnnnnncc
26. en the sinusoidal component commences The source wave at time fo and to togser 18 In Phase if the amplitude values at times fo and to fogser have the same sign 1 e or as shown in Figure 1 The source wave at time fo and to tofset 18 Out of Phase if the amplitude values at times fo and fo togser have different signs BSDSolver User s Manual Baziw Consulting Engineers Ltd 11 COMMERCIALLY CONFIDENTIAL BCE Ltd BSDSolver The standard procedure in selecting the FBS option is to first select two closely spaced seismograms or even the same seismogram twice to process them and to determine the output RMS error residual after processing the data file with the In Phase option set Next process the same data files utilizing option Out of Phase and determine once again the RMS error output The FBS result which gives the lowest RMS error residual is then selected when processing the remaining seismic data generated from the same source mechanism and captured at that site When implementing the PPD algorithm it is important that the seismogram has an unambiguous first break or source wave arrival time t as illustrated in Figure 9 The source wave arrival time is determined automatically by initially normalizing the portion of the seismogram to be processed as shown in Figure 9 and then identifying the reference time fo when the source wave exceeds amplitude 0 1 The first break or source wave arrival time t is then obtain
27. eries is obtained The implementation of the WLT is a fast and simple approach if there is minimal source wave variation within the seismogram If however significant source wave variation did occur within the seismogram then a recursive PPD approach could be utilized In that case the PPD algorithm is applied recursively to the residual seismogram until the total seismogram has been processed and the complete reflection series is estimated Wi PPD Results Seles Amplitude Time ms v Ls s T 30 go 40 45 50 55 Time ms Figure 22 Normalized estimated source wave and reflection series BSDSolver User s Manual Baziw Consulting Engineers Ltd 18 COMMERCIALLY CONFIDENTIAL BCE Ltd BSDSolver Data File Save irr B Noisy Data ap E El resula5w1 bxt er E a ST E E E 22 2010 txt My Recent El BerlageswW2_5T Result from 6m B May 22 2 Documents Type Text Document Date Modified 22 05 2010 5 40 PM E BerlagesW _ 5ST Result from 6m May 22 2 Size 35 2 KB El BerlagesW ST Result from 6m May 22 20107 7 TFreeconmdseremodramz sT Dept E Berlage5W2_5T Result May 22 2010 Ext E aE at 2 57 Dept E Berlages Ww ST txk E secondsSeismogram 2 57 Dept E FirstSeismogram 2 57 Depth Sm Yar 10 TO 0 01 Ext E secondseismogram 2 57 Dept El Firstseismogram 2 57 Depth Sm var 10 TC 0_1 Ext E secondseismogram 2 57 Dept E FirstSeismogram 2 57 Depth Sm var 20 TC 0 01 Ext E FirstSeismogram Depth 2 57 Sm txt
28. erlapping source waves Nmax 3 The minimum time separation between the reflection coefficients RT min Parameter Tmax defines the maximum possible length of the source wave from the initial start until 95 of the signal has decayed This parameter is unlikely to exceed 2 57 where T is the corresponding period of the dominant frequency of the source wave 1 e T f where f w 21 For example the finite difference source wave of Amini and Howie outlined in Figure 1 has an approximate source wave time length of 1 57 Parameter Nmax defines the maximum number of reflection coefficients within the source wave time span Nmax does not reflect the total number of reflection coefficients within the seismogram but the maximum number of reflection coefficients which can reside within the time duration of the source wave This concept is illustrated in Figure 2 where a source wave is superimposed upon a series of reflection coefficients As is illustrated in Figure 2 there are a total of 15 reflection coefficients within the seismogram that covers a 110 ms time span The source wave shown in Figure 2 has a time duration of approximately 32 ms from 10 to 42 ms and only 5 reflection coefficients reside within that time span Since it is very unlikely that there are more reflection coefficients in a source wave the default value of Nmax 18 set at 5 Amplitude O wm 0 30 40 50 60 70 80 90 100 110 Time ms Senne Source Wave Reflection Coe
29. es in a two 07_2008 11 08 0 a De 11 10 45 a 50 E scPT 22 Che dimensional vertical seismic profile Hada 08 11 16 19 a SCL ad Bor a F A E twell E E SCPT 22 Che display The VSP display pr ovides a 3 e a E CPT 22 Che i a E CPT 22 Che Depth vs Time plot where the user can es specify interval velocity trend lines for preliminary velocity estimation In addition the user can display acceleration velocity or displacement e particle motions along with the peak f Mimun ra ama ear ra ergo a A 4 ME E CPT 22 Che 2 Chartwell westfield59_0L14_07_2008 11 30 14 a_5C1 aci scpT 22 Che Chartwell Westfield510_0114_0 20085 11 55 51 a_5 1 aci E scpt 22 Che 2 Chartwell WestfieldS11_ 0114 07 2008 11 59 23 a 501 aci E scPT 22 Che artwell Westfields12 0114 07 2008 12 01 42 p 5C1 aci E scPT 22 Che My Documents 7 a SCPT 22 Chartwell WestfieldS13_0114_07 2008 12 04 55 p_5C1 aci E scPT 22 Che Ea 5c 50 50 50 SC asc Ej 50 50 E E SCPT 22 Chartwell Westfield514_0114_07_2008 12 07 10 p_SCi aci E sCPT 22 che particle accelerations velocities or a ji gt displacements respectively My Network Filename SEFT 22 Chartwell WestfieldS13_0L14_07_ y dae Files of type Cancel Figure 40 File input dialog box When the user selects VSP the file input dialog box illustrated in Figure 40 appears The user can input multiple seismic files in this dialog box ie lt SHIFT gt l
30. esults in the WLT output illustrated in Figure 27 Wi Water Level Tec hnique Sele f Reflection Coefficents C Residual Selsmogram poi 33 013 7 1 0550 Source Wave Utilized and Estimated Reflection Coefficients v Ez 2 E T BO S 100 120 140 160 130 Time ms seismogram Amplitude BO ou 100 120 140 160 Time ms Figure 27 WLT output The top chart of Figure 27 shows the estimated normalized reflection series and inputted and normalized source wave The estimated and normalized reflection series is very similar in shape to that shown in Figure 13 but there is significant energy leakage where we have a bell shaped series The bottom chart in Figure 27 illustrates the inputted seismogram which has been filtered with a 200 Hz low pas filter BSDSolver User s Manual OBaziw Consulting Engineers Ltd 24 COMMERCIALLY CONFIDENTIAL BCE Ltd BSDSolver The WLT technique can initially be implemented until a time index t is identified where the reflection coefficients change shape signifying source wave time variance 1 The PPD algorithm can then be re applied at time index t by moving the cursor in the top chart and then pressing the middle mouse button or lt ctrl gt left mouse button or lt ctrl gt right mouse button The selected time index can be cleared by double clicking the left mouse button For example the time index at 35ms is selected in Figure 28 Pressing button will result in applying the WLT algo
31. fficients Figure 2 Illustrating the concept behind parameters Tmax and N max BSDSolver User s Manual OBaziw Consulting Engineers Ltd 4 COMMERCIALLY CONFIDENTIAL BCE Ltd BSDSolver Parameter RTin allows for constraining of the PPD algorithm solution space For example the reflection coefficients Ro R R2 R3 Ry must arrive subsequently later within the time series 1 e t7 lt t2 lt t3 ty based upon the physics of reflection seismology Parameter RT in allows the investigator to set the minimum allowable time separation between the reflection coefficients The maximum resolution i e minimum RT min specification capability of the PPD algorithm is dependent upon the input parameter values such as the user specified dominant frequency analysis window and the properties of the additive measurement noise The RT pin parameter defaults to 3ms due to the fact that it is unlikely that the reflection coefficients would be time separated less than 3ms 1 and to reduce computational requirements for smaller spaced reflection coefficients As expected with smaller values of parameters Tmax and Nmax and a larger value of RTmin 1t will take less time for the program to process the seismic data The PPD program is designed to process two closely spaced seismograms simultaneously utilizing multi threading and making use of standard dual core processor technology This is done so that the solution space for estimating the source
32. grams had a source length and MCFL specified as 2 5T which equates to an approximate duration for an estimated 56 Hz dominant frequency 1 e T f 18 ms of 45 ms If we increase the MCFL value to a slightly larger value of 2 77 the new cost function length is then approximately 49 ms The seismograms shown in Figures 15 and 16 are reprocessed for this value and the results for test case outlined in Figure 15 are shown in Figure 25 As is shown in the top chart of Figure 25 a slightly greater portion of the seismogram t 2 7T 59 ms was utilized when minimizing the cost function compared to the results illustrated in Figures 19 t 2 5T 55 ms However the estimated source wave and reflection series shown in Figure 25 are very similar to those given in Figures 19 indicating that this increase in MCFL had minimal impact on the analysis outcome BSDSolver User s Manual OBaziw Consulting Engineers Ltd 19 COMMERCIALLY CONFIDENTIAL d In situ testing Electronic source trigger ion in an vehicle Hammer beam source SH wave particle mot BCE Ltd BSDSolver 2908 9 8 98 98 8 8 9 E 4 9 8 8 8 8 8 6 DI DI a at ate a a a a a a a aa at a a a a a a a a a a Source wave reflections Direct source SA 9 99 9 95 59 000 0 9 0959 a a a a a a C a C OS Push rods gt Da O a OI O A D 9 9 9 998999 9 9 999 999 9 959 A 2 90000 90 a a Oo oo Oo a a a O a a a a a a a a a Ci
33. gt P q the resulting estimated reflection coefficients become significantly bandlimited and the result converges to the Fourier transform of the cross correlation between the recorded seismogram and the source wave 1 e Z S If a check is placed within checkbox Automatic Frequency Filter Specification then the currently configured frequency filter s 1s are applied automatically on the user specified seismogram prior to deconvolving the source wave If the Automatic Frequency Filter Specification is disabled then the digital frequency filter user interface appears see Section 4 1 1 and Figure 7 when the Begin Processing button is pressed BSDSolver User s Manual OBaziw Consulting Engineers Ltd 23 COMMERCIALLY CONFIDENTIAL BCE Ltd BSDSolver Implementation 1 e placing check in checkbox of WLT option Normalize Input Output will result in the source and seismogram in 11 being normalized prior to the implementation of 11 The estimated reflection series will also be normalized This is the recommended configuration due to the fact that there can be significant energy leakage of the reflection series as previously described where the peak amplitudes of the estimated reflection coefficients are considerably reduced therefore it makes greater sense to normalized the reflection series Specifying the estimated source wave illustrated in Figures 19 21 and 22 and seismogram shown in Figure 16 with a 200 Hz low pass filter r
34. hartwell WestfieldS11_0L14_07_2008 11 59 23 a_SC1 aci 0 5 120 5 mis gt g J0 Ss 20 25 ted 36 40 5 50 997 60 69 70 75 60 Ge 98 85 100 105 119 1207129 130 135 Time ms F Legend e v1 a Figure 42 Filtered 30 to 100Hz bandpass seismic trace profile illustrating trend lines with corresponding interval velocity estimates BSDSolver User s Manual OBaziw Consulting Engineers Ltd COMMERCIALLY CONFIDENTIAL 35 BCE Ltd BSDSolver 6 0 Chart Formatting Exporting and Printing k Fi The graphical edit button bis e g Figures 19 20 amp 22 allows for chart formatting printing and exporting Figure 43 illustrates the graphical interface that appears when this button is selected which allows for extensive modification of the displayed data and chart attributes In addition the data can be printed by selecting the Print tab which brings up the Chart Printing Dialogue Box as shown in Figure 44 Finally this utility has an extensive electronic Help function which is accessed though the Help button at the bottom left of the screen Editing chtAcg Ei Seres General Axis Titles Legend Panel Paging walls 30 Figure 43 Chart Editing Dialogue Box Editing cht ca Figure 44 Chart Printing Dialogue Box BSDSolver User s Manual OBaziw Consulting Engineers Ltd 36 COMMERCIALLY CONFIDENTIAL BCE Ltd BSDSolver 7 0 Help Menu The main menu shown in Figure includes a Help
35. ient Time Offset e Enter the Maximum Cost Function Length MCLF e Set RO to Maximum The Minimum Reflection Coefficient Time Offset represents the RT min parameter previously described in Section 2 0 and as mentioned before its default value is 3ms BSDSolver User s Manual OBaziw Consulting Engineers Ltd 9 COMMERCIALLY CONFIDENTIAL BCE Ltd BSDSolver The MCFL denotes the length of the time window length for which the error residual cost function 1 e the RMS difference between the estimated seismogram and the true seismogram over time window ty source wave arrival time to tp MCFL as shown in Figure 8 is calculated It is specified as a multiple of T where T is the corresponding period of the dominant frequency of the source wave 1 e T 1 f where f w 2z and its default value is 2 57 The MCFL should never be smaller than Tmax due to the fact that we are estimating the complete source wave which has a maximum possible time length of Taa However the MCFL can exceed Tmax 1f the number of reflection coefficients within the seismogram is less than or equal to Nmax 1 e In case of a so called sparse reflection series Such a sparse reflection series would be encountered for example when carrying out a vertical seismic profile within a remediation site containing stone columns A larger value of the MCFL also allow for more time series information to be taken into account when minimizing the cost function within the PPD algorithm
36. ion A fundamental task for the seismologist is to estimate the impedance as a function of the depth from the recorded seismogram A commonly adopted simple model in applied seismology is that of a horizontally layered one dimensional earth referred to as the Goupillaud layered medium 1 Here the impedance of the kth layer is defined as Ex PV 2 where pz and V are the density and velocity in the kth layer respectively The relationship between ex and ux the reflection coefficient assuming only primary reflection of the kth layer is L Ek 1 Ek 3 Ek Ek Rearranging 3 gives 1 u k 1 u 4 at l Ly jal 1 4 Therefore it is required to estimate the reflection series uin order to determine eg This means that in extracting the reflection series the source wave must first be estimated and then deconvolved from the recorded seismogram An alternative mathematical representation of the recorded time series z t defined in 1 1s given as a t eS 1 dT vt 2 The discrete representation of 5 is given as 6 2k YN uS k 1 k k 12 N 6 i l where N is the length of the time series BSDSolver User s Manual OBaziw Consulting Engineers Ltd 2 COMMERCIALLY CONFIDENTIAL BCE Ltd BSDSolver The primary goal of seismic deconvolution is to remove the characteristics of the source wave from the recorded seismic time series so that one is ideally left with only the reflection coefficient
37. lowing excerpt from a standard BSDSolver file has the sampling rate specified as 0 05 ms followed by the depth of 5 m which is subsequently followed by the time series data 0 05 5 6 34584242695294E 0003 9 79220908943435E 0003 1 32385757519157E 0002 1 71980495395 148E 0002 Wi BSDSolver File Seismic Signal Analysis Utilities Help a pz 3 a E lt r 40 50 60 FO 80 90 100 110 120 Time ms Source Wave Seismogram Reflection Coefficients Figure 3 Main Menu in BSDSolver BSDSolver User s Manual OBaziw Consulting Engineers Ltd 7 COMMERCIALLY CONFIDENTIAL BCE Ltd BSDSolver 4 0 Seismic Signal Analysis As is illustrated in Figure 4 the Seismic Menu Analysis menu option allows the user to carry out either a Blind Seismic Deconvolution BSD for source wave and reflection series estimation or implement the water level technique WLT for reflection series estimation based upon an inputted PPD estimated source wave Selection of Main Menu option File gt Open will also result in the initiation of a BSD analysis Wl BsDSolver File FE ras Utilities Help Blind Seismic Deconwolution Water Level Technique a Ez i EL E T 5 an 40 50 60 Time ms eee Peflection Coefficients Source Wave Selsmogram Figure 4 Seismic Signal Analysis software options mex A Blind Seismic Deconvolution Specify Seismic Time Seres and Filter Parameters Seismogram
38. n checking the appropriate check box respectively For example Figure 21 illustrates only the seismogram error residual time series within the top chart User interface buttons and allow for the removal and display of all the time series respectively Y PPD Results ely e e EE PEA ESA 7 1 055 7 0 415 a aS ALA Time ms Amplitude 5 5 cn a n v T a E T 60 YO 80 90 100 110 120 130 140 150 160 170 180 190 200 210 Time ms Figure 19 BSDSolver algorithm output after processing the noisy seismograms illustrated in Figures 15 and 16 with a 200 Hz low pass filter applied BSDSolver User s Manual Baziw Consulting Engineers Ltd 16 COMMERCIALLY CONFIDENTIAL BCE Ltd BSDSolver Editing chtP1t2f Chart Series Data Tools Export Print Series General Axis Titles Legend Panel Paging walls 3D AS DAK e AAA FAST park Y Estimated Reflection Coefficients FAST park Y Seismogram Processed FAST park Y Estimated Seismogram FAST park Y Seismogram Error Residual Figure 20 BSDSolver program chart editing formatting and printing user interface EA PPD Results Amplitude _ l 25 30 Time ms T 2 O E lt r b i E oo co 40 50 60 F S Y 100 110 120 130 140 150 160 170 180 190 00 210 Time ms Figure 21 Display of seismogram error residual time series BSDSolver User s Manual OBaziw
39. nonoccnonnnnnnnononannnnnss 16 Figure 20 BSDSolver program chart editing formatting and printing user interface 17 Figure 21 Display of seismogram error residual time series occccccccncnnnnnnononinonnnncnnncncnnnnnnonnnnnos 17 Figure 22 Normalized estimated source wave and reflection SETIES oooooonnnnnnnncnnnonnnnnnnnnnnnnnss 18 Figure 23 Saving the estimated source wave reflection series and residual seismogram 19 Figure 24 Illustration of overlapping source waves when conducting a SCPT investigation within a remediation site containing stone columns ccccccccnnnoocnnnnnnnnnnononinnnnnnnononononnnnnnnnnnnnnnnnnnnos 20 Figure 25 BSDSolver algorithm output after processing the noisy seismograms illustrated in Figures 15 and 16 with a 200 Hz low pass filter applied and a MCFL parameter setting of 2 7T ee eo o ee ee 21 Fist 20 WLI main user mMer AC mi 23 Pone 2 WE OU casitas tando citosiiescabeido 24 Figure 28 Selecting the reference time within the WLT algorithm so that the resdiual So Urol A o nn tanameeurenbbiaacemusennt aehboussausasieiatteondtosgasbeieton 25 Figure 29 Residual seismogram illustrated as red time series in bottom chaft c cesses 26 Preure 50 Utilities SOMW are OU ONS sicsss canscteaennceonciidneteasuivadsasdeaateadnaccdestianctecievaiesstaacteatenccmesbeenets 27 Pouc le Sensor Doed or DOK seee E E E A 27 BSDSolver User s Manual OBaziw Consulting Engineers Ltd 11
40. nts E 5 10 15 20 25 30 35 40 45 50 55 60 65 ZO 80 85 30 95 400 105 110 115 420 Figure 12 The output after convolving Berlage wave of Figure 10 with reflection coefficients illustrated in Figure 11 1 0 8 0 6 04 3 02 30 a 0 2 0 4 0 6 0 8 1 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 8 90 95 100 105 110 115 120 Time ms Figure 13 Seismogram 2 reflection coefficients E E lt o 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 Time ms Figure 14 The output after convolving Berlage wave of Figure 10 with reflection coefficients illustrated in Figure 13 TM BSDSolver User s Manual OBaziw Consulting Engineers Ltd 13 COMMERCIALLY CONFIDENTIAL BCE Ltd BSDSolver TABLE I REFLECTION SERIES PARAMETERS Reflection Coefficients Reflection Coefficients Amplitude Amplitude 0 45 2 0625 25 06 As is evident from Figures 11 and 13 and Table I the reflection series for seismograms 1 and 2 are very similar which would be the case where we have recorded seismic traces from two relatively closely spaced receivers Although there are minor variations between the reflection series of seismograms 1 and 2 the resulting seismograms have significant differences as illustrated in Figures 12 and 14 To these synthetic seismograms a Gauss Markov measurement noise was added with a variance and time constant set to 10 units s and 0 01 ms respectively and the outc
41. ome is shown in Figures 15 and 16 Amplitude m s2 o 40 45 50 55 60 65 70 75 50 55 90 95 100 105 110 115 120 Time ms O 5 10 15 20 25 30 35 Figure 15 Seismogram of Figure 12 with additive Gauss Markov measurement noise Amplitude m s2 0 5 10 15 20 2 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 Time ms Figure 16 Seismogram of Figurel4 with additive Gauss Markov measurement noise These seismograms are stored in data files firstSeismogram 2 5T Depth 5m Var 10 TC 0_01 txt and secondSeismogram 2 5T Depth 6m Var 10 TC 0_01 txt respectively and pre processed with a 200 Hz low pass zero phase digital filter as illustrated in Figure 17 The filtered seismograms are then fed into the PPD algorithm with parameters fmin fmax and RT min Set BSDSolver User s Manual OBaziw Consulting Engineers Ltd 14 COMMERCIALLY CONFIDENTIAL BCE Ltd BSDSolver to 45 Hz 60Hz and 3 ms respectively In addition the parameters MCEL Tmax i and MRR are set to 2 5 2 5 1 2 and 0 9 respectively The FSB parameter is set to In Phase and Set RO to Maximum is enabled The parameter settings are illustrated in Figure 18 These settings were selected for the following reasons Wi Filter Parameter Specification i Enabled Low Pass Frequency Hz 200 e The source bandwidth specification of 45 Hz to 60 Hz was based upon experience and the frequency spectra sure 17 Specifying a 200 Low Pass of the
42. option that includes the following About provides software version information on BSDSolver User s Manual will output the BSDSolver user s manual in a default pdf browser Appendix 1 will output the paper entitled Incorporation of Iterative Forward Modeling into the Principle Phase Decomposition Algorithm for Accurate Source Wave and Reflection Series Estimation in a default pdf browser Appendix 2 will output the paper entitled Implementation of the Principle Phase Decomposition Algorithm in a default pdf browser Appendix 3 will output the paper entitled Principle Phase Decomposition A New Concept in Blind Seismic Deconvolution in a default pdf browser BSDSolver User s Manual OBaziw Consulting Engineers Ltd 37 COMMERCIALLY CONFIDENTIAL BCE Ltd BSDSolver References 1 Baziw E Incorporation of Iterative Forward Modeling into the Principle Phase Decomposition Algorithm for Accurate Source Wave and Reflection Series Estimation to be published in the IEEE Transactions on Geosci Remote Sensing 2010 2 Baziw E Implementation of the Principle Phase Decomposition Algorithm IEEE Transactions on Geoscience and Remote Sensing TGRS vol 45 No 6 pp 1775 1785 June 2007 3 Baziw E and Ulrych T J Principle Phase Decomposition A New Concept in Blind Seismic Deconvolution IEEE Transactions on Geoscience and Remote Sensing TGRS vol 44 No 8 pp 2271 2281 A
43. raphical interface in View Seismogram software option Figure 33 illustrates the graphical results after specifying a low pass filter of 200 Hz The user may then overlay the unfiltered seismic trace onto the filtered trace by selecting checkbox Overlay as illustrated in Figure 34 The smoothed Fast Fourier Transform FFT of either the unfiltered or filtered seismic trace is derived and displayed by selecting checkbox FFT The frequency spectrum of the filtered trace is displayed if the checkbox Filter is selected along with the FFT checkbox Otherwise the unfiltered seismic trace s frequency spectrum is displayed Figure 35 illustrates the frequency spectrum of the unfiltered data file illustrated in Figure 32 Figure 36 shows the dominant frequency window 45Hz to 60Hz for the frequency spectrum illustrated in Figure 35 This portion of the frequency spectrum was selected by pressing the right mouse button and panning left to right with the mouse The user can zoom out to the original display by pressing the right mouse button and panning right to left with the mouse BSDSolver User s Manual OBaziw Consulting Engineers Ltd 28 COMMERCIALLY CONFIDENTIAL BCE Ltd BSDSolver Selection of user interface button facilitates the user to read in a new data file Button allows the user to re filter the seismogram by redisplaying the Filter Parameter Specification user interface shown in Figure 7 Buttons and Melisfacilitate the user in saving the cu
44. re at most 2 257 This means that min If fmin 50 Hz then Amin 66 665 sec or 0 066665 ms Ma 3 2 25T yay 1 333 f Although a default value for RT nin of 3ms values have been specified it is the intention of BCE ltd to explore and quantified this issue further BSDSolver User s Manual OBaziw Consulting Engineers Ltd 5 COMMERCIALLY CONFIDENTIAL BCE Ltd BSDSolver Maximum attenuation value Based on analytical source wave representations and numerous real data examples it can be assumed that the time for the source wave to decay to 5 of AMTyax is at least 0 57 This means that ae 7 3 0 5T nin OF ane If fmax 60 Hz then Ing 360 sec or 0 36 ms BSDSolver User s Manual OBaziw Consulting Engineers Ltd 6 COMMERCIALLY CONFIDENTIAL BCE Ltd BSDSolver 3 0 Main Menu The main menu of BSDSolver as illustrated in Figure 3 has four options e File e Seismic Signal Analysis e Utilities e Help The desired submenu is chosen either by moving the mouse over the desired option and pressing the left hand mouse button by pressing function lt F10 gt on the keyboard and selecting the desired highlighted option or by pressing the corresponding menu item letter on the keyboard The seismograms processed by the PPD program are required to be in ASCII format with the sample rate in ms and depth at which the trace was acquired in m in the header followed by the time series data For example the fol
45. red to process the seismograms Source wave input parameters of Max Length Max Peak Maximum Relative Ratio and First Break Specification are illustrated in Figure 9 o eee Tmax 2 5 T Amplitude T max E MRR AAi 25 30 35 Time ms Figure 9 Source wave input parameters The Maximum Possible Length Tmax 18 specified as a multiple of T and the default setting is 2 57 Parameter im denotes the maximum possible time location of the maximum peak of the source wave from t as is shown in Figure 9 It is specified as a multiple of T and the default setting is 2T It should be noted that seismic source waves are not maximum phase i e energy concentrated at end of source wave therefore it would not be expected that the source wave would peak near the end of its time window The parameter Maximum Relative Ratio MRR is illustrated in Figure 8 The MRR parameter allows the user to specify a minimal decay of the source wave when moving from the maximum peak A in Figure 9 to the next peak A2 in Figure 9 at a O S5T time offset It is expected that the source wave decays from the maximum peak and parameter MRR allows the investigator to specify a minimum decay ratio a priori The MRR parameter default value is set to 0 9 The First Break Specification FBS has two possible settings e In Phase e Out of Phase As previously illustrated in Figure 1 togse is the offset time from the arrival time of the source wave to wh
46. rithm from t 0 tot t with the inputted source wave and subsequently deriving the residual seismogram as 1s illustrated in Figure 29 The PPD algorithm can then be applied to the residual seismogram Wi Water Level Technique f Reflection Coefficents C Residual Seismogram El 35 014 Z 0 3173 Source Wave Utilized and Estimated Reflection Coefficients v T a 2 E T 50 100 120 Time ms Selsmoagram A Ahaio oo ij a RUA Ac ieee cat Amplitude S 100 120 140 160 150 Time ms Figure 28 Selecting the reference time within the WLT algorithm so that the resdiual seismogram is derived BSDSolver User s Manual OBaziw Consulting Engineers Ltd 25 COMMERCIALLY CONFIDENTIAL BCE Ltd BSDSolver Wi Water Level Technique fe Reflection Coefficents C Residual Seismogram a 205 750 0 0943 Source Wave Utilized and Estimated Reflection Coefficients Afi feo 4 v gz q a E T BO aa 100 120 140 160 Time ms Seismogram Amplitude Time ms Figure 29 Residual seismogram illustrated as red time series in bottom chart 1ate radio The estimated reflection series and residual seismogram can be saved by selecting the appropr AS The button Reflection Coefficients and Residual Seismogram respectively and pressing button user is then instructed to specify the file name and directory as was illustrated in Figure 23 BSDSolver User s Manual OBaziw Consulting Engineers Ltd 26 COMMERCIA
47. rrently configured chart settings and loading previously configured chart settings respectively A Seismic Data EN B Filet Overlay I FFT 87 980 33 200 Aft A t ehit to where t gt to to inttial decay time and h decay factor Initial Decay Time mej 2 0 Decay Factor 1m 10 5 if Front End Decay Vv el EB Data File CWJOBSIPPO VVEiMutichannel 2010 _ 57 DataiDataiNoisy DataisecondSeiamagram 2 57 Depth Gm var 10 TC 0201 txt Ol La E a a E T g0 100 110 120 130 140 150 160 170 180 190 200 Time ms Figure 33 Filtered seismic trace in View Seismic in software option View Seismogram E Seismic Data Si B M Filter ie yea M FFT 94 003 32 700 Aft A t e lt to Where t gt to to mitial decay time and h decay factor Initial Decay Time mz 2 0 Decay Factor 1 ma 05 if Front End Decay y Eal Data File 0 JOBS PPPOE Mutichannel 20102_5T DataDataWNoisy DatasecondSeismogram 2 57 Depth 6m ar 10 TE 0_01 txt Amplitude m s2 45 50 Time ms Figure 34 Overlaying unfiltered seismic trace onto filtered seismic trace illustrated in Figure 31 BSDSolver User s Manual OBaziw Consulting Engineers Ltd 29 COMMERCIALLY CONFIDENTIAL BCE Ltd BSDSolver W Seismic Data AE ES Bl I Filter M vela 4 FFT 4666 730 0 086 AH At eh t to where t gt to to inital decay time and h decay factor Initial Decay Time m 2 0 Decay Factor 17m 105 e Front End Decay v
48. s These coefficients identify and quantify the impedance mismatches between different geological layers that are of great interest to the geophysicist A very challenging and yet common seismic deconvolution problem is where the source wave is unknown This is referred to as blind seismic deconvolution BSD the situation where we have one known measured seismogram with additive noise and two unknowns source wave and reflection coefficients In the PPD algorithm an innovative model of the source wave is utilized This source wave model is referred to as the amplitude modulated sinusoid AMS 1 2 and 3 The AMS is demonstrated to be a highly robust and accurate approximation for many analytical representations of seismic source waves such as the exponentially decaying cyclic waveform the mixed phase Berlage wave the zero phase Ricker wave and the zero phase Klauder wave In addition the AMS wave has proven to be very accurate in modeling seismic data acquired during passive seismic monitoring and vertical seismic profiling The mathematical representation of the AMS source wave is given as x t x t sin t o 7 where x t is an approximation to the seismic source wave x2 t is the seismic waves amplitude modulating term AMT is the dominant frequency of the wave and is the corresponding phase Amini and Howie 4 and 5 utilized a finite difference program FLAC to model downhole seismic source waves Fig
49. seismogram utilizing BSDSolver option Filter Utilities gt View Seismogram as outlined in Section 5 2 LEMA and Fi gures 35 and 36 Specify Seismic Time Series and Filter Parameters gt T max was set to the default value of 2 31 due to the fact Seismogram 1 C JOBSSBSDSolver 2_5T Data Data Noisy Data firstS eismo that we have no a pr iori information on the time KY Seismogram 2 C JOBS BSDSolvert2_ST Data Data Noisy Data secondSei length of the source wave and source waves do not general exceed time lengths of 2 5T O A e MCFL was set to the default value of 2 5T due to the Source Wave Parameters Bandwidth Minimum Hz 140 Max Length n T 2 5 Max Peak n T 11 2 fact that there is no reason to assume that we are dealing with a sparse reflection series o e was set to 1 2T based upon experience and the fact the source waves tend to be minimum and mixed phase e Parameter MRR is set to the default value of 0 9 due to the fact that we would expect some decay moving from the maximum peak to the next peak o Maximum Hz First Break Specification Maximum Relative Ratio 10 9 C Out of Phase e In Phase X spot fico y ito yf j of r Paes N bel Figure 18 BSDSolver Parameter Settings Once the input parameters have been specified the Begin Processing push button is selected The output from the PPD algorithm is shown in Figure 19 The top chart of Figure 19 shows the normalized estimated sourc
50. to the denominator which is referred to as the water level A Implementation of these two modifications to 10 gives poj Z2S 0 _ Z 8 11 S O S M A Ps A where Py denotes the power spectrum of the source wave 1 e the Fourier transform of the autocorrelation of S t In general terms the setting of the water level is a trial and error approach ASsA gt 0 the resulting estimated reflection coefficients approach Dirac delta functions When A gt gt P q the resulting estimated reflection coefficients become significantly bandlimited and the result converges to the Fourier transform of the cross correlation between the recorded seismogram and the source wave 1 e Z S BSDSolver User s Manual OBaziw Consulting Engineers Ltd 22 COMMERCIALLY CONFIDENTIAL BCE Ltd BSDSolver 4 2 1 WLT Implementation A Water Level Technique Specity Data Files and WLT Filter Parameters The main user interface for the WLT is shown in Figure 26 The first step in implementing the WELT Scalar 0 0002 WLT is to specify the source wave and seismogram file by selecting Bl When button is selected the file input user interface is displayed see Figure 6 where the user is requested to input the source wave file Hf Close first and then the seismogram file As outlined 0 in Figure 24 the WLT parameters required for user input are popa Edd Figure 26 WLT main user interface W Normalize Input Output e WLT
51. ug 2006 4 Amini A and J A Howie T J Numerical simulation of downhole seismic cone signals Canadian Geotechnical Journal vol 42 2 pp 574 586 2005 5 E Baziw State space seismic cone minimum variance deconvolution In Proceedings of the 2nd International Conference on Geotechnical Site Characterization ISC 2 vol 1 pp 835 843 Porto Portugal Millpress Science Publishers 2004 BSDSolver User s Manual OBaziw Consulting Engineers Ltd 38 COMMERCIALLY CONFIDENTIAL
52. ure illustrates the simulated source wave generated by Amini and Howie obtained by personal communication This source wave was generated by assuming a uniform halfspace with an in situ shear wave velocity of 180 m s and a sampling interval of 0 02 ms Superimposed upon this finite difference source wave is a scaled 140 Hz sinusoid with zero crossing at 10 3 ms as well as an exponential decay peaking at 15 ms and decaying at an exponential rate of 0 8 ms tOffset Amplitude m s2 O 5 10 15 20 25 30 35 Time ms Finite Difference Source Wave Exponential Decay 140 Hz Sinusoid Figure 1 Finite difference source wave with superimposed 140 Hz sinusoid and exponential decay with rate 0 8 ms BSDSolver User s Manual OBaziw Consulting Engineers Ltd 3 COMMERCIALLY CONFIDENTIAL BCE Ltd BSDSolver The three parameters that define the AMS source wave can then be described as follows w the source wave s dominant frequency togser the offset time from the arrival time of the source wave t to the start of the sinusoidal component This parameter is inherently related to the phase y due to the fact that the arrival time of the source wave fg is readily obtained from the seismogram h the exponential decay rate of the source wave Before implementation of the PPD algorithm there are three main parameters that must be specified 1 The maximum possible length of the source wave Tmax 2 The maximum number of possible ov
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