IMPROVEMENT OF DATA INTERPRETATION METHOD FOR DOWNHOLE SEISMIC METHOD

4 th Internatonal Conference on Earthquake Geotechncal Engneerng June -8, 7 Paper No. 8 IMPROEMENT OF DATA INTERPRETATION METHOD FOR DOWNHOLE SEISMIC METHOD Eun-Seok Bang, Dong-Soo Km ABSTRACT Mean refracted ray path method (MRM) whch s combned the advantage of drect method and refracted ray path method s proposed. It can provde reasonable S profle automatcally consderng travel tme measurement error. The overall procedure of MRM s smlar to the drect method. However, corrected travel tme data s based on the result of refracted ray path method for consderng refracted ray path and the R value of regresson curve s employed for automaton. Accordng to the R value, sol model s constructed and S value of each layer s evaluated from the slope of regresson curve at each dvded layer automatcally by programmed routne. The relablty and applcablty of the proposed method was verfed by usng numercal and feld study. Keywords: downhole sesmc method, nterpretaton method, shear wave velocty, ste nvestgaton INTRODUCTION The shear wave velocty ( S ) profle s very mportant geotechncal parameter n practce. In addton to dynamc problems, the S value has also been used for statc problems (Stokoe et al., 4). For these reasons, the demand for obtanng relable and detaled S profle s rapdly ncreasng n the feld of geotechncal engneerng. The downhole sesmc method s very attractve because ths method requres just one bore-hole to perform the test and uses a smple surface source. Drect method (DM) has been wdely used to determne general S profle, but ths method provdes mean S value of each roughly dvded layer. Recently, the demand for evaluatng detaled S profle of a ste s ncreasng for geotechncal applcatons, and nterval method (IM), modfed nterval method (MIM) and refracted ray path method (RRM) have been ntroduced (Km et al., 4). It has been known that the refracted ray path method provdes the most relable S profle for downhole sesmc test. However, the S profle determned by RRM shows some meanngless repettve fluctuatons wth depth when some errors are ncluded n the estmated travel tme data. Estmatng the frst arrval pont of shear wave on sgnal traces s very dffcult. Therefore, the obtaned travel tme data are sometmes naccurate and s forced to determne erroneous S profle. In ths study, a new method whch combnes the advantages of drect method and refracted ray path method s proposed to reduce downhole sesmc data more relably. The proposed method can provde detaled S profle automatcally consderng errors n the travel tme measurement. Ths proposed method was verfed by usng synthetc travel tme data that were generated by forward modelng consderng refracted ray path and by addng some errors to smulate the dffcultes n travel tme measurements. Fnte element modelng was also performed to smulate and generate synthetc sgnals n the downhole test. The S profle determned by proposed method was compared wth the model Senor Researcher, Geotechncal Engneerng Dvson, Korea Insttute of Geoscence and Mneral Resources, Korea, Emal: esbang@kgam.re.kr Professor, Department of Cvl & Envronmental Engneerng, Korea Advanced Insttute of Scence and Technology, Korea, Emal: dskm@kast.ac.kr

values together wth the results of other conventonal data reducton methods. Fnally, the proposed method was appled to the data reducton of several feld test data and the applcablty and relablty were assessed by comparng the estmated S profle wth SPT-N value, CPT profle, and drllng log. CONENTIONAL DOWNHOLE INTERPRETATION METHODS There are two categores n downhole nterpretaton methods. One s determnng the general S profle by obtanng mean S value of each dvded sol layer n the constructed sol model. The other s determnng S profle n detal at every testng nterval. The former s drect method and nverson method and the latter s nterval method, modfed nterval method and refracted ray path method. The drect method s most wdely used downhole nterpretaton method n Korea. The frst arrval tme of an elastc wave from the source to a recever at each testng depth can be obtaned from the feld test. The measured travel tme (t) n the nclned path can be corrected to the travel tme, t C, n the vertcal. By plottng the corrected travel tme versus depth, the velocty of each layer can be obtaned from the slope of the fttng curve usng the data ponts whch have smlar trend (Mok, 987). In nterval method, the wave velocty of a layer between two recevers or successve testng depths s obtaned by dvdng the travel dstance dfference by the travel tme delay (Campanella and Stewart, 99). In the modfed nterval method, t s assumed that the ste s composed of stacks of horzontal layers dvded as each testng nterval and the elastc wave (shear wave n ths study) propagates ts own velocty on each dvded layers as shown n Fgure. The passage length of elastc wave on each layer s determned usng Eq. and the wave velocty at each testng layer s determned usng Eq. (Batsla, 99). L R j = Z () j D = T L j= L j j () where s the wave velocty of th layer, D,l s th testng depth of lower recever, DT s travel tme delay between the upper and lower recevers, T s travel tme at th testng depth, and L j s the length of ray-path on j th layer of th testng at the lower recever and Z j s the thckness of j th layer. S Source Plank S Source Plank L,u L,l S Z θ,u L,u θ,l L,l S Z L,u L,l S Z L,u θ,l θ,u L,l S Z D,u D,u D,l D,l R,u L (-),u L (-),l S - Z - L (-),u θ (-),u θ (-),l L (-),l S- Z - L,l S Z θ,l L,l S Z Recever R,l Recever SN- Z N- SN- Z N- S N Fgure The schematc dagram of modfed nterval method, refracted ray path method. S N In refracted ray path method, t s assumed that the wave propagates along a refracted ray path based on Snell s law as shown n Fgure and the followng relatons (Eq. 3 and Eq. 4) should be satsfed. The evaluaton process s manly same as modfed nterval method but the passage length of

each layer s determned by consderng refracted ray-path and Eq. s appled nstead of Eq.. Ths method requres the teraton process as the velocty of th layer should be assumed for determnng refracted ray path n usng Eq. 3 (Km et al., 4). snθ snθ snθ snθ j = = = = = (3) j + + Z j tanθj + + Z tanθ = Z tanθ S (4) L = / cosθ () j Z j j wherej s ncdent angle from j th layer to next layer of th ray path, and S s the dstance from the source to the borehole. COMPARISONS OF S PROFILES DETERMINED BY ARIOUS INTERPRETATION METHODS USING TRAEL TIME DATA WITH ADDED ERRORS In practce, t s very dffcult to estmate the exact frst arrval pont of shear wave on sgnal traces and some errors are ncluded. In order to examne ths problem properly, comparson study on varous downhole nterpretaton methods was performed on condton of havng errors n travel tme measurement. The source offset s 3m and the fnal testng depth s 3m wth m testng nterval. Theoretcal travel tme data were generated to the.ms unt by forward modelng consderng refracted ray path and some travel tme errors were added to them. Errors were generated automatcally usng random functon wthn fxed lmtaton and dfferent errors could be added to the theoretcal travel tme at each testng depth. The fxed lmtatons n ths comparson work were ±.ms, ±.ms, ±.ms, ±.3ms, ±.ms, and ±.ms. In case no error s added, the refracted ray path method provdes exact S value, but t provded meanngless repettve fluctuaton S value wth depth as ncreasng the errors. When the added error s hgher than ±.ms, t provdes dssmlar results to the model as shown n Fgure. From ths parametrc study, t can be found that we should measure travel tme exactly wthn the maxmum error of.ms unt to determne relable S profle when usng refracted ray path method. As decreasng testng nterval and ncreasng S value, the lmtng error wll be more rgorous. Drect method has been usefully appled when the condton of acqured sgnals (sgnal to nose rato) s not good and the measured travel tme s erroneous. It can adjust the error n travel tme measurement by obtanng mean value at the dvded nterval. However, t s dffcult to dscrmnate layer boundary relably except the case of S value changes abruptly and the S profle can be determned by the subjectvty of the nterpreter. Then, S profles determned by four nterpreters can be dfferent as shown n Fgure. Addtonally, drect method overestmated the second layer because t consders just straght ray path. MEAN REFRACTED RAY PATH METHOD From the comparatve study, t was found that there s no perfect nterpretaton method n the case of added errors n travel tme measurement, and t s also very dffcult to montor the travel tme wthout error n the feld. However, the sutable modelng of S profle s nterpreter's duty even though the data to nterpret s somewhat problematc. In ths paper, mean refracted ray path method (MRM) s proposed to obtan relable and effectve S proflng n downhole sesmc test. Ths method combnes the advantages of drect method and refracted ray path method and t can provde S profle automatcally consderng errors n travel tme measurement.

The overall procedure of propose method s smlar to the drect method. After correctng measured travel tme data for source offset, the sol layer s dvded and S value of each layer s calculated. When correctng source offset effect, proposed method uses the result of the refracted ray path method nstead of usng smple correcton as n drect method. Corrected travel tme of th layer, t c, s represented as Eq. 6. Refracted ray path method provdes S value at each testng nterval consderng refracted ray path. Procedure of correctng travel tme usng Eq. 6 s more relable than that of drect method whch consders just straght ray path. Z Z Z t c = + + + (6) Where s wave velocty of th layer determned by refracted ray path method, Z s the thckness of th layer or testng nterval. 4 6 4 6 3 3 IM MIM RRM 3 3 DM # DM # DM #3 DM #4 Fgure Comparng S profles usng synthetc travel tmes added maxmum.ms errors determned by: nterval method, modfed nterval method and refracted ray path method, drect method. Fgure 3 shows the comparson of corrected travel tmes calculated by drect and proposed methods and determned S profles were also ncluded. The model used for ths comparson work s threelayered model whose layer thckness s m and velocty of each layer s m/s, 6m/s and m/s, respectvely. Source offset s 3m and testng nterval s m. The theoretcal travel tme s calculated by forward modelng based on Snell s law. The wave velocty of each layer s determned by fttng process of seres of travel tme data whch has smlar slant. Calculated S value at each layer s nserted wth related R value f layer boundares are equally dvded wth the model n Fgure 3. The R value means the smlarty of grouped data. The wrtten n the left s for the drect method and the wrtten n the rght s for the proposed method. In these methods, t s very mportant that corrected travel tmes wth depth show same slant n a layer for the relable data nterpretaton. In the frst layer, the corrected travel tme data and calculated S value are all concdent n both drect and proposed methods because there s only one homogeneous layer from source to recevers. In the second layer, the corrected travel tmes for drect method show somewhat dfferent trend even havng same velocty n a layer and ths makes t dffcult to dvde layer boundary exactly as shown n Fgure 3. Though the boundary of layer s dvded exactly, the R value s very small as.9 and calculated S s 68.m/s (DM #3). In the thrd layer, the trend of corrected travel tmes for drect method are smlar and related R value s.9967, but the calculated S value of the thrd layer s 66.3m/s whch s much smaller than the model value. Ths problem s caused by consderng just straght ray path. On the other hand, the corrected travel tmes for mean refracted ray path method

show exactly same slant n each layer as related R value s one and the calculated S values are concdent wth the model values. Ths model study shows the superorty of source offset correcton process n ths proposed method.... Corrected Travel Tme (ms) 7 DM#3 S =m/s R = S =68.4m/s R =.9 MR M S =m/s R = S =6m/s R =... 7.. DM # DM # DM #3 MRM. For DM For MRM S =66.3m/s R =.9967 S =m/s R = Fgure 3 Comparson of the drect method (DM) and the proposed method (MRM) usng synthetc travel tme: corrected travel tme and calculated S value ncludng related R value n each layer, The determned S profles. It s desrable that nterpretaton method s automated for excludng nterpreter s subjecton. In the proposed method, automatc data groupng procedure usng R value of regresson curve s employed. Accordng to the R value, boundares of layer are determned and S value of each layer s evaluated from the slope of regresson curve at each dvded layer automatcally by programmed routne. In the case of the model n Fgure 3, the model s dvded three layers wth R value of one and S value of each layer s calculated automatcally. In the case of some errors are added to the travel tme data, f R value for layer dvson s set to one, the model wll be dvded more than three layers and S values wll be calculated wth some errors. In order to dvde model as three layers and calculate correspondng S value consderng added error automatcally for obtanng the most smlar S profle to the model, R value should be below one. Namely, accordng to the specfed R value, the S profle can be evaluated consderng errors n the travel tme measurements n the proposed method. All of the proposed procedures were programmed by MATLAB, and nput values are measured travel tme data from feld test and the specfed R value. Ths automaton scheme s not adequate for the drect method because the corrected travel tmes nclude the wrong correcton effect for source offset usng straght ray path as dscussed n Fgure 3. If the specfed R value s near, the detaled S profle wll be determned because the data wll be grouped only whose slants are very smlar. But correcton effect of errors n travel tme measurement wll be not promnent. On other hand, f the specfed R value s far below, the correcton effect s promnent, but the determned S profle wll be rough. Therefore, the R value should be specfed accordng to the accuracy of measured travel tme data and the need for subdvson. As ncreasng S value and the added travel tme error, the R value for recognzng the travel tme data as one layer becomes smaller. In Table, the recommended R values are tabulated accordng to the S value and added error n the case of testng nterval of m. The R values n Table were calculated though the parametrc study usng synthetc travel tme ncludng errors. Usually, accuracy of travel tme measurement s hgh at the shallow depth because the S value of sol s generally small and S/N rato s hgh. As the testng depth ncreases, the S value of sol wll be larger and S/N rato becomes lower. Therefore, the R value whch s reference value for dvdng sol layers needs to be specfed dfferently at the upper and lower layers of the profle...

Table The R value accordng to the model S value and magntude of travel tme measurement error (testng nterval s m). model s value lmtaton of added travel tme measurement error (ms) ±. ±. ±. ±. ±..99999.99998.9999.9998.9994 4.99999.9999.99964.9976.997 6.99999.99986.9987.99348.988 8.99999.99978.99836.9893.9849.99999.9999.9938.976.96 * R alues were calculated though parametrc study usng synthetc travel tme ncludng travel tme measurement error. ERIFICATION OF MEAN REFRACTED RAY PATH METHOD Synthetc travel tme data dscussed prevously n Fgure were used for the verfcaton of proposed method and coded program. Fgure 4 shows the S profles determned by mean refracted ray path method. The nput R values were specfed by referrng to the Table. In case of usng exact travel tme, the determned S profle s concdent wth the model. In the case of added errors lower than ±.ms, the result s nearly concdent wth the model. By comparng wth the results determned by conventonal methods shown n Fgure, t s clearly notced that proposed method s far superor to the conventonal methods. Proposed method s desgned to obtan relable S profle by consderng errors n travel tme measurement adequately. However, t cannot be dstngushed when the varatons of S value n the model s too small to be corrected. Also, n case the added error s above ±.3ms, the layer boundares and S value of each layer are not adequately determned compared to the model as shown n Fgure 4, because the proposed method cannot overcome bg errors n travel tme measurements. However, t can be mentoned that the result determned by proposed method s more relable compared to the result determned by conventonal reflected ray path method whch provdes meanngless fluctuaton of S values when error s ncluded. 3 4 6 3 4 6 3 3 MRM_.ms MRM_.error MRM_.error MRM_.error 3 3 MRM_.3error MRM_.error MRM_.error Fgure 4 The S profles determned by proposed method usng varous synthetc travel tmes: the case of added error s relatvely small (±.ms, ±.ms, and ±.ms), the case of added error s relatvely large (±.3ms, ±.ms, and ±.ms). NUMERICAL SIMULATION OF DOWNHOLE SEISMIC METHOD

To understand the effect of errors n feld travel tme measurement and to verfy the applcablty of the proposed method, a numercal modelng of downhole sesmc test was performed usng the fnte element method (FEM). The three-layered model that has dfferent S values at each layer was desgned. The sze of model s 3m*m*m (W*L*H). An eght-node element (C3D8) wth an nfnte element (CIN3D8) was mplemented. The form of each element s cubc and the sze of each sde s.m. The nterval of testng depth s.m and source offset s 3m. The calculaton step and record length were determned as.msec and msec, respectvely. From ths numercal smulaton, rght and left strkng sgnal were acqured wth depth as shown n Fgure and the estmated frst arrval ponts were ndcated by downward arrow. The S profles determned by conventonal methods such as nterval, modfed nterval and refracted ray path methods are compared as shown n Fgure. Whle the result of refracted ray path method have smlar trend wth the model, the result of nterval and modfed nterval method do not match well wth the model. However, the S profle determned by refracted ray path method shows the fluctuaton n a layer because of the errors n the travel tme measurement. Real feld data has also the possblty of havng more errors n travel tme measurement because the sgnal to nose rato s generally lower than synthetc waveform from numercal study. Therefore, t s consdered that the refracted ray path method can cause some problems n nterpretaton of downhole data. On other hand, proposed method dvdes three layers exactly and provdes mean S value well. The result matched well wth the model as shown n Fgure (c). Testng Depth.m.m.m.m.m 3.m 3.m 4.m 4.m.m.m 6.m 6.m 7.m 7.m 8.m 8.m 9.m 4 Travel Tme (ms) 3 4 6 7 8 9 3 6 9 IM MIM RRM 3 4 6 7 8 9 3 6 9 (c) Fgure The S profles determned by varous downhole nterpretaton methods wth the model based on the fnte element modelng: the synthetc sgnal traces the results of nterval method (IM), modfed nterval method (MIM) and refracted ray path method (RRM), (c) the results of drect method (DM) and proposed method (MRM). DM # DM # MRM FIELD CASE STUDIES Downhole sesmc method was performed at rver sde ste n Kyeongju, Korea. Based on SPT N values, the stffness of sol decreases slowly wth depth up to 9.m and the notceably stffness ncrease occurs at depths of about 8 to m as shown n the rght sde of Fgure 6. The shear wave velocty profles determned by varous reducton methods are plotted n the left sde of Fgure 6. The refracted ray-path method provded the relable results followng the stffness trends expected by SPT-N values. To obtan mean S profle, drect method and proposed method were appled. Fourlayered model was constructed at both methods and the layer boundares were nearly concdent wth the drllng log. However, the calculated S values are somewhat dfferent between them because the ray path assumpton of each method s dfferent. From ths case study, t was found that consderng refracted ray path s very mportant and the mean reflected ray path method has the possblty of provdng most relable results.

To evaluate the consoldaton effect on soft clay, downhole sesmc method was performed at soft clay ste n Jnhae, Korea (Fgure 6). The detaled S profle was requred for evaluatng local consoldaton condton of soft clay n ths ste. In the refracted ray path method, meanngless fluctuaton was shown and t was caused by travel tme measurement error. For correctng ths error, the drect method and the mean refracted ray path method were appled. In drect method, the sol model was dvded nto just four layers and the determned S profle s so rough. It was not adequate to evaluate the local consoldaton condton of soft clay. In the propose method, the relatvely detaled S profle can be evaluated. The local consoldaton condton of soft clay can be guessed from the obtaned S profle. Shear Wave elocty(m/s) 3 6 9 Tp Resstance (kpa) 3 3 4 IM MIM RRM DM MRM Depth(m) 6 3 3 8 4 4 RRM DM MRM 6 6 Fgure 6 The results of downhole sesmc method: rver sde ste, soft clay ste. CPT CPT* CONCLUSIONS Mean refracted ray path method (MRM) whch combnes the advantages of drect method and refracted ray path method was proposed. It can provde relable S profle automatcally wth consderaton of travel tme error. The travel tme data s corrected based on the refracted ray path and the R value of regresson curve s employed for automaton. When the estmated travel tme data was somewhat naccurate, meanngless repettve fluctuatons were shown n the S profle determned by the conventonal methods. On the other hand, MRM provded the most relable S profles. From numercal and feld case studes, the relablty and applcablty of the proposed method was verfed. AKNOWLEDGEMENTS Ths study was supported by a fund of the Constructon Research and Development Program (4 constructon kernel B-4) contrbuted by the Mnstry of Constructon and Transportaton (MOCT). It s gratefully acknowledged. REFERENCES Batsla, E. Investgaton of Ray Path Assumpton on Downhole elocty Profle, Master Thess, The department of cvl engneerng, The Unversty of Texas at Austn 99. Campanella RG and Stewart WP. Sesmc cone analyss usng dgtal sgnal processng for dynamc ste characterzaton. Canadan Geotechncal Journal, 9, 477-486, 99.

Km DS, Bang ES and Km WC. Evaluaton of varous downhole data reducton methods to obtan relable s profle, Geotechncal Testng Journal, 7(6): 8-97, 4 Mok YJ. Analytcal and Expermental Studes of Borehole Sesmc Methods, Ph.D. Dssertaton, The department of cvl engneerng, The Unversty of Texas at Austn 987. Stokoe KH, Joh SH and Woods RD. Some contrbutons of n stu geophyscal measure-ments to solvng geotechncal engneerng problems. Internatonal Ste Characterzaton ISC Porto, Portugal, 9-4, 4.