Estimating V s(30) (or NEHRP Site Classes) from Shallow Velocity Models (Depths 30 m)

Transcription

1 Bulletin of the Seimological Society of America, Vol. 94, No. 2, pp , April 4 Etimating V () (or NEHRP Site Clae) from Shallow Velocity Model (Depth m) by David M. Boore Abtract The average velocity to m [V ()] i a widely ued parameter for claifying ite to predict their potential to amplify eimic haking. In many cae, however, model of hallow hear-wave velocitie, from which V () can be computed, do not extend to m. If the data for thee cae are to be ued, ome method of extrapolating the velocitie mut be devied. Four method for doing thi are decribed here and are illutrated uing data from 15 borehole in California for which the velocity model extend to at leat m. Method uing correlation between hallow velocity and V () reult in ignificantly le bia for hallow model than the implet method of auming that the lowermot velocity extend to m. In addition, for all method the percent of ite miclaified i generally le than 1% and fall to negligible value for velocity model extending to at leat 25 m. Although the method uing correlation do a better job on average of etimating V (), the implet method will generally reult in a lower value of V () and thu yield a more conervative etimate of ground motion [which generally increae a V () decreae]. Introduction The average hear-wave velocity of the top m of the Earth [V (), which i computed by dividing m by the travel time from the urface to m] i an important parameter ued in claifying ite in recent building code (e.g., Dobry et al., ; BSSC, 1) and in lo etimation. The ite clae etimated from hallow hear-wave velocity model are alo important in deriving trong-motion prediction equation (e.g., Boore et al., 1997), in contruction of map of National Earthquake Hazard Reduction Program (NEHRP) ite clae (e.g., Will et al., ), and in application of building code to pecific ite. Many meaurement of near-urface hear-wave velocity, however, do not reach m. For example, with one exception the hear-wave velocitie at the Kyohin Network (K-NET) tation in Japan (data ource: are between 1 and m (the one exception i K-NET tation AKT19, with a depth to bottom of 5.4 m). Another example come from a recent compilation of hear-wave velocitie from 277 borehole in California, more than half (142) of which are hallower than m (Boore, ). A hitogram of the depth to the deepet meaurement for borehole in that compilation i given in Figure 1, from which it can be een that mot of the hallow hole were drilled and logged before 199. Although mot of the hole are near m, 1 have value le than 25 m. A third example i eimic cone penetrometer meaurement made in the Oakland Alameda area of California (Holzer et al., 2, 4), where 19 out of 2 ounding are le than m, with 146 of thee being le than m. Thi note compare everal way of etimating V () from velocity model that do not reach m (the model could be determined from either invaive or noninvaive method). The implet method aume that the lowermot velocity of the model extend to m; the other method ue correlation of hallow velocitie and V (). Method of Extrapolation In the method dicued here, a key quantity i the time-averaged velocity V (d) to a depth d. Generally d i the depth to the bottom of the velocity model, which i not necearily the depth to the bottom of the borehole or the depth of the deepet meaurement in a borehole if the velocity model wa determined from borehole logging. I refrain from uing the phrae depth to bottom of borehole, which i meaningle for velocity model determined from noninvaive method. The time-averaged velocity i computed from the equation V (d) d/tt(d), (1) where the travel time tt(d) to depth d i given by d dz tt(d). (2) V (z) 591

2 592 D. M. Boore Table 1 Definition of NEHRP Site Clae in Term of V (), the Average Shear-Wave Velocity to m Site cla Range of V () (m/ec) Number of Borehole all borehole borehole pot 1989 A 15 V () B 76 V () 15 C 6 V () 76 D 18 V () 6 E V () 18 Contructed from information in BSSC, 1. E Depth to Bottom (m) Figure 1. Ditribution of the depth to the bottom of borehole from California tabulated by Boore (). Note that mot of the hole have depth near m (the two highet bar have been capped o a to how better the ditribution of other depth; the number indicate the height of the bar). NEHRP Cla D C In equation (2), V (z) i the depth-dependent velocity model. NEHRP clae are determined by V (), a indicated in Table 1. The purpoe of thi note i to invetigate way of approximating V () if d m. If all that i deired i the NEHRP cla, a imple method i to ue correlation between the NEHRP cla and V (d). I tudied the correlation from the 15 California borehole that extended to at leat m, for variou aumed depth, and found that there wa ome overlap in ite cla for a given value of V (d) (an example i hown in Fig. 2). For thi reaon, and becaue V () i ueful a a continuou parameter for characterizing ite repone in regreion equation (e.g., Boore et al., 1997), I invetigate here ome method that make more ue of the travel-time information from borehole. Extrapolation Auming Contant Velocity If the velocity model i available only to depth d, an aumption about the velocity between d and m can be ued to compute an etimate of V () uing the following equation: V () /(tt(d) ( d)/v eff ), () where V eff i the aumed effective velocity from depth d to m. The implet aumption i that V eff equal the velocity at the bottom of the velocity model: Veff V (d). (4) B V (d) Figure 2. An example of NEHRP cla a a function of V (d) for 15 borehole. In thi example, d 16 m. Becaue the velocity in general increae with depth for both geological and geotechnical reaon, however, thi method for determining V eff will uually lead to an underetimate of V () and therefore to ite clae that may be biaed toward larger letter value (the problem hould be wore the hallower the model). Thi drawback to the implet method led to the method decribed next. Extrapolation Uing the Correlation between V () and V (d) Another method ue the correlation between V () and V (d). Uing the ame et of 15 borehole for which the actual depth reached or exceeded m, I found that plot of V () againt V (d) for a erie of aumed depth d could be fit by a traight line. The catter in thee plot, however, increaed with V (d). For thi reaon, a power-law relation between V () and V (d) wa aumed, for which a traight line can be fit to the logarithm of the quantitie. Figure how example for four aumed depth. The correlation i

3 Etimating V () (or NEHRP Site Clae) from Shallow Velocity Model (Depth m) 59 good, even for the hallowet depth conidered here (1 m). Table 2 give the regreion coefficient for the equation log V () a b log V (d) (5) for depth ranging from 1 to 29 m. The velocity at the bottom of the model [V (d)] rather than the average velocity V (d) wa alo conidered a the predictor variable, but the catter wa wore. V (d) ha the advantage, however, that it can be ued if hallower part of the velocity model are miing, a i often the cae with upenion log reult; I dicu later a method for determining NEHRP cla that ue V (d). Equation (5) wa ued in two way to determine V () and thu NEHRP cla. The firt wa imply to inert the value of V (d) computed from the velocity model into equation (5). A econd, omewhat more elaborate method ued an etimate of log V () randomly drawn from a Gauian ditribution with mean given by equation (5) and tandard deviation given in Table 2 (the contribution to the variance due to uncertainty in the lope of the line i inignificant). Extrapolation Baed on Velocity Statitic to Determine Site Cla Another way to account for the general increae of velocity in a tatitical way i dicued briefly in the appendix to Atkinon and Boore () and i elaborated on here. For each borehole, I computed the ratio of V (d) to the effective velocity (V eff ) needed to raie the ite cla to the next tiffer cla than given by the imple extrapolation uing equation () and (4), for a erie of depth ranging in 1-m increment from 1 to 29 m. For each depth, the value of V eff /V (d) were tabulated in increment of.1 unit, tarting from.4, d = 1 m d = 16 m 2.8 log V () *x^ *x^ d = 22 m d = 28 m B 2.8 C log V () D 2.2 E *x^ e-4 +1.*x^ log V (d) log V (d) Figure. Fit of traight line to log V () a a function of log V (d), for d 1, 16, 22, and 28 m. Velocitie in meter per econd. The gray line how the boundarie between NEHRP ite clae; the clae are hown in the lower right-hand graph.

4 594 D. M. Boore Table 2 Coefficient of the Equation log V () a b logv (d) d a b r E E 7.126E E E E E E 5.95E E E E E E 5.86E E E E E E E E E.9422E E E.665E E E.2E E E.181E E E 2.71E E E 2.487E E E 2.826E E 2 1.4E E E E E E 1.45E E E 1.4E 8.871E E 4 1.1E E E E 2.755E r i the tandard deviation of the reidual about the fitted line; velocitie in meter per econd. and a complementary cumulative ditribution in term of percent (with a maximum value of 1) wa computed and plotted. A power law of the form b P(n V eff/v (d)) a(v eff/v (d)) (6) wa then fit to the empirical ditribution in a elected range of V eff /V (d). A variety of function were tried, but the power law wa imple and gave a good fit in mot cae. Where the power law failed to provide a good fit [uually at mall value of V eff /V (d) and deeper depth], P wa given a value of 1 for argument le than a ubjectively choen value. Figure 4 give four example of the fit at elected depth, and Table give value of the coefficient for all depth conidered. Equation (6) give the probability P(n V eff /V (d)) of exceeding V eff /V (d) and can be ued to decide if the ite cla hould be changed, following thi procedure: 1. Compute a proviional ite cla baed on the imple extrapolation (equation and 4). 2. Ue equation () to olve for the V eff /V (d) needed to move to the next tiffer ite cla (ofter ite clae are not conidered becaue in only a few cae from the et of 15 borehole would the ite cla actually become ofter; thi example may not be univerally applicable, for there may be region in which velocitie might generally decreae with depth in the upper ten of meter).. Evaluate equation (6) for thi value of V eff /V (d) (paying attention to the value below which P i taken to be 1; ee Table ). If P equal 1, then the proviional ite cla i changed. 4. If P from the previou tep doe not equal 1, then a random number r uniformly ditributed between and 1 i generated. If r P, then the proviional ite cla i changed to the next tiffer cla (e.g., D to C), and if r P the cla i et to the proviional ite cla (no change in cla). If the procedure i applied many time, thi tep guarantee that the number of cla change will agree with the number expected from the probability value P that a change hould occur. Illutration of the Method The method for etimating V () are illutrated uing a ubet of the 277 borehole model compiled by Boore (). The ubet conit of 15 borehole whoe velocity model extend to at leat m. All of the borehole are from California, with 5 from northern California, 8 from the San Francico Bay area, 26 from central California, and 66 from outhern California. Of thoe from outhern California, about 6 are from the greater Lo Angele area and 18 are from the Imperial Valley. The formation near the urface are motly Holocene in age, followed in number by thoe of Pleitocene age. A few borehole are located at ite with highly weathered Meozoic rock at the urface. Except for the implet method (equation and 4), the ue of thi ubet of borehole doe not contitute a true tet of the method becaue the ame dataet ued to derive the tatitical quantitie ued in the method i ued for the application of the method. A random ubet of the 15 hole could have been elected for determination of the quantitie in Table 2 and and the method then teted againt the ret of the hole. In view of the rather limited number of borehole, I opted intead for a better determination of the tatitical quantitie. Thu the comparion between actual and derived ite clae are more a conitency check and an illutration of the method than a tet of the method. Depth ranging in 1-m increment from 1 to 29 m were choen, auming for each depth that the deeper part of the velocity model wa unknown. Example of the imple method and the method baed on the tatitic of V eff /V (d) are given in Table 4 for an aumed depth to bottom of 1 m. The entrie in the column will help in undertanding the method. For example, for hole a, V eff /V (d) 1.1 i required to move the cla baed on imple extrapolation (D) to the next tiffer cla (C); from equation (6) and Table, the probability P of uch a value i 1%, but the random probability r i 79%, o no change wa made in the cla (the value of r depend on the particular eed ued in the random number generator; other eed might reult in a change in ite cla). The example in Table 4 were choen to illutrate four cae: (1) both method gave the ame ite cla a the actual ite cla; (2) the imple extrapolation gave the wrong cla, but the probabilty-baed method gave the correct cla; () the imple extrapolation gave the correct cla, but the probabilty-baed method gave the wrong

5 Etimating V () (or NEHRP Site Clae) from Shallow Velocity Model (Depth m) d = 1 m 8 d = 16 m P( _>V (d)) 6 4 oberved ditribution ued for fit 6 4 oberved ditribution ued for fit d = 22 m 8 d = 28 m P( _>Veff/V (d)) 6 4 oberved ditribution ued for fit 6 4 oberved ditribution ued for fit Veff/Vbot Veff/Vbot Figure 4. The complement of the cumulative probability of the ratio V eff /V (d) (ee text) from 15 borehole in California, for bottom depth of 1, 16, 22, and 28 m. Alo hown are the power-law fit to the indicated obervation (open circle), a ued in the analyi [with P et equal to 1 for V eff /V (d) le than the value given in the fourth column of Table ]. cla; and (4) both extrapolation method gave the wrong cla. For each method, an error count wa kept for each aumed depth to bottom, with eparate count being kept for no change, change to a tiffer cla, and change to a ofter cla, according to how far apart the reaigned ite clae were from the actual ite clae (in practice, thi never exceeded one ite cla, o the count array were only incremented by unity). For example, if the real cla were C but the reaigned cla were D, then the array for erroneou change to a ofter ite would be incremented by 1 (the array for erroneou change to tiffer ite wa incremented by 1). For each aumed depth, the cumulative number of erroneou change wa converted to a percentage of all borehole with an erroneou change of ite cla. The reult for all method, plotted a a function of depth, are hown in Figure 5. Alo included are the reult of adding the percent of erroneou change to tiffer and ofter ite; thi can be thought of a the total bia for each procedure. Figure 5 how that the imple method give a reult biaed toward ofter ite, a expected. The biae for the other method are ignificantly maller for all depth. The verion of the method uing a Gauian ditribution about the regreion relation (equation 5) give omewhat maller bia than uing equation (5) by itelf. The more fully probabilitic method uing equation (6) give better reult than uing the linear regreion method [but that method only yield an etimate of ite cla and not the continuou variable V ()]. Overall, the chance of an error in ite claification i le than 1% for all but the hallowet depth; for the borehole dataet ued in thi article, with mot hole cloer to or deeper than m (Fig. 1), the chance of an error i negligible uing any method. Dicuion and Concluion Uing 15 borehole for which the velocity model extend to at leat m, everal method for extrapolating V to m were invetigated. Method uing the tatitical propertie of the relation between V () and hallower velocitie reulted in ignificantly le bia for hallow model than the imple method of auming that the lowermot velocity extend to m. In addition, for all method the percent of ite miclaified i generally le than 1% and fall to negligible value for velocity model extending to at leat 25 m. The reult ugget that determination of ite clae for the USGS dataet of Boore () will have few error uing any method. The reult, however, might prove ueful

6 596 D. M. Boore Table Coefficient of Power-Law Fit (Equation 6) to the Complementary Cumulative Ditribution of Value of V eff /V (d) d(m) a b n 1 :ue n 1 :pwr The column headed n 1 :ue give the value of V eff /V (d) below which P i et to 1 in ue, and the column headed n 1 :pwr give the value of V eff /V (d) that yield P 1 when inerted into equation (6). Table 4 Example of Determination of NEHRP Site Cla uing Simple Extrapolation and Probability-Baed Extrapolation Hole V ():a V ():x V eff /V (d) P r Cla:a Cla:x Cla:p a D D D b C D C c D D C d D E E The value are for a velocity model topping at 1 m. Velocitie are in meter per econd. In the column label, :a, :x, and :p tand for actual value, extrapolated baed on the imple model, and extrapolated value baed on the probability model, repectively. The value of V eff /V (d) i that required to change to a tiffer cla than given by the imple extrapolation. The actual borehole are not identified becaue the procedure i not intended to make the proper prediction on a hole-by-hole bai; it hould make the proper prediction on the average when applied to a large et of borehole. for other dataet, uch a the K-NET dataet or other ite for which hear-wave velocity model might extend to depth ignificantly le than m (uch a many eimic cone penetrometer ounding). An important caveat: none of the method are likely to give a correct value of V () for a pecific ite. The procedure are inherently tatitical, and over many ite the value hould be correct on the average; the procedure only make ene when the data from many tation are being ued in a tatitical way, uch a a regreion analyi, and V () or ite cla for any particular ite i not important. The reult here could be extended to determine the correlation between V () and the average velocity between a depth range that doe not reach the urface (i.e., uing a nonzero lower limit in equation 2). Thi would be ueful for application to upenion log reult, which never reach the urface. The reult could alo conider geological information, uch a whether the ite i expected to be underlain to m by Holocene material alone, Pleitocene material alone, or ome combination. A it i, the analyi i dominated by cla NEHRP C and D ite, and the method might not work a well for NEHRP cla E or cla B ite. A way of incorporating poible overall difference in the velocity model due to different type of ite i to ue ome meaure of the gradient of the velocity model a a bai for extrapolation. Thi would alo help deal with ituation where the velocity might not generally increae with depth, a it doe for the California borehole ued to illutrate the method in thi article. Acknowledgment I thank Tom Holzer, Chri Stephen, and two anonymou reviewer for comment that ignificantly improved the article. I alo thank Tom Holzer and Mike Bennett for providing the eimic cone penetrometer data for the Oakland Alameda region. Reference Atkinon, G. M., and D. M. Boore (). Empirical ground-motion relation for ubduction-zone earthquake and their application to Cacadia and other region, Bull. Seim. Soc. Am. 9, Boore, D. M. (). A compendium of P- and S-wave velocitie from urface-to-borehole logging: ummary and reanalyi of previouly publihed data and analyi of unpublihed data, U.S. Geol. Surv. Open-File Rept. -191, 1 pp.; boore (lat acceed February 4). Boore, D. M., W. B. Joyner, and T. E. Fumal (1997). Equation for etimating horizontal repone pectra and peak acceleration from wetern North American earthquake: a ummary of recent work, Seim. Re. Lett. 68, Building Seimic Safety Council (BSSC) (1). NEHRP recommended proviion for eimic regulation for new building and other tructure, Edition, Part 1: Proviion, prepared by the Building Seimic Safety Council for the Federal Emergency Management Agency (Report FEMA 68), Wahington, D.C. Dobry, R., R. D. Borcherdt, C. B. Croue, I. M. Idri, W. B. Joyner, G. R. Martin, M. S. Power, E. E. Rinne, and R. B. Seed (). New ite coefficient and ite claification ytem ued in recent building eimic code proviion, Earthquake Spectra 16, Holzer, T. L., M. J. Bennett, T. E. Noce, A. C. Padovani, and J. C. Tinley III (2). Liquefaction hazard and haking amplification map of Alameda, Berkeley, Emeryville, Oakland, and Piedmont, California: a digital databae, U.S. Geol. Surv. Open-File Rept ; geopub.wr.ug.gov/open-file/of2-296/ (lat acceed February 4). Holzer, T. L., M. J. Bennett, T. E. Noce, A. C. Padovani, and J. C. Tinley III (4). Shear-wave velocity of urficial geologic ediment: tatitical ditribution and depth dependence, Earthquake Spectra, (in pre). Will, C. J., M. Peteren, W. A. Bryant, M. Reichle, G. J. Saucedo, S. Tan, G. Taylor, and J. Treiman (). A ite-condition map for California baed on geology and hear-wave velocity, Bull. Seim. Soc. Am. 9, S187 S8.

7 Etimating V () (or NEHRP Site Clae) from Shallow Velocity Model (Depth m) 597 a) b) 1 1 Percent of hole Too oft Too hard Percent of hole Too oft Too hard -1 Uing contant velocity extrapolation Uing log V () v logv (d); no probability model Depth (m) -1 Uing contant velocity extrapolation Uing log V () v logv (d) and probability model Depth (m) c) Percent of hole 1 Too oft Too hard -1 Uing contant velocity extrapolation Uing Veff/V (d) probability model Depth (m) Figure 5. Summary of change to the NEHRP clae uing variou method to obtain V (): (a) uing the regreion fit of log V () a a function of log V (d), without accounting for the catter about the line; (b) uing the regreion fit and the catter about the line; and (c) uing the probability ditribution of V eff /V (d). For comparion, the gray line in each graph how the reult of uing imple extrapolation auming a contant velocity from the bottom depth to m. Nonzero value indicate incorrect cla change, a the percent of hole, with poitive and negative value indicating a new cla that i too oft and too hard compared to the actual cla, repectively. The dahed line are the overall bia, obtained by adding the number of ite miclaified a being too hard and being too oft. U.S. Geological Survey 45 Middlefield Rd., MS 977 Menlo Park, California 9425 boore@ug.gov Manucript received 29 May.