9th Japan Earthquake Engineering Symposium, Tokyo, Dec., 1994

by Yoshiaki Hisada*

* Research Associate, Department of Earth Sciences, University of Southern California

We successfully simulated the long-period ground motion observed at the PAS and USC stations during the 1990 Upland earthquake using the surface wave boundary element method, and found strong 3-D effects of the Los Angeles basin structure on the ground motion at USC.

Since the unprecedented damage in Mexico City and the Bay Area of San Francisco during recent earthquakes, it has been widelyrecognized that surface waves locally generated in sedimentary basins, have great influence on long-period structures, such as high-rise buildings, oil storage tanks, and long-span bridges. Recent observations using seismic array data have indicated that the generation and propagation of those surface waves are strongly affected by three dimensional structure of the basins (e.g., Frankel et al., 1991; Kinoshita et al., 1992). In order to simulate those surface waves, finite difference methods and finite element methods, so far, have been most widely used (Toshinawa and Ohmachi, 1992; Frankel, 1993; Graves, 1993; Yomogida and Etgen, 1993). However, their applications to 3-D models have been restricted to relatively small-scale basins, because of the huge amount of computer memory and CPU time needed, and also because of the accumulation of numerical errors (e.g., numerical dispersion; see Frankel and Vidale, 1992).
Recently, Kato et al.(1993) and Hisada et al.(1993) successfully simulated long-period (6-10 sec) strong ground motion for 3-D models of the Kanto sedimentary basin using the surface wave Gaussian beam method (Yomogida and Aki, 1985) and the surface wave boundary element method (Hisada et al., 1993). The Gaussian beam method, under the assumption of a smoothly varying medium, successfully simulated both the absolute amplitudes and the phases of the early part of the long-period motion, but underestimated the observed duration. On the other hand, the boundary element method successfully reproduced the duration caused by trapping of seismic energy in a low-velocity basin composed of flat-layers.
In this study, we applied the 3-D surface wave BEM to the long-period ground motion records observed at the PAS (Pasadena) and USC (University of Southern California) very-broad-band stations during the 1990 Upland earthquake. Yamamoto et al.(1992) simulated the same set of records using 2-D BEM and concluded that the 2-D modelings can reproduce the long duration at USC but not the amplitude. We checked whether the 3-D effects of the basin structures of the Los Angeles basin and San Gabriel valley can simulate the observed amplitude.

Fig.1 shows the geological condition in and around the Los Angeles basin together with the locations of the epicenter of the 1990 Upland earthquake and the PAS (N34.15, E118.17) and USC (N34.02, E118.29) stations. Note that the PAS and USC stations are located on the Pre-Tertiary bedrock and the Quaternary sediment, respectively. Fig.2 shows the velocity records observed at the two stations. The record at USC shows much longer duration than the one at PAS, which clearly indicates the effects of the surface waves excited in the sedimentary layers in the Los Angeles basin and San Gabriel valley.
Before going to the 3-D modelings, we simulated the two recordes using 1-D structure models and the normal mode solution (Harkrider, 1964). We adopted the 1-D structure models shown in the right- and left-hand sides of Fig.4(b) for the PAS and USC stations, respectively. These models are based on the models used by Dreger and Helmberger (1990), Vidale and Helmberger (1988), and Yamamoto et al.(1992). We used the source parameters shown in Table 1, which were derived by Dreger and Helmberger (1991). Fig.3 shows the comparisons of the displacements between the observations and the simulations, which are bandpass filtered between periods of 5 sec and 8 sec by a trapezoidal filter with flat range from 6 sec to 7 sec. Times are measured from the origin time of the earthquake. The 1-D model for PAS works well for the all components, as already shown by Dreger and Helmberger (1990 and 1991). On the contrary, the 1-D model for USC poorly reproduces the observation, especially smaller amplitudes for the N-S components. This is because the USC station is close to the nodal plane of the Love wave radiation pattern. It is clear that the 2-D modelings would also not work for this record, because of the same reason. A similar phenomenon was observed in the Kanto basin (Kato et al., 1993; Hisada et al., 1993).
Table 1 The fault geometry and the kinematic source parameters of the 1990 Upland earthquake
location of source depth (km) strike direction dip angle rake angle
(N34.15',E118.17') 6 N216'E 77' 5'
length (km) width (km) dislocation (m) rise time (sec)
3.5 3.5 0.62 0.4
repture velocity (km/sec) moment (dyne*cm) repture type
3.0 2.5*10**24 bilateral
In order to investigate the 3-D effects of the basin structure on the USC record, we used the surface wave BEM (Hisada et al. 1993). Because we needed to assume a vertical interface between the basin and the surrounding bedrock in our current BEM code, in addition to the flat-layered structures, we tried two different models shown in Fig.4(a). In the first modeling (Model 1), we set the vertical interface along the 4000 feet (about 1.22km) contour on the Pre-Tertiary basement (Yerkes et al., 1965). Fig.4(b) shows the cross section of Model 1 along the A-A' line shown in Fig.4(a). In these figures, the bold lines indicate the areas of BEM mesh. In the second modeling (Model 2), we put the interface along the 6000 feet (about 1.83km) contour. Although we terminated the boundary elements at certain vertical and horizontal locations, as shown in the figures, we checked that the choice of the locations had little effects to the simulation results at PAS and USC.
Fig.5 and Fig.6 show the simulation results using Model 1 and 2, respectively. Although there are little differences in the results at PAS, we see clear distinctions at USC between the two models. Extremely large surface waves are generated in Model 1 and arrive at USC much later than the observations. We confirmed that those surface waves come from the source direction. On the other hand, Model 2 successfully reproduces not only the amplitudes, but also the phases of the observation. We checked that the main motion of this simulation comes from the bedrock located at the north-west direction of USC, rather than from the source. Similar phenomena were observed in the Santa Clara valley (Frankel and Vidale, 1992) and the Kanto basin (Toshinawa and Ohmachi, 1992; Kato et al., 1993; Hisada et al., 1993). These results clearly indicate that strong 3-D effects of the basin structures to the USC record, and also simple assumptions used in our modelings work well in this long-period range (5-8 sec) for this earthquake.

We found that the strong 3-D effects of the Los Angeles basin in the long-period ground motion (5-8 second) during the 1990 Upland earthquake. First, we confirmed that the 1-D modelings are poor at USC, because it is close to the nodal plane of the Love wave radiation pattern. We then tried 3-Dmodelings using the surface wave BEM, and found a model (Model 2) can successfully reproduce not only the amplitudes, but also the phases observed at USC. The main motions of this period range come from the north-west direction through the northern bedrock, rather than from the source direction.

I would like to thank Prof. Keiiti Aki for the comments and supports on this study. The English of this paper was improved by David Adams. This work was in part supported by the Kajima Foundation's Research Grant, NSF under contract ACS-9318163, and Southern California Earthquake Center through NSF cooperative agreement EAR-8920136 and USGS cooperative agreement through 14-08-0001-A0899. The simulations in this study were in part performed by the CRAY Y-MP8/862 of the San Diego Supercomputer Center.

  1. Dreger, D.S., and D.V.Helmberger (1990). Broadband modeling of local earthquakes, Bull. Seism. Soc. Am., 80, 1162-1179.
  2. Dreger, D.S., and D.V.Helmberger (1991). Complex faulting deduced from broadband modeling of the 28 February 1990 Upland earthquake (ML=5.2), Bull. Seism. Soc. Am., 81, 1129-1144.
  3. Frankel, A., S.Hough, P.Friberg, and R.Busby (1991). Observations of Loma Prieta aftershocks from a dense array in Sunnyvale, California, Bull. Seism. Soc. Am., 81, 1900-1922.
  4. Frankel, A.(1992). Three-dimensional simulations of ground motions in the San Bernardino valley, California, for hypothetical earthquakes on the San Andreas fault, Bull. Seism. Soc. Am., 83, 1020-1041.
  5. Frankel, A., and J.Vidale (1992). A three-dimensional simulation of seismic waves in the Santa Clare valley, California, from a Loma Prieta aftershock, Bull. Seism. Soc. Am., 82, 2045-2074.
  6. Graves, R.W., (1992). Modeling three-dimensional site response effects in the Marina district basin, San Francisco, California, Bull. Seism. Soc. Am., 83, 1042-1063.
  7. Harkrider, D.G. (1964). Surface waves in multilayered elastic media. Part 1, Bull. Seism. Soc. Am., 54, 627-679.
  8. Hisada, Y., K.Aki, and T.-L.Teng (1993). 3-D simulations of the surface wave propagation in the Kanto sedimentary basin, Japan (Part 2: Application of the surface wave BEM), Bull. Seism. Soc. Am., 83, 1700-1720.
  9. Kato, K., K.Aki, and T.-L.Teng (1993). 3-D simulations of the surface wave propagation in the Kanto sedimentary basin, Japan (Part 1: Application of the surface wave Gaussian Beam method), Bull. Seism. Soc. Am., 83, 1676-1699.
  10. Kinoshita, S., H.Fujiwara, T.Mikoshiba, and T.Hoshino (1992). Secondary Love waves observed by a strong-motion array in the Tokyo lowland, Japan, J.Phys. Earth, 40, 99-116.
  11. Toshinawa, T., and T.Ohmachi (1992). Love wave propagation in a three-dimensional sedimentary basin, Bull. Seism. Soc. Am., 82, 1661-1677.
  12. Yamamoto, S., Y.Hisada, and S.Tani (1992). Simulations of long-period strong ground motions during the 1990 Upland earthquake, California, Proc. 9th World Conf. of Earthq. Engng.
  13. Yerkes, R.F., T.H.McCulloh, J.E.Schoellhamer, and G.Vedder (1965). Geology of the Los Angeles basin, California-Introduction, Geological Survey Professional Paper 420-A.
  14. Yomogida, K., and K.Aki (1985), Waveform synthesis of surface waves in a laterally heterogeneous Earth by the Gaussian beam method, J.Geophs. Res, 90, 7665-7688.
  15. Yomogida, K., and J.T.Etgen (1993). 3-D wave propagation in the Los Angeles basin for the Whittier-Narrows earthquake, Bull. Seism. Soc. Am., 83, 1325-1345.