Effect of Structural Heterogeneity and Slip Distribution on Coseismic Vertical Displacement from Rupture on the Seattle FaultBy Eric L. Geist^{1} and Shoichi Yoshioka^{2}Open File Report 20041010 2004 Use of any trade, firm or product name is for descriptive purposes only and does not constitute endorsement by the U.S. Government. U.S. GEOLOGICAL SURVEY ^{1}U.S. Geological Survey, Menlo Park, California 94025 Skip Navigation Bar  Introduction  Elastic FiniteElement Model  IntroductionWorkshops in 2001 and 2002 were convened to determine critical issues in the development of tsunami inundation maps for the Puget Sound region. The Tsunami Inundation Mapping Effort (TIME) is conducted under the multiagency National Tsunami Hazard Mitigation Program (NTHMP). The Puget Sound Tsunami/Landslide Workshop in 2001 focused on integrated tsunami research involving a wide range of research studies and tsunami hazard mitigation issues. The 2002 Puget Sound Tsunami Sources workshop (González et al., 2003) made specific recommendations for tsunami source modeling and improving our state of knowledge for sources in the Puget Sound region. One of the recommendations stated in González et al. (2003) is "Develop methods to assess the sensitivity of coastal areas to tsunami inundation, based on multiple simulations that reflect the possible range of variations in the source parameters." Tsunami inundation models rely heavily on the imposed initial conditions which, for an earthquake source, is the coseismic vertical displacement field. For example, Koshimura et al. (2002) use the geologic uplift observations (Buknam et al., 1992) to constrain the slip distribution for the event that occurred 1100 years ago, resulting in an average slip of 3.7 m and a magnitude of 7.6. Walsh et al. (2003) develop a tsunami inundation map for Elliot Bay based on a M 7.3 earthquake and the geologic uplift observations from the 1100 y.b.p. event as in Koshimura et al. (2002), though they use a constant fault dip of 60° rather than different dips for deep and shallow segments. The objective of this report is to examine how coseismic vertical displacement from a smaller M 6.5 Seattle Fault earthquake (as in Hartzell et al., 2002) is affected by structural heterogeneity and different slip distribution patterns. The threedimensional crustal structure of the Puget Sound region has recently been defined using shallow seismic reflection data (Pratt et al., 1997; Johnson et al., 1999) and reflection and wideangle recordings from the largescale SHIPS experiments (e.g., Brocher et al., 2001; ten Brink et al., 2002). The presence of a deep sedimentary basin (Seattle Basin) adjacent to the Seattle Fault has led to the question of whether structural heterogeneity has an effect on our estimate of vertical displacement for earthquake scenarios in the region. We use a threedimensional elastic finiteelement model (Yoshioka et al., 1989) to calculate vertical displacements from rupture on a twosegment (deep and shallow) Seattle fault using a heterogeneous crustal structure. Similar studies by Geist and Yoshioka (1996) and Masterlark et al. (2001) used threedimensional, finiteelement models (FEM) to study the effect of structural heterogeneity on coseismic displacement fields. Results for the Puget Sound study are compared to calculations using a homogeneous structure as assumed with conventional elastic dislocation solutions. Effects of slip distribution patterns on vertical displacement is computed using the stochastic source model adopted for tsunami studies by Geist (2002). Finally, we examine an alternate model for shallow faulting proposed by ten Brink et al. (2002) and Brocher et al. (submitted) and its effect on the vertical displacement field. Top of pageElastic FiniteElement ModelInitial conditions for tsunami propagation from a seismic source are determined from the static, vertical displacement field. To account for both lateral and vertical heterogeneity of crustal elastic properties in the Puget Sound region, we use a threedimensional elastic FEM developed by Hashimoto (1982) and Yoshioka et al. (1989). This method uses 8node isoparametric elements with infinite elements (Beer and Meek, 1981) around the edges of the model and a splitnode technique to model dislocations. The entire model consists of 7524 nodes and 6426 elements. The model in this study has been specifically designed to follow the heterogeneous model of broadband ground motion in this region recently published by Hartzell et al. (2002). Elastic properties and fault geometry specific to this study are given below: Elastic PropertiesThree geological layers with variable thickness are defined, each with a different shear modulus, that is simplified from the depthdependent, shearwave velocity model described by Hartzell et al. (2002):
For all cases, a Poisson ratio of 0.25 is used. For the homogeneous case, a constant shear modulus of 30 GPa is used. Fault GeometryTwo rupture geometries are initially considered:
Rupture area and position for the deeper segment is consistent with previous studies (Pratt et al., Hartzell et al. (2002). Rupture of shallow segment extends from this position to the surface through mostly sedimentary rocks of the Seattle Basin. (The effects of a different dip for the shallow segment is explored in the Alternate Tectonic Model section.) Uniform slip of 0.8 m is used in the Structural Heterogeneity section, yielding a magnitude of M_{w}=6.45 for the deeper segment and M_{w}=6.51 for combined rupture on the deep and shallow segments. In the Stochastic Source Model section, we will consider variable slip (average approximately 0.8 m) using a stochastic source as in Geist (2002) and Hartzell et al. (2002). For strongground motion modeling, Hartzell et al. (2002) also examines the effect of different hypocenter locations. For tsunami generation, variation in hypocenter location within a fixed rupture area is not as important as the static slip distribution (Geist, 1999). A persistent problem in this region is whether to scale the magnitude of slip based on geologic observations (e.g., elevated wavecut platforms at Restoration Pt., Buknam et al. 1992) or based on the average value for crustal earthquakes in western North America (Boore, 1996; Hartzell et al., 2002). Koshimura et al. (2002) used the geologic observations to constraint the amount of slip that occurred along the Seattle fault during an earthquake that occurred approximatel 1100 years ago. This results in an average slip of 3.7 m and a magnitude of M 7.6 for this earthquake. This scenario describes larger amounts of vertical displacement over a wider area than the scenario M 6.5 earthquake used in this study. Top of pageEffect of Structural HeterogeneityDeep SegmentShown below is the vertical displacement for the homogeneous and heterogeneous crustal structure models. The third figure below shows the difference between these two models (homogeneous  heterogeneous). In this case, the deeper part of the Seattle fault is within higher modulus basement rocks that underlie lower modulus sedimentary rock such that the displacement is less than expected from homogeneous models. This is consistent with theoretically derived effects of vertical layering described by Ma and Kusznir (1994) and Savage (1998). The maximum discrepancy is approximate 30%. Shallow SegmentThe vertical displacement field for the rupture on the shallow, steeply dipping segment of the Seattle fault is shown below. Because the effects of structural heterogeneity are complex for the combined rupture (next section), we show the effects for each segment separately. It is unlikely than rupture would occur on the shallow segment only. In this case, the shallow segment rupture occurs in the lower modulus sedimentary rocks of the Seattle basin. The effect here is to increase the displacement over what would be expected from using a homogeneous model, again agreeing with the results of Ma and Kusznir (1994) and Savage (1998). Combined RuptureThe vertical displacement field for combined rupture on the deep and shallow segments of the Seattle fault. Using the heterogeneous structure produces a more diffuse pattern of deformation. The difference of the displacement fields shows the combined effects of rupture progressing from basement rocks (deep segment) through the Seattle basin (shallow segment). Numerical ErrorsNumerical errors associated with the FEM are estimated by comparing vertical displacement from homogeneous model for the combined rupture on the deep and shallow segments with the vertical displacement from analytic expression of Okada (1985). Shown below is the difference (homogeneous FEM minus analytic): Numerical errors for this FEM are approximately ±3 cm. Overall, the FEM tends to slightly over predict the vertical displacements. There also appears to be some small numerical errors near the fault edges. Top of pageStochastic Source ModelTo examine the effect of different slip distribution patterns on the coseismic displacement field, we employ a stochastic source model of Herrero and Bernard (1994). For each slip distribution, the overall seismic moment and average slip is held constant. The spectral decay exponent for the slip distribution is specified a priori. Typically, this exponent is determined from the displacement spectrum of farfield seismograms. Because there is not sufficient data for Seattle fault earthquakes, we assume a slip decay exponent of 2 as in the canonical case described by Aki (1967). Further details of the stochastic source model related to tsunami generation are discussed by Geist (2002). Below are examples of slip distribution patterns produced by the stochastic source model. (Warm colors indicate high slip; cool colors low slip.) For each case, the average slip is approximately 0.8m. Strike direction is horizontal; dip direction is vertical
Top of pageEffect of Slip DistributionThe coseismic vertical displacement field is calculated for each slip distribution pattern, using superimposed pointsource solutions of Okada (1985) (Geist, 2002). In this case, we assume a homogeneous Poisson solid with a shear modulus of 30 GPa. For one of the slip distributions, the vertical displacement field for the deep segment rupture is shown below: In general, for shallow water depths and long displacement wavelengths, the initial tsunami wavefield mimics the coseismic vertical displacement field. For tsunamis generated along inland waterways, only the part of the coseismic vertical displacement field that is under water is applied to tsunami generation. Looking at a NS profile along the main channel of Puget Sound (NS solid line in figure above), we can assess what effect different slip distributions have on the wave profile in the main Puget Sound channel for tsunamis generated by the deeper segment of the Seattle fault. In the figure below, the thin black lines are profiles for 10 different slip distributions. The 2 red dashed lines represent the envelope (maximum and minimum values) for 100 slip distributions. As explained in the previous section, the average slip and total seismic moment is approximately the same in each case. We present results for the shallow segment of the Seattle fault in a similar manner. The vertical displacement field for the shallow segment rupture and for one of the slip distributions is shown below: Wave profiles for 10 slip distributions (black lines) and the wave profile envelope for 100 slip distributions (red dashed lines) are shown below: Top of pageAlternate Tectonic ModelAn alternate model to that of a shallow fault segment extending into the Seattle basin from the deeper basement thrust is the passive roof duplex model of Brocher et al. (submitted). Slip on the basementinvolved floor thrust is accompanied by shallow slip on a roof thrust as well as on distributed faulting in the Seattle basin along steep, northdipping en echelon thrusts (see also ten Brink et al., 2002). In a simplified version of the model proposed by ten Brink et al. (2002) and Brocher et al. (submitted), we examine the effect dip and dip direction on the shallow segment has on the vertical displacement field. Shown below is a combined rupture on a deep segment as before and on a shallow segment that dip 70° to the north. The vertical displacement field for the combined rupture is shown below for the two cases. In this example, a homogeneous structure and uniform slip of 0.8 m is used. The effect of the change in dip direction is to change the asymmetry in the NS direction. For the southdipping shallow segment, the resulting tsunami would have a higher leading wave steepness propagating to the north than the southward propagating tsunami. In contrast, the tsunami generated by combined rupture with the northdipping shallow segment would have a higher leading wave steepness in the southward propagation direction. The effect of increasing the dip of the shallow segment is to increase the amplitude and decrease the dominant wavelength of the initial tsunami. These results are consistent with the findings of ten Brink et al. (2002). Top of pageConclusionsUsing a twosegment Seattle Fault rupture geometry that includes (1) a deeper segment in high shearmodulus basement rocks and (2) a shallow segment that ruptures updip through the Seattle sedimentary basin, we established the effect of structural heterogeneity and slip distribution on the coseismic vertical displacement field. The effect of structural heterogeneity is dependent on the shear modulus of rocks surrounding the fault in comparison to an average shear modulus value one may use for a homogeneous model. In general, vertical displacement increases above faults that rupture into relatively lower shear modulus material and decreases above faults that rupture into relatively higher shear modulus material. These results are consistent with past theoretical work (Ma and Kusznir, 1994; Savage,1998). Although the effect of structural heterogeneity is low in comparison to variation in other earthquake source parameters, where structural and material data is available, heterogeneous models should be used. Unlike structural heterogeneity which can be determined using geophysical techniques, the slip distribution pattern for a potential earthquake cannot be predicted beforehand. Using many different slip distribution patterns that all follow the same spectral scaling law can help to determine the expected variation in vertical displacement for tsunami generation. For approximately the same seismic moment and average slip, the maximum vertical displacement (and initial tsunami amplitude) in the main NS channel of Puget Sound averages 17.1 cm among 100 different slip distributions and has a standard deviation of 1.7 cm. Larger variation in the maximum vertical displacement is predicted for the shallow segment rupture: 30.4±5.7 cm. For earthquakes that occur completely underwater in the openocean, the entire vertical displacement field contributes to tsunami generation. In contrast, for inland waterways such as Puget Sound, the waterways act as a blocking filter that selectively samples only a part of the vertical displacement field for tsunami generation. For this reason, tsunami generation may be more sensitive to variations in the slip distribution patterns. Finally, other "firstorder" earthquake source parameters such as geometry and earthquake magnitude effect the tsunami that is generated (Geist, 1999). We show the effect that changes in dip for the shallow fault segment has on the vertical displacement field. In addition, the initial tsunami will scale with the overall size of the rupture area and average slip (i.e., the total seismic moment). The rupture geometry used in this report is consistent with what was inferred from seismic reflection data (Pratt et al., 1997; Johnson et al., 1999) and previous modeling studies of broadband ground motion (Hartzell et al., 2002). However, multiple interpretations of the shallow structure of the Seattle fault system have emerged (ten Brink et al., 2002; Brocher et al., submitted) that, in part, explain the uplift of elevated wavecut platforms at Restoration Pt. (Buknam et al., 1992). Rather than using these more complex structural models, Koshimura et al. (2002) and Walsh et al. (2003) use the geologic uplift observations to determine the slip distribution for the event that occurred 1100 years ago. However, the uncertainty in firstorder source parameters, as well as structural heterogeneity and slip distribution, has a large effect on determining regions for potential tsunami inundation and is a topic for future research. Top of pageAcknowledgementsWe thank Professor Manabu Hashimoto for making available the FEM program. We also thank Hal Mofjeld (NOAA), Tom Brocher, and Steve Hartzell for helpful reviews and Laura Torresan for help with the web page design and review. ReferencesAki, K., 1967, Scaling law of seismic spectrum: Journal of Geophysical Research, v. 72, p. 12121231. Beer, G., and J. L. Meek, 1981, 'Infinite domain' elements: International Journal for Numerical Methods in Engineering, v. 17, p. 4352. Boore, D. M., 1996, SMSIMFortran program for simulating ground motions from earthquakes: Version 1.0, U.S. Geological Survey OpenFile Report 9680A, 73 pp. Brocher, T. M., et al., 2001, Upper crustal structure in Puget Lowland, Washington: Results from the 1998 Seismic Hazards Investigation in Puget Sound: J. Geophys. Res., vol.106, p.13,54113,564. Brocher, T. M., R. J.Blakely,and R.E.Wells, submitted, Interpretation of the Seattle uplift, Washington, as a passive roof duplex: Bull. Seismol. Soc. Am. Bucknam, R. C., E. HemphillHaley, and E. B. Leopold, 1992, Abrupt uplift within the past 1700 years at southern Puget Sound, Washington: Science, v. 258, p. 16111613. Geist, E. L., 1999, Local tsunamis and earthquake source parameters: Advances in Geophysics, v. 39, p. 117209. Geist, E. L., 2002, Complex earthquake rupture and local tsunamis: J. Geophys. Res., v. 107, no. B5, 16 pp. Geist, E. L., and Yoshioka, S., 1996, Source parameters controlling the generation and propagation of potential local tsunamis along the Cascadia margin: Natural Hazards, v. 13, p. 151177. González, F., B. Sherrod, B. Atwater, A. Frankel, S. Palmer, M. Holmes, B. Karlin, B. Jaffe, V. Titov, H. Mofjeld, and A. Venturato, 2003, 2002 Puget Sound Tsunami Sources Workshop Report. A contribution to the Inundation Mapping Project of the U.S. National Tsunami Hazard Mitigation Program, NOAA OAR Special Report, 34 pp. Hartzell, S., A. Leeds, A. Frankel, R. A. Williams, J. Odum, W. Stephenson, and W. Silva, 2002, Simulation of broadband ground motion including nonlinear soil effects for a magnitude 6.5 earthquake on the Seattle Fault, Seattle, Washington: Bull. Seismol. Soc. Am., v. 92, p. 831853. Hashimoto, M., 1982, Numerical modeling of the threedimensional stress field in southwestern Japan: Tectonophysics, v. 84, p. 247266. Herrero, A., and Bernard, P., 1994, A kinematic selfsimilar rupture process for earthquakes: Bulletin of the Seismological Society of America, v. 84, p. 12161228. Johnson, S. Y., Dadisman, S. V., Childs, J. R., and Stanley, W. D., 1999, Active tectonics of the Seattle fault and central Puget Sound, WashingtonImplications for earthquake hazards: Geol. Soc. Am. Bull., v. 111, p. 10421053. Koshimura, S., Mofjeld, H. O., González, F.I., Moore, A. L., 2002, Modeling the 1100 bp paleotsunami in Puget Sound, Washington: Geophys. Res. Lett., v. 29, p. 91  94. Ma, X. Q., and N. J. Kusznir, 1994, Effects of rigidity layering, gravity, and stress relaxation on 3D subsurface fault displacement fields: Geophys. J. Int., v. 118, p. 201220. Masterlark, T., C. DeMets, H. F. Wang, O. Sánchez, and J. Stock, 2001, Homgeneous vs heterogeneous subduction zone models: Coseismic and postseismic deformation: Geophys. Res. Lett., v. 28, p. 40474050. Okada, Y., 1985, Surface deformation due to shear and tensile faults in a halfspace: Bull. Seismol. Soc. Am., v. 75, p. 11351154. Pratt, T. L., S. Johnson, C. Potter, W. Stephenson, and C. 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Hirahara, 1989, Displacement fields due to the 1946 Nankaido earthquake in a laterally inhomogeneous structure with the subducting Philippine Sea platea threedimensional finite element approach: Tectonophys., v. 159, p. 121136. Top of page
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