*Science* **270**, 1628-1632.

K.B. Olsen(*), R.J. Archuleta(*), and J.R. Matarese (**)

(*) Institute for Crustal Studies

University of California, Santa Barbara

Santa Barbara, CA 93106-1100

(**) Earth Resources Laboratory

MIT, Dept. Earth Plan. Sci.

Cambridge, MA 02142

To estimate the seismic hazard from a M 7.75 along the 170 km section of the San Andreas fault between Tejon Pass and San Bernardino we have simulated two minutes of ground motion in the Los Angeles area (19,975 km2) including the Los Angeles and San Fernando Valley basins using a three-dimensional finite-difference method on a parallel supercomputer. The maximum ground velocities occur near the fault (2.5 m/s) and in the Los Angeles basin (1.4 m/s) where large amplitude surface waves prolong the shaking for more than 60 seconds. Spectral amplitudes within the Los Angeles basin are an order of magnitude larger than those at sites outside the basin at similar distances from the San Andreas.

The damage in Mexico City from the Michoacan earthquake (19 Sep. 1985) and in the Marina District of San Francisco from the Loma Prieta earthquake (19 Oct. 1989) have clearly illustrated the risks for population centers located in basins even at a significant distance from the causative fault. The sedimentary structure of the basins with their smaller elastic moduli amplifies the seismic waves relative to the surrounding bedrock. The edges of the basins can generate large-amplitude waves that can significantly prolong the shaking in the basins. Moderate-sized events, such as the magnitude (M) 6.7 Northridge earthquake (17 Jan. 1994), the M 6.0 Whittier Narrows earthquake (1 Oct. 1987) and the M 6.6 San Fernando earthquake (9 Feb. 1971), have emphasized the seismic hazard from faults on the Los Angeles (LA) fault system (1, 2, 3, 4, 5). Nonetheless, the San Andreas fault (SAF) remains potentially the most hazardous for the LA area since it is the one fault in southern California known to have produced very large earthquakes in historical time (2, 6, 7).

To determine the amount of shaking that could occur in the LA area we simulated a M 7.75 earthquake on the section of the SAF closest to LA. We considered a propagating rupture for 170 km from Tejon Pass to San Bernardino (Fig. 1a). This part of the SAF which consists of two segments, the Mojave and part of the San Bernardino Mtns. segment (2), is believed to have produced the M 7.5 earthquake on 12 Dec. 1812 (8). The average recurrence time between large earthquakes with surface rupture on the Mojave segment is 150 -71+123 yrs; on the San Bernardino segment the average recurrence time is 146 -60+91 yrs (2). The Working Group on California Earthquake Probabilities (WGCEP), 1995, calculated mean conditional probabilities of 26 +-11% (M 7.53) and 28 +-13% (M 7.30) for earthquakes on the Mojave and San Bernardino segments, respectively, to occur before the year 2024. Since both segments have about the same recurrence interval and the same conditional probability, and have ruptured together in previous events, it is reasonable to consider a scenario where this section of the SAF ruptures again in a single earthquake.

To realistically estimate the ground shaking from such an earthquake (9) we need to incorporate the three-dimensional (3D) structure of the medium through which the seismic waves will travel from the SAF to LA. This region spans a large variation in geology from igneous and metamorphic basement rocks in the Mojave Desert and San Gabriel Mountains (10) and deep sedimentary basins in LA and San Fernando Valley (SFV) (11). The seismic energy will propagate for at least 35 km through igneous and metamorphic rocks before impinging on the sedimentary basins of greater LA (Fig. 1b). Were it not for the basins beneath SFV and LA (including San Gabriel Valley (SGV)) (Fig. 1b), the model would consist of horizontal layers (12) where the material parameters varied only with depth. However, with their irregular geometry and different material properties, these sedimentary basins strongly affect the ground motion by amplifying the seismic waves, prolonging their duration, and generating waves at the basin edges (3, 13, 14).

To approximate a M 7.75 earthquake on the SAF we started with a fault plane 16.5 km deep and 170 km long that extends from Quail Lake (10 km southeast of Gorman) to Mill Creek (11 km northeast of Redlands). The fault plane had a constant strike (118 deg) that follows the strike along most of this segment of the SAF with a slight deviation (maximum of 6 km) at the northwestern end (Fig. 1a). The rupture initiates at a point, 2 km from the northwestern end of the fault segment, at 10 km depth and dextrally offsets the two sides of the fault by 4.82 m (15) everywhere (Table 1). The earthquake lasts 68 s before terminating at Mill Creek. The seismic shear waves that are continuously radiated from the rupture impinge on the basins about 20 s after the earthquake starts. Some areas of the LA basin continues to vibrate for more than 60 s because of the continual stimulation from waves arriving from different parts of the fault, waves generated at the basin edges, and resonances within the basin.

We subdivided a large volume (230 km x 140.4 km x 46 km) of southern California into 23,209,875 cubes 0.4 km on a side with a gridpoint at each vertex. Each gridpoint is assigned a compressional wave velocity, a shear wave velocity and a density (15). The 3D structure does not include the basins beneath the Upper Santa Ana Valley, the San Bernardino Valley or the Ventura area (14, 17) because currently there is no discretized 3D model available of the elastic and material properties. The amplitude and duration of the simulated ground motion is therefore most likely underestimated in these areas (14, 18).

We kinematically simulate the earthquake as a constant slip that radially propagates outward with a velocity 85% of the local shear wave speed. The slip rate function is Gaussian-shaped with a dominant period of 4.5 s. This function is later deconvolved from the synthetic records to obtain a slip rate with uniform spectral response to displacement for frequencies up to 0.4 Hz that is constant everywhere on the fault. This formulation allows the seismic moment and all of the synthetics to be scaled by a single value of slip. The effective rise time is about 3 s everywhere on the fault (19).

The source was implemented in the finite-difference grid by adding -Mij(t)/V to Sij(t), where Mij(t) is the ijth component of the moment tensor for the earthquake, V is the cell volume, and Sij(t) is the ijth component of the stress tensor on the fault at time t (Table 2). We use a staggered-grid finite-difference scheme to solve the 3D elastic equations of motion (20); the accuracy is 4th-order in space and 2nd-order in time. The numerical implementation of the 3D scheme is described in (21). In order to eliminate artificial reflections from the boundaries of the grid we implemented absorbing boundary conditions coupled with a buffer zone of strong attenuation (22). In the following we have removed these zones and present the simulation results within the 174 km by 114.8 km rectangular area (Fig. 1a) that encompasses the population centers of the greater LA area.

Finite-difference modeling of elastic waves in large-scale 3D models, such as the one used in the SAF simulation, consumes vast quantities of computational resources. The earth model and the calculated stress and velocity fields require gigabytes of physical memory and tens of gigaFLOPS/s-hours of CPU time to simulate the total duration of ground motion within a reasonable period of time. Such computational requirements are beyond the resources for workstations and most supercomputers with shared-memory configurations. To carry out our simulation we used grid-decomposition techniques on the massively parallel processors of the nCUBE 2 at MIT's Earth Resources Laboratory.

Figure 2 illustrates how we decompose a three-dimensional volume of the model over 8 parallel processors. Each processor is responsible for performing stress and velocity calculations for its portion of the grid, as well as dealing with boundary conditions at the external edges of each volume. At the internal edges, where neighboring portions of the earth volume are contained on separate nodes, the processors must exchange stress and velocity information to propagate the waves correctly. On the nCUBE 2, this communication time represents a negligible part of the total run time. In other words, the same simulation can be performed twice as fast on twice as many processors as long as the internal edges represent a minor part of the model held by each processor.

For the SAF simulation, with grid dimensions of 576 by 352 by 116 points, the most memory-efficient decomposition involved assigning 36 by 44 by 29 point subgrids to the individual processors. In keeping with the 4th-order finite- difference scheme, a two-point-thick padding layer was added to the outside of each subgrid bringing the total subgrid dimensions to 40 by 48 by 33 points. To store 12 arrays (three elastic coefficients, three components of velocity and six components of stress) of this size required just over 2.9 megabytes of the 4 megabytes of physical memory on each processor. The remaining memory was consumed by the program logic and additional variables as well as the operating system kernel. Using a grid decomposition code based upon the portable Message Passing Interface (MPI) standard, the finite-difference simulation took 17 s per timestep or nearly 23 hours to complete the 120 s of simulated ground motion. More than a gigabyte of disk space was used to store the time history of the ground motion at the surface. (Storing the time history for the entire model would require up to a terabyte of disk space.)

To illustrate the development of the ground motion as the rupture propagates along the SAF we show snapshots of ground velocity (Fig. 3) over the 19,975 km2 rectangular area outlined in Fig. 1a. We consider only the 118 deg horizontal component that represents shaking in the direction parallel to the SAF (23). By 20 s, the S waves (green coloring) have entered San Fernando Valley. By 30 s, when the rupture has propagated about halfway along the SAF, the S waves have entered the main LA basin. The area near the I-5, I-405 freeway intersection shows intense (red) ground motion; this is due to resonance within this deep part of the SFV basin radiating secondary waves as seen by the faint circular wavefronts centered on this area at 40 s. At 40 s the ground motion in the LA basin has intensified: the SGV, just southeast of the I-10, I-605 intersection and the area just south of downtown LA show large amplitude ground motion (red). At 50 s the entire LA basin is excited by large amplitude surface waves. The rupture is almost complete by 60 s, at which time, the wavefronts in the basin slowly begin changing direction from southeast parallel to the long axis of the LA basin to the southwest. At 70 s the large amplitude waves are reflections from the steep northeast sides of the basin; the peaks and troughs of the waves align with the long axis of the basin and propagate west into the offshore area. This pattern persists, but is diminishing, through 100 s where only faint shadows mimic the larger amplitudes that existed 30 s before.

To encapsulate many of these effects we show a suite of seismograms and the shear wave velocity structure (Fig. 4) from the Ventura basin to the mountains east of San Clemente (Fig. 1a). By visually correlating the suite of seismograms with the shear wave velocity structure the effect of the basin on the amplitude and duration of shaking is clearly evident. The basin affects all three components of motion (Fig. 4, lower left quadrant) but primarily the component parallel (118 deg) to the axis of the trough. To examine the frequency content of the shaking we compare the Fourier spectral amplitudes of the 118 deg component for three sites (Fig. 4, lower right quadrant): 1) over the deepest part of the basin, 2) above the edge of the basin and 3) outside the basin. The maximum spectral amplitude for the edge site is a factor of 2 larger than for a site over the deepest part of the basin. The edge site has its spectral maximum at a higher frequency (0.25 Hz) compared to the site above the central basin where the first broad peak occurs around 0.16 Hz\013the fundamental resonant frequency of the LA basin (24). The spectral amplitude for a site at the edge of the basin is 10 times larger than the spectral amplitude for a site outside the basin even though both are at the same distance from the SAF (25).

Contours of the peak particle velocity over the 19, 975 km2 area reveal effects due to both rupture and structure (Fig. 5). The 118 deg component has its largest amplitudes near the fault and within the LA basin. The amplitudes near the fault were expected; the amplitudes (> 0.5 m/s) in the LA basin \01160 km from the fault were not. The 0.25 m/s contour basically outlines the SGV and LA basins. Moreover, there is a large area with amplitudes larger than 0.75 m/s corresponding to the deeper parts of the LA basin.

The large lobe with peak velocity greater than 0.75 m/s for the 28 deg component (Fig. 5) reflects the directivity of the rupture (4, 26) and the radiation pattern from the source (23) which combine to produce the maximum slip velocity 2.5 m/s. While we have concentrated on the effects within the LA basin, this component clearly shows that those areas in the forward direction of the rupture will be as severely shaken as LA. Most of the area with peak velocity greater than 0.75 m/s is confined to the less densely populated San Gabriel Mountains. However, the southeastern part of the 0.75 m/s lobe overprints the region in the populated Upper Santa Ana Valley (including cities such as Ontario, Pomona, Upland) and the San Bernardino Valley (including cities such as San Bernardino, Redlands). Because the fault passes just northwest of these areas, the severity of the shaking increases simply by proximity to the fault. The amplitude of the waves clearly attenuates with distance from the fault except for the amplification due to the LA basin where amplitudes on the 28 deg component also exceed 0.5 m/s.

The smallest of the three components is the vertical as expected from strike- slip motion on a vertical fault. However, like the horizontal components, the LA basin amplifies the vertical motion relative to the surrounding area. The net result is that the total ground motion in the LA region is much larger than would be predicted by a 1D model of earth structure (3, 13, 14). We illustrate this point by mapping the total cumulative kinetic energy (27) that takes into account the amplitude and duration of shaking for all three components of motion (Fig. 6). A large swath within 30 km of the SAF experiences significant shaking. The cumulative kinetic energy decreases with distance from the fault except for the basins, especially the LA basin\013where, for frequencies up to 0.4 Hz, the kinetic energy is equivalent to that near the fault. The expected attenuation with distance of the amplitude of the seismic waves (25) is counteracted by the basin structure.

Regardless of the frequency content, directivity, anelastic attenuation, and the component being shown, the ground velocity at certain parts in LA area exceeds 1.0 m/s; the LA basin is outlined by the 0.25 m/s contour of peak particle velocity with the central region delineated by the 0.75 m/s contour (Fig. 5). In other words, the level of ground velocity in the LA basin almost equals the level near the fault in spite of the fact that the main trough of the basin is about 60 km from the fault. These peak velocities are similar to those observed near the fault for some very damaging earthquakes (4, 26).

There are three extenuating circumstances: (i) The component of motion perpendicular to the fault (28 deg component), not shown, is 43% larger than the parallel component near the fault (Table 3). This perpendicular component is strongly amplified by directivity of the rupture and almost always has the maximum particle velocity (4, 26). However, the observed near-fault peak velocities are generally associated with pulses dominated by frequencies 1.0 Hz or less (4, 26) so that the lower frequency of 0.4 Hz may not be a critical factor. (ii) Because of computational limitations the maximum frequency is 0.4 Hz. Observed ground motions contain higher frequencies that will increase the amplitudes especially near the fault where anelastic material attenuation has less effect than for distances far from the fault (25). (iii) The minimum shear wave surficial velocity is 1.0 km/s. In a geotechnical sense all of the ground motion is for rock (28). Inclusion of the lower-velocity sediments will increase the ground motion amplitudes (27). The omission of higher frequencies and lower near-surface velocities in the simulation define our results as a lower bound for the expected ground motion for the simulated SAF rupture scenario.

Because of RAM and computer time limitations we could not include the lower-velocity sediments in the upper 100\055200 m of the basins nor extend the frequency band of ground motion beyond 0.4 Hz. The structures most affected by the computed ground motion are those that have their lowest-mode response with frequencies less than 0.4 Hz (periods 2.5 s or longer); almost all one- and two-story structures have their response at much higher frequencies (30).

Our kinematic rupture model is smooth in that the slip, slip rate and rupture velocity are constant everywhere on the fault. The slip and the slip rate have very plausible values (15) but could certainly be allowed to vary spatially with the effect of such variation larger on signal duration than amplitude (9). Almost certainly the rupture velocity varies over such a fault length. A variable rupture velocity would decrease the coherency of the waves leaving the fault. Whether this would increase or decrease the ground motion in LA is unknown. The strength in using low frequencies is that the results are dependent mostly on gross features, and not the details, of the structure and rupture kinematics. Our simulated low-frequency ground motion provides a baseline around which the ground motion from a real earthquake will deviate.

1. J. Dolan et al., Science 267, 199 (1995).

2. Working Group on California Earthquake Probabilities, Bull. Seism. Soc. Am.,
85, 379 (1995).

3. K. Olsen and R. Archuleta, 3-D Simulation of Earthquakes on the Los Angeles
Fault System, submitted to Bull. Seism. Soc. Am. (1995).

4. T. Heaton et al., Science, 267, 206 (1995).

5. The moment magnitude M (T. Hanks and H. Kanamori, J. Geophys. Res., 84,
2348 (1979)) was defined so that it may be uniformly applied to any size
earthquake. It is derived from the seismic moment: M = (2/3) log M0 \055 6.03 where
seismic moment M0 (K. Aki, Earthquake Res. Inst. Bull., 44, 73 (1966)) is given in
Nm. Seismic moment is defined as M0=\065As where \065 is the shear modulus, A is
the area of the fault over which slip has occurred and s is the average slip over
the area A. In our model the average material properties at the SAF are: density
2770 kg/m3, shear modulus 3.62 x 1010 N/m2 and shear wave velocity 3.59 km/s.

6. K. Sieh et al., J. Geophys. Res. 94, 603 (1989).

7. W. Ellsworth, in U. S. Geol. Surv. Prof. Pap. 1515, 153 (1990).

8. G. Jacoby et al., Science 241, 196 (1988), see note (7).

9. Previous simulations of the great 1857 earthquake have estimated displacements
for only a few locations in the LA area using a 1D velocity model (R. Butler and
H. Kanamori, Bull. Seism. Soc. Am., 70, 943 (1980); M. Bouchon and K. Aki, ibid.,
70, 1669). H. Kanamori (ibid., 69, 1645 (1979)) simulated the 1857 earthquake by
adding time lagged discrete subevents whose ground motion was modeled using
scaled data from the 1968 Borrego Valley M 6.7 earthquake. In each of these
papers the dominant ground motion is due to the longer period waves, and the
duration is primarily controlled by the time it takes for the rupture to propagate
from the hypocenter to the ends of the fault (fault length of 305-375 km).

10. P. Ehlig, in Calif. Div. Mines Geol. Spec. Rep. 118 pp. 177-186 (1975).

11. R. Yerkes et al., U. S. Geol. Surv. Prof. Pap. 420-A, (1965); T. Wright, in Active
Margin Basins : Am. Assoc. Pet. Geol. Mem. 52, K. T. Biddle, ed., 35 (1991).

12. D. Hadley and H. Kanamori, Geol. Soc. Am. Bull. 88, 1469 (1977).

13. J. Vidale and D. Helmberger, Bull. Seism. Soc. Am. 78, 122 (1988); K.
Yomogida and J. Etgen ibid. 83, 1325 (1993); R. Graves. Geophys. Res. Lett. 22, 101
(1995).

14. A. Frankel, Bull. Seism. Soc. Am. 83, 1020 (1993).

15. When an earthquake occurs, the two sides of the fault move in opposite
directions. In a strike-slip fault the primary movement is horizontal and parallel
to the fault line. A dextral offset occurs when the displacement of the fault block,
on the opposite side of the fault from the viewer, moves to the right. This is true
regardless of which side of the fault a person views the displacement. With an
average slip of 4.82 m we deduce a seismic moment of 4.75 x 1020 Nm giving M
7.75. The slip of 4.82 m is within the range of characteristic slip (4.5 \061 1.5 m) for
earthquakes on the Mojave segment but is slightly larger than the characteristic
slip (3.5 \061 1.0 m) on the San Bernardino segment (Working Group on California
Earthquake Probabilities, ibid., 85, 379 (1995)). Similarly the stress drop s for a
long strike-slip fault with width W is given by (L. Knopoff,
Geophys. J., 1, 44 (1958)) from which we deduce a stress drop of 69 bars\013a value
consistent with average earthquakes (H. Kanamori and D. Anderson, Bull.
Seism. Soc. Am. 65, 1073 (1975).

16. H. Magistrale et al., Seism. Res. Lett. 65, 39 (abstr.) (1994).

17. R. Yeats et al., in Santa Barbara and Ventura Basins, Coast Geological Society
Field Guide 64, A. Sylvester and G. Brown, eds., pp. 133-144 (1988).

18. H. Kawase and K. Aki, Bull. Seism. Soc. Am. 79, 1361 (1989).

19. A propagating rupture is analogous to a double zipper. The first zipper,
moving at the velocity of the rupture, unlocks the two sides of the fault. A
second zipper arrives later to lock the two sides of the fault that are now offset
with respect to each other. In the time between the two zippers the two sides of
the fault move relative to each other. The total amount of relative movement
before the second zipper locks the two sides is the offset or slip. The time it takes
for the slip to occur is the rise time. The slip divided by the rise time is slip rate,
i.e., how fast the slip occurs on the fault.

20. A. Levander, Geophysics 53, 1425 (1988).

21. K. Olsen, thesis, University of Utah (1994).

22. C. Cerjan et al., Geophysics, 50, 705 (1985); R. Clayton and B. Engquist, Bull.
Seism. Soc. Am. 71, 1529 (1977).

23. The movement of the ground is three dimensional and can be completely
described by examining it on three perpendicular axes. The natural choices are
along the vertical and two horizontal directions. We have chosen the headings
of 118 deg and 28 deg, parallel and perpendicular to the San Andreas, respectively, for
positive horizontal ground velocity. Earthquakes do not radiate waves
isotropically. The earthquake radiation pattern depends on the fault geometry
and the style of faulting. For our particular case the dominant shear wave
radiation pattern would look like the superposition of two four-leaf clovers. One
of the clovers would be aligned such that the fault trace bisected the fore and aft
clover with the other two perpendicular to the fault trace. The second clover
would be rotated such that its leaves would be oriented at 45\032 with respect to the
fault trace.

24. Y. Hisada et al., in Proc. Fourth Int. Conf. Seismic Zonation, Vol. II, Stanford
CA 245 (1991); A. Edelman and F. Vernon, unpublished report \063The Northridge
Portable Instrument Aftershock Data Set\062 (1995).

25. The amplitude of seismic waves can be attenuated by many different
mechanisms, but the primary mechanisms are geometrical spreading and
intrinsic attenuation. Geometrical spreading of the wave front attenuates the
amplitude as a direct result of conservation of energy. As the wavefront expands
with distance from the source, the energy is spread over a greater surface area
resulting in a smaller energy per unit area and accordingly a smaller amplitude.
A simple approximation to geometrical spreading for body waves is:
where A is the amplitude of the wave and R is the distance between the source
and the observer. For surface waves (Love and Rayleigh) the geometrical
attenuation is approximately: so that surface waves decay more slowly
than body waves. Intrinsic attenuation is the irreversible loss of wave energy
due to internal friction as the waves propagate through the medium. The
amplitude decay due to internal friction can be approximated by:
where f is frequency, t is the time it takes for a wave to travel from the source to
the observer, and Q is a measure of the energy loss due to internal friction. We
have omitted intrinsic attenuation in our simulation. However, comparison of
observed seismic data from the 17 January 1994 M 6.7 Northridge event to an
elastic simulation of the earthquake suggests that intrinsic attenuation has very
limited effects on ground motion for frequencies less than 0.4 Hz, as used in this
study.

26. The rupture directivity is an effect that modifies the energy in seismic waves
depending on the angle between the observation point and the direction of
rupture propagation (A. Ben-Menahem, Bull. Seism. Soc. Am. 51, 401 (1961)). It
increases the energy in the direction the rupture front propagates and decreases
the energy in the back direction. A seismic pulse in the forward direction
increases in amplitude and contracts in time; a seismic pulse in the back
direction decreases in amplitude and expands in time. The directivity effect
combined with the radiation pattern of S waves leads to large velocity pulses (on
the order of 1.0 m/s) in the forward direction of earthquake ruptures (R.
Archuleta and S. Hartzell, Bull. Seism. Soc. Am. 71, 939 (1981); R. Archuleta, J.
Geophys. Res., 89, 4559 (1984)).

27. The cumulative kinetic energy for each grid point (x,y) on the surface is
given by: where k is the component of motion, is
the density, is the velocity seismogram, and T is the duration of the
seismogram. The cumulative energy includes both the amplitude and duration
of the signal. The total energy is the sum of all three components:
.

28. There are many papers documenting the amplification of seismic waves due
to local near-surface geology, for example, K. Aki, Am. Soc. Civil Eng.: Proc. Spec.
Conf. Earthquake Eng. and Soil Dynamics, 2, 1, (1988).

29. The classification of soils and rock in geotechnical engineering depends on
the value of the shear wave velocity. A firm to hard rock has an average shear-
wave speed greater than 700 m/s (R. Borcherdt, Earthquake Spectra, 10, 617,
(1994)). The lowest surficial velocity in our model is 1.0 km/s (Table 2).

30. There are formulas for relating height of structures with the period of the
lowest-mode response. For example, with (Uniform
Building Code, International Conference of Building Officials, Whittier, CA,
1988), a 3.0 s period corresponds to a 377 ft high steel frame building. Such
formulas serve as a guides; more flexible buildings or buildings made of different
materials may be significantly shorter. For example, the Sherman Oaks building
has a lowest-mode period of 3 s (0.33 Hz) but is only 166 ft (13 stories) (Chapter 2,
Earthquake Spectra, Supplement C 11, 13 (1995)).

31. We are grateful to MIT\071s Earth Resources Laboratory for permission to use the nCUBE 2 parallel computer. We give special thanks to H. Magistrale for allowing us to use his 3D LA basin model and to S. Day for valuable advice on insertion of the double-couple source into the finite-difference scheme. This work was supported by the Southern California Earthquake Center (SCEC), USC 572726 through the NSF cooperative agreement EAR-8920136.

SE fault limit (lat., long.) | 34.089, -117.064 |

NW fault limit (lat., long.) | 34.808, -118.688 |

Hypocenter (lat., long.) | 34.800, -118.669 |

Hypocenter depth (km) | 10.0 |

Slip (m) | 4.82 |

Moment magnitude (M) | 7.75 |

Width, length (km) | 16.0, 170.0 |

Depth to top of fault (km) | 0.5 |

Dip, strike, rake (deg) | 90, 118, 180 |

Spatial discretization (km) | 0.4 |

Temporal discretization (s) | 0.025 |

Lowest P-wave velocity (km/s) | 2.41 |

Lowest S-wave velocity (km/s) | 1.00 |

Lowest Density (kg/m3) | 2070 |

Number of grid points along 118 deg | 576 436* |

Number of grid points along 28 deg | 352 288* |

Number of grid points along vertical | 116 |

Number of timesteps | 4800 |

Simulation time (s) | 120 |

* shown in Figures.

Component | Ground Motion Parameter | Near Fault | Basin |

118 deg | Peak particle velocity (m/s) | 1.74 | 1.37 |

28 deg | Peak particle velocity (m/s) | 2.49 | 0.70 |

Vertical | Peak particle velocity (m/s) | 0.91 | 0.54 |

118 deg | Cumulative kinetic energy (J-s) | 11408 | 11408 |

28 deg | Cumulative kinetic energy (J-s) | 12353 | 2341 |

Vertical | Cumulative kinetic energy (J-s) | 1616 | 1131 |