Geology topics
Publications and source records attributed to P. Spudich.
[No abstract available]
We study how heterogeneous rupture propagation affects the coherence of shear and Rayleigh Mach wavefronts radiated by supershear earthquakes. We address this question using numerical simulations of ruptures on a planar, vertical strike-slip fault embedded in a three-dimensional, homogeneous, linear elastic half-space. Ruptures propagate spontaneously in accordance with a linear slip-weakening friction law through both homogeneous and heterogeneous initial shear stress fields. In the 3-D homogeneous case, rupture fronts are curved owing to interactions with the free surface and the finite fault width; however, this curvature does not greatly diminish the coherence of Mach fronts relative to cases in which the rupture front is constrained to be straight, as studied by Dunham and Bhat (2008a). Introducing heterogeneity in the initial shear stress distribution causes ruptures to propagate at speeds that locally fluctuate above and below the shear wave speed. Calculations of the Fourier amplitude spectra (FAS) of ground velocity time histories corroborate the kinematic results of Bizzarri and Spudich (2008a): (1) The ground motion of a supershear rupture is richer in high frequency with respect to a subshear one. (2) When a Mach pulse is present, its high frequency content overwhelms that arising from stress heterogeneity. Present numerical experiments indicate that a Mach pulse causes approximately an ω −1.7 high frequency falloff in the FAS of ground displacement. Moreover, within the context of the employed representation of heterogeneities and over the range of parameter space that is accessible with current computational resources, our simulations suggest that while heterogeneities reduce peak ground velocity and diminish the coherence of the Mach fronts, ground motion at stations experiencing Mach pulses should be richer in high frequencies compared to stations without Mach pulses. In contrast to the foregoing theoretical results, we find no average elevation of 5%-damped absolute response spectral accelerations (SA) in the period band 0.05–0.4 s observed at stations that presumably experienced Mach pulses during the 1979 Imperial Valley, 1999 Kocaeli, and 2002 Denali Fault earthquakes compared to SA observed at non-Mach pulse stations in the same earthquakes. A 20% amplification of short period SA is seen only at a few of the Imperial Valley stations closest to the fault. This lack of elevated SA suggests that either Mach pulses in real earthquakes are even more incoherent that in our simulations or that Mach pulses are vulnerable to attenuation through nonlinear soil response. In any case, this result might imply that current engineering models of high frequency earthquake ground motions do not need to be modified by more than 20% close to the fault to account for Mach pulses, provided that the existing data are adequately representative of ground motions from supershear earthquakes.
In two previous articles we presented a formulation for inferring the strains and rotations of the ground beneath a seismic array having a finite footprint. In this article we derive expressions for the error covariance matrices of the inferred strains and rotations, and we present software for the calculation of ground strains, rotations, and their variances from short baseline array ground-motion data.
We present correction factors that may be applied to the ground motion prediction relations of Abrahamson and Silva, Boore and Atkinson, Campbell and Bozorgnia, and Chiou and Youngs (all in this volume) to model the azimuthally varying distribution of the GMRotI50 component of ground motion (commonly called 'directivity') around earthquakes. Our correction factors may be used for planar or nonplanar faults having any dip or slip rake (faulting mechanism). Our correction factors predict directivity-induced variations of spectral acceleration that are roughly half of the strike-slip variations predicted by Somerville et al. (1997), and use of our factors reduces record-to-record sigma by about 2-20% at 5 sec or greater period. ?? 2008, Earthquake Engineering Research Institute.
The 28 September 2004 Parkfield, California, earthquake (Mw 6.0) and four aftershocks (Mw 4.7-5.1) were recorded on 12 accelerograph stations of the U.S. Geological Survey Parkfield seismic array (UPSAR), an array of three-component accelerographs occupying an area of about 1 km2 located 8.8 km from the San Andreas fault. Peak horizontal acceleration and velocity at UPSAR during the mainshock were 0.45g and 27 cm/sec, respectively. We determined both time-varying and peak values of ground dilatations, shear strains, torsions, tilts, torsion rates, and tilt rates by applying a time-dependent geodetic analysis to the observed array displacement time series. Array-derived dilatations agree fairly well with point measurements made on high sample rate recordings of the Parkfield-area dilatometers (Johnston et al., 2006). Torsion Fourier amplitude spectra agree well with ground velocity spectra, as expected for propagating plane waves. A simple predictive relation, using the predicted peak velocity from the Boore-Atkinson ground-motion prediction relation (Boore and Atkinson, 2007) scaled by a phase velocity of 1 km/sec, predicts observed peak Parkfield and Chi-Chi rotations (Huang, 2003) well. However, rotation rates measured during Mw 5 Ito, Japan, events observed on a gyro sensor (Takeo, 1998) are factors of 5-60 greater than those predicted by our predictive relation. This discrepancy might be caused by a scale dependence in rotation, with rotations measured over a short baseline exceeding those measured over long baselines. An alternative hypothesis is that events having significant non-double-couple mechanisms, like the Ito events, radiate much stronger rotations than double-couple events. If this is true, then rotational observations might provide an important source of new information for monitoring seismicity in volcanic areas.
[1] We present a two-stage nonlinear technique to invert strong motions records and geodetic data to retrieve the rupture history of an earthquake on a finite fault. To account for the actual rupture complexity, the fault parameters are spatially variable peak slip velocity, slip direction, rupture time and risetime. The unknown parameters are given at the nodes of the subfaults, whereas the parameters within a subfault are allowed to vary through a bilinear interpolation of the nodal values. The forward modeling is performed with a discrete wave number technique, whose Green's functions include the complete response of the vertically varying Earth structure. During the first stage, an algorithm based on the heat-bath simulated annealing generates an ensemble of models that efficiently sample the good data-fitting regions of parameter space. In the second stage (appraisal), the algorithm performs a statistical analysis of the model ensemble and computes a weighted mean model and its standard deviation. This technique, rather than simply looking at the best model, extracts the most stable features of the earthquake rupture that are consistent with the data and gives an estimate of the variability of each model parameter. We present some synthetic tests to show the effectiveness of the method and its robustness to uncertainty of the adopted crustal model. Finally, we apply this inverse technique to the well recorded 2000 western Tottori, Japan, earthquake ( Mw 6.6); we confirm that the rupture process is characterized by large slip (3-4 m) at very shallow depths but, differently from previous studies, we imaged a new slip patch (2-2.5 m) located deeper, between 14 and 18 km depth.
Using a short-baseline seismic array (U.S. Geological Survey Parkfield Dense Seismograph Array [UPSAR]) about 12 km west of the rupture initiation of the 28 September 2004 M 6.0 Parkfield, California, earthquake, we have observed the movement of the rupture front of this earthquake on the San Andreas fault. The sources of high-frequency arrivals at UPSAR, which we use to identify the rupture front, are mapped onto the San Andreas fault using their apparent velocity and back azimuth. Measurements of apparent velocity and back azimuth are calibrated using aftershocks, which have a compact source and known location. Aftershock back azimuths show considerable lateral refraction, consistent with a high-velocity ridge on the southwest side of the fault. We infer that the initial mainshock rupture velocity was approximately the Rayleigh speed (with respect to slower side of the fault), and the rupture then slowed to about 0.66?? near the town of Parkfield after 2 sec. The last well-correlated pulse, 4 sec after S, is the largest at UPSAR, and its source is near the region of large accelerations recorded by strong-motion accelerographs and close to northern extent of continuous surface fractures on the southwest fracture zone. Coincidence of sources with preshock and aftershock distributions suggests fault material properties control rupture behavior. High-frequency sources approximately correlate with the edges of asperities identified as regions of high slip derived from inversion of strong-motion waveforms.
Numerous researchers have obtained estimates of slip-weakening distance, Dc, and fracture energy for recent earthquakes. Dc, is often observed to be a significant fraction of the total slip and tends to correlate with total slip. Although these observations may well be true of real earthquakes, we show that low-pass filtering of strong-motion seismograms can also produce some of these effects in inverted rupture models. We test the accuracy of Dc, estimates by calculating them in low-pass-filtered versions of models A and B of Guatteri and Spudich (2000). Models A and B are two different rupture models for a hypothetical M 6.5 earthquake, and they have nearly identical rupture time, slip, and stress-drop distributions, and nearly identical predicted seismograms, but Dc, for model B is about twice that for model A. By low-pass filtering slip models A and B at 1.0 Hz, we simulate the blurring effects of band-limited waveform inversions on these slip models. At each point on a fault, D???c is defined to be the slip at the time of the peak slip speed at that point. Low-pass filtering the slip models causes an upward bias in Dc inferred from stress-slip curves, and it causes an artificial correlation between D???c and the total slip. Low-pass filtering might also bias fracture energy high and radiated energy low. These biases should be considered when interpreting Dc derived from band-limited slip models of real earthquakes.
We consider the applicability of laboratory-derived rate-and state-variable friction laws to the dynamic rupture of the 1995 Kobe earthquake. We analyze the shear stress and slip evolution of Ide and Takeo's [1997] dislocation model, fitting the inferred stress change time histories by calculating the dynamic load and the instantaneous friction at a series of points within the rupture area. For points exhibiting a fast-weakening behavior, the Dieterich-Ruina friction law, with values of d c = 0.01–0.05 m for critical slip, fits the stress change time series well. This range of d c is 10–20 times smaller than the slip distance over which the stress is released, D c , which previous studies have equated with the slip-weakening distance. The limited resolution and low-pass character of the strong motion inversion degrades the resolution of the frictional parameters and suggests that the actual d c is less than this value. Stress time series at points characterized by a slow-weakening behavior are well fitted by the Dieterich-Ruina friction law with values of d c ≥0.01–0.05 m. The apparent fracture energy G c can be estimated from waveform inversions more stably than the other friction parameters. We obtain a G c ≈ 1.5×l0 6 J m −2 for the 1995 Kobe earthquake, in agreement with estimates for previous earthquakes. From this estimate and a plausible upper bound for the local rock strength we infer a lower bound for D c of about 0.008 m.
The Calaveras fault lies within a low velocity zone (LVZ) 1-2 km wide near Gilroy, California. Accelerographs G06, located in the LVZ 1.2 km from the Calaveras fault, and G07, 4 km from G06, recorded both the M 6.2 1984 Morgan Hill and the M 6.9 1989 Loma Prieta earthquakes. Comparison of the ground motions shows that a large 0.6-1.0 Hz velocity pulse observed at G06 during the Morgan Hill event may be amplified by focussing caused by the LVZ. Such amplified waves might be a mappable seismic hazard, and the zone of increased hazard can extend as much as 1.2 km from the surface trace of the fault. Finite-difference simulations of ground motions in a simplified LVZ model show a zone of amplified motion similar to the observations.
Dislocation models of the 1995 Hyogo-ken Nanbu (Kobe) earthquake derived by Yoshida et al. (1996) show substantial changes in direction of slip with time at specific points on the Nojima and Rokko fault systems, as do striations we observed on exposures of the Nojima fault surface on Awaji Island. Spudich (1992) showed that the initial stress, that is, the shear traction on the fault before the earthquake origin time, can be derived at points on the fault where the slip rake rotates with time if slip velocity and stress change are known at these points. From Yoshida's slip model, we calculated dynamic stress changes on the ruptured fault surfaces. To estimate errors, we compared the slip velocities and dynamic stress changes of several published models of the earthquake. The differences between these models had an exponential distribution, not gaussian. We developed a Bayesian method to estimate the probability density function (PDF) of initial stress from the striations and from Yoshida's slip model. Striations near Toshima and Hirabayashi give initial stresses of about 13 and 7 MPa, respectively. We obtained initial stresses of about 7 to 17 MPa at depths of 2 to 10 km on a subset of points on the Nojima and Rokko fault systems. Our initial stresses and coseismic stress changes agree well with postearthquake stresses measured by hydrofracturing in deep boreholes near Hirabayashi and Ogura on Awaji Island. Our results indicate that the Nojima fault slipped at very low shear stress, and fractional stress drop was complete near the surface and about 32% below depths of 2 km. Our results at depth depend on the accuracy of the rake rotations in Yoshida's model, which are probably correct on the Nojima fault but debatable on the Rokko fault. Our results imply that curved or cross-cutting fault striations can be formed in a single earthquake, contradicting a common assumption of structural geology.
No abstract available.
The Northridge earthquake caused 1.78 g acceleration in the east-west direction at a site in Tarzana, California, located about 6 km south of the mainshock epicenter. The accelerograph was located atop a hill about 15-m high, 500-m long, and 130-m wide, striking about N78°E. During the aftershock sequence, a temporary array of 21 three-component geophones was deployed in six radial lines centered on the accelerograph, with an average sensor spacing of 35 m. Station C00 was located about 2 m from the accelerograph. We inverted aftershock spectra to obtain average relative site response at each station as a function of direction of ground motion. We identified a 3.2-Hz resonance that is a transverse oscillation of the hill (a directional topographic effect). The top/base amplification ratio at 3.2 Hz is about 4.5 for horizontal ground motions oriented approximately perpendicular to the long axis of the hill and about 2 for motions parallel to the hill. This resonance is seen most strongly within 50 m of C00. Other resonant frequencies were also observed. A strong lateral variation in attenuation, probably associated with a fault, caused substantially lower motion at frequencies above 6 Hz at the east end of the hill. There may be some additional scattered waves associated with the fault zone and seen at both the base and top of the hill, causing particle motions (not spectral ratios) at the top of the hill to be rotated about 20° away from the direction transverse to the hill. The resonant frequency, but not the amplitude, of our observed topographic resonance agrees well with theory, even for such a low hill. Comparisons of our observations with theoretical results indicate that the 3D shape of the hill and its internal structure are important factors affecting its response. The strong transverse resonance of the hill does not account for the large east-west mainshock motions. Assuming linear soil response, mainshock east-west motions at the Tarzana accelerograph were amplified by a factor of about 2 or less compared with sites at the base of the hill. Probable variations in surficial shear-wave velocity do not account for the observed differences among mainshock acceleration observed at Tarzana and at two different sites within 2 km of Tarzana.
We address the following two questions. Can a microearthquake's ground motions be modeled by incident P and S waves that excite a site transfer-function that is a smooth function of incidence angle? Given recorded ground motions from a set of earthquakes having known locations and mechanisms, can we derive such a site transfer-function and use it to obtain the ground motions that would result from an earthquake source occurring somewhere in the same volume but having a location and mechanism that are different from the recorded events? Although many factors will cause two distinct microearthquake sources to have different seismograms at a common station, in this paper we concentrate only upon the differences caused by source mechanisms, P- and S-wave travel-time variations and by variations in the site transfer-function. We specifically exclude the effects of waves scattered from heterogeneities in the geologic structure away from the seismic site. We express the site transfer-function as a sum of several terms having simple dependences upon incidence angle and azimuth. Each term is an independent function of time. Given a set of seismograms observed at the site, we solve a linear system of equations for the time dependences of each term. These time series may be used to calculate the seismograms that would have resulted from an earthquake having arbitrary mechanism and location. This step is an interpolation. We have applied this technique to seismograms after aftershocks of the 1986 North Palm Springs earthquake. Our interpolation technique works fairly well within the volume occupied by the recorded events, but the method is not very successful at providing accurate seismograms for sources located outside the aftershock volume. The primary causes of the inaccuracy are the inadequacy of our chosen angular functions to model the site response fully and the likely scattering of seismic waves by geological heterogeneities (in this case, the Banning and Mission Creek faults) near the seismic stations. Our methods could be used to determine the effects of single scattering from lateral heterogeneities in geologic structure.
The Morgan Hill, California, earthquake (magnitude 6.1) of 24 April 1984 ruptured a 30-kilometer-long segment of the Calaveras fault zone to the east of San Jose. Although it was recognized in 1980 that an earthquake of magnitude 6 occurred on this segment in 1911 and that a repeat of this event might reasonably be expected, no short-term precursors were noted and so the time of the 1984 earthquake was not predicted. Unilateral rupture propagation toward the south-southeast and an energetic late source of seismic radiation located near the southeast end of the rupture zone contributed to the highly focused pattern of strong motion, including an exceptionally large horizontal acceleration of 1.29g at a site on a dam abutment near the southeast end of the rupture zone.