Showing papers in "Bulletin of the Seismological Society of America in 1982"

Fault zone models, heat flow, and the depth distribution of earthquakes in the continental crust of the United States

Abstract: Models of fault zones in continental crust, based on the analysis of rock deformation textures, suggest that the depth of seismic activity is controlled by the passage from a pressure-sensitive, dominantly frictional regime to strongly temperature-dependent, quasi-plastic mylonitization at greenschist and higher grades of metamorphism. Sufficient knowledge now exists concerning the frictional and rheological properties of quartz-bearing rocks to construct crude strength-depth curves for different geotherms. In such models, shear resistance peaks sharply at the inferred seismic-aseismic transition. The maximum depth of microseismic activity in various heat flow provinces of the conterminous United States generally correlates well with the frictional to quasi-plastic transition modeled for the different geotherms. Larger earthquakes ( M L > 5.5) also tend to nucleate near the base of the seismogenic zone. This region is postulated to have the highest concentration of distortional strain energy for stress levels at failure, and can be regarded as the prime asperity in crustal fault zones.

The standard error of the magnitude-frequency b value

Abstract: Estimated b values in log N = a − bM are widely used in seismicity comparisons and risk analysis, but uncertainties have been little explored. In this paper, the usual F probability density distribution for b is given and compared with an asymptotic form for temporally varying b . Convenient tables for the standard error of b are given that allow statistical tests to accompany investigations of both temporal and spatial variations of b . With large samples and slow temporal changes in b , the standard error of b is σ ( b ^ ) = 2.30 b 2 σ ( M _ ) , where σ 2 ( M _ ) = ∑ i − 1 n ( M i − M _ ) 2 / n ( n − 1 ) . In an example from central California, stable estimates of b require a space-time window containing about 100 earthquakes. From 1952 to 1978, the average b and 90 per cent confidence limits are 0.95 (+0.94, −0.30). Some fluctuations of b are statistically significant but some are not. Within 90 per cent confidence limits, b changes from a low of 0.60 (+0.11, −0.09) in 1955 to a high of 1.39 (+0.25, −0.21) in 1967 and drops to 0.72 (+0.13, −0.10) in 1975. In this example, no correlation between large earthquakes ( M > 5) and b variations occurred.

Automatic phase pickers: Their present use and future prospects

Abstract: Automatic phase-picking algorithms are designed to detect a seismic signal on a single trace and to time the arrival of the signal precisely. Because of the requirement for precise timing, a phase-picking algorithm is inherently less sensitive than one designed only to detect the presence of a signal, but still can approach the performance of a skilled analyst. A typical algorithm filters the input data and then generates a function characterizing the seismic time series. This function may be as simple as the absolute value of the series, or it may be quite complex. Event detection is accomplished by comparing the function or its short-term average (STA ) with a threshold value (THR), which is commonly some multiple of a long-term average (LTA) of a characteristic function. If the STA exceeds THR, a trigger is declared. If the event passes simple criteria, it is reported. Sensitivity, expected timing error, false-trigger rate, and false-report rate are interrelated measures of performance controlled by choice of the characteristic function and several operating parameters. At present, computational power limits most systems to one-pass, time-domain algorithms. Rapidly advancing semi-conductor technology, however, will make possible much more powerful multi-pass approaches incorporating frequency-domain detection and pseudo-offline timing.

Scaling laws for large earthquakes: Consequences for physical models

Abstract: It is observed that the mean slip in large earthquakes is linearly proportional to fault length and does not correlate with fault width. This observation is interpreted in the light of the two possible classes of models for large earthquakes: W models, in which stress drop and slip are determined by fault width, and L models, in which these parameters are fundamentally determined by fault length. In the W model interpretation, stress drop systematically increases with L/W , the aspect ratio, and, as a consequence, seismic moment. The correlation of slip with length means that the rupture length is determined by the dynamic stress drop. This conflicts with the observation that the length of large earthquakes is often controlled by adjacent rupture zones of previous earthquakes or by tectonic obstacles. It also conflicts with the observations for small earthquakes that stress drop is nearly constant and does not correlate with source radius over a broad range. In the L model interpretation, the correlation between slip and length means that stress drop is constant, namely about 7.5, 12, and 60 bars for interplate strike-slip, thrust, and Japanese intraplate earthquakes, respectively. L models require that the fault be mechanically unconstrained at the base. W models predict that mean particle velocity increases with fault length, but rise time is constant. L models predict the opposite.

Three-dimensional simulation of spontaneous rupture: The effect of nonuniform prestress

Abstract: We use a finite difference method to study crack propagation in a three-dimensional continuum, for conditions of both uniform and nonuniform prestress. The rupture criterion employed satisfies two fundamental physical requirements: it ensures finite stresses in the continuum and finite energy dissipation in crack extension. The finite stress numerical simulations exhibit abrupt jumps in rupture velocity when sharp changes in prestress are encountered on the crack plane, behavior analogous to that predicted theoretically for two-dimensional, singular cracks. For uniform prestress conditions, the slip velocity function is approximately a low-pass filtered version of that of a singular, constant rupture velocity crack. For nonuniform prestress, spatial variations of peak slip velocity are strongly coupled to spatial variations of rupture velocity. For uniform prestress and low cohesion, rupture velocity is predicted to exceed the S -wave velocity in directions for which mode II (inplane) crack motion dominates. A subshear rupture velocity is predicted for directions of predominantly mode III (antiplane) crack motion. Introduction of stress heterogeneities is sufficient, in each of the three cases studied, to reduce average rupture velocity to less than the S velocity, but local supershear rupture velocities can still occur in regions of high prestress. Rupture models with significant segments of supershear propagation velocities may be consistent with seismic data for some large earthquakes, even where average rupture velocity can be reliably determined to be subshear.

Finite faults and inverse theory with applications to the 1979 Imperial Valley earthquake

Abstract: Using a representation theorem from elastodynamics, subsurface slip on a known fault is formulated as the solution to an inverse problem in which recorded surface ground motion is the data. Two methods of solution are presented: the least-squares method, which minimizes the squared differences between theory and data, and the constrained least-squares method which simultaneously maintains a set of linear inequalities. Instabilities in the solution are effectively eliminated in both methods, and the sensitivity of the solution to small changes in the data is quantitatively stated. The inversion methodology is applied to 77 components of near-field ground acceleration recorded during the 15 October 1979 Imperial Valley earthquake. The faulting is constrained to propagate bilaterally away from the epicenter at an average velocity of 90 per cent of the shear wave speed on a vertical fault plane extending from the surface to 10 km depth. Inequality constraints are used to keep the faulting sequence physically reasonable by maintaining right-lateral motion and positive slip velocity. The preferred solution is stable and provides a good fit to the data; it is also realistic and consistent with observed surface offsets and independent estimates of seismic moment

Variable rupture mode of the subduction zone along the ecuador-colombia coast

Abstract: Three large earthquakes occurred within the rupture zone of the 1906 Colombia-Ecuador earthquake (M_W = 8.8): in 1942 (M_S = 7.9); 1958 (MS = 7.8); and 1979 (M_S = 7.7). We compared the size and mechanism of these earthquakes by using long-period surface waves, tsunami data, and macroseismic data. The 1979 event is a thrust event with a seismic moment of 2.9 × 10^(28) dyne-cm, and represents subduction of the Nazca plate beneath South America. The rupture length and direction are 230 km and N40°E, respectively. Examination of old seismograms indicates that the 1906 event is also a thrust event which ruptured in the northeast direction. The seismic moment estimated from the tsunami data and the size of the rupture zone is 2 × 10^(29) dyne-cm. The 1942 and 1958 events are much smaller (about 1/5 to 1/10 of the 1979 event in the seismic moment) than the 1979 event. We conclude that the sum of the seismic moments of the 1942, 1958, and 1979 events is only Formula of that of the 1906 event despite the fact that the sequence of the 1942, 1958, and 1979 events ruptured approximately the same segment as the 1906 event. This difference could be explained by an asperity model in which the fault zone is held by a discrete distribution of asperities with weak zones in between. The weak zone normally behaves aseismically, but slips abruptly only when it is driven by failure of the asperities. A small earthquake represents failure of one asperity, and the rupture zone is pinned at both ends by adjacent asperities so that the effective width and the amount of slip are relatively small. A great earthquake represents failure of more than one asperity, and consequently involves much larger width and slip.

Body-wave seismograms in inhomogeneous media using Maslov asymptotic theory

Abstract: Asymptotic ray theory is widely used to describe body waves in inhomogeneous media, but caustics, shadows, critical points, etc. have to be treated as special cases. Unfortunately, these singularities are often the points of greatest interest as they are caused by inhomogeneities in the model. Transform methods, e.g., the reflectivity method and WKBJ seismograms, are used to investigate waves at these singular points but are restricted to laterally homogeneous media. Maslov asymptotic theory uses the ideas of asymptotic ray theory and transform methods, combining the advantages—simplicity and generality—of both techniques. In this paper, Maslov asymptotic theory is developed for the computation of body-wave seismograms. The eikonal equation of asymptotic ray theory is equivalent to Hamilton9s canonical equations, and the ray trajectories can be considered in the phase space of position and slowness. Normal asymptotic ray theory gives the wave solution in the spatial domain. However, the asymptotic solution for other generalized coordinates in phase space can also be found. For instance, normal transform methods find the solution in the mixed domain where the horizontal slowness replaces the coordinate. Maslov asymptotic theory extends this idea to inhomogeneous media, and the asymptotic solution in a mixed domain (position and slowness) is obtained by a canonical transformation from the spatial domain. The method is useful as the singularities in the mixed and spatial domains are at different locations, and Maslov theory provides a uniform result, combining the solutions in the different domains. These transforms between the mixed-frequency and spatial-time domains are evaluated exactly using the WKBJ seismogram algorithm. This avoids the oscillatory integrals of asymptotic theory and stabilizes the numerical solution by providing the smoothed, discrete seismograms directly. The result is a rigorous but simple method for computing body-wave seismograms in inhomogeneous media. The theory is developed in outline, and numerical examples are included.

Three-dimensional finite difference simulation of fault dynamics: Rectangular faults with fixed rupture velocity

Abstract: We analyze three-dimensional finite difference solutions for a simple shear-crack model of faulting to determine the effects of fault length and width on the earthquake slip function. The fault model is dynamic, with only rupture velocity, fault dimensions, and dynamic stress-drop prescribed. The numerical solutions are accurate for frequencies up to 5 Hz, and are combined with asymptotic results for shear cracks in order to characterize the slip function at higher frequencies. Near the hypocenter, the slip velocity exhibits a square-root singularity whose intensity increases with hypocentral distance. At distances greater than the fault width, w , growth of the velocity intensity ceases, and the slip function becomes nearly invariant with distance along the fault length. Closed-form expressions are developed for the dependence of static slip ( s ∞), slip rise time ( TR ), and slip velocity intensity ( V ) on fault geometry. Along the center line of a long, narrow fault, at hypocentral distances exceeding w , these expressions reduce to s ∞ ≈ w Δτ/μ, TR ≈ 0.5 w/vR , and V ≈ √ w /2 vR Δτ/μ, where Δτ is the dynamic stress drop, μ the shear modulus, and vR the rupture velocity. The numerical results imply that uniform-dislocation kinematic earthquake models in which slip is represented by a ramp time function will underpredict high-frequency ground motion relative to low-frequency ground motion. A further implication of the numerical solutions is that the nature of inelastic processes at the advancing edge of a long fault will depend on fault width, but will be independent of rupture length.

Dynamic loads in the interior of a layered stratum: An explicit solution

Abstract: This paper presents an explicit, closed-form solution for the Green functions (displacements due to unit loads) corresponding to dynamic loads acting on (or within) layered strata. These functions embody all the essential mechanical properties of the medium and can be used to derive solutions to problems of elastodynamics, such as scattering of waves by rigid inclusions, soil-structure interaction, seismic sources, etc. The solution is based on a discretization of the medium in the direction of layering, which results in a formulation yielding algebraic expressions whose integral transforms can readily be evaluated. The advantages of the procedure are: (a) the speed and accuracy with which the functions can be evaluated (no numerical integration necessary); (b) the potential application to problems of elastodynamics solved by the boundary integral method; and (c) the possibility of comparing and verifying numerical integral solutions implemented in computer codes.

Estimates of Q in central Asia as a function of frequency and depth using the coda of locally recorded earthquakes

Abstract: Digital recordings of microearthquake codas from shallow and intermediate depth earthquakes in the Hindu Kush region of Afghanistan were used to determine the attenuation factors of the S -wave coda ( Qc ) and primary S waves ( Qβ ). An anomalously rapid decay of the coda shortly after the S -wave arrival, observed also in a study of coda in central Asia by Rautian and Khalturin (1978), seems to be due primarily to depth-dependent variations in Qc . In particular, we deduce the average Qc in the crust and uppermost mantle (<100-km depth) is approximately four times lower than the deeper mantle (<400-km depth) over a wide frequency range (0.4 to 24 Hz). Further, while Qc generally increases with frequency at any depth, the degree of frequency dependence of Qc depends on depth. Except at the highest frequency studied here (∼48 Hz), the magnitude of Qc at a particular frequency increases with depth while its frequency dependence decreases. For similar depths, determinations of Qβ and Qc agree, suggesting a common wave composition and attenuation mechanism for S waves and codas. Comparison of these determinations of Qc in Afghanistan with those in other parts of the world shows that the degree of frequency dependence of Qc correlates with the expected regional heterogeneity. Such a correlation supports the prejudice that Qc is primarily influenced by scattering and suggests that tectonic processes such as folding and faulting are instrumental in creating scattering environments.

The leaf-spring seismometer: Design and performance

Abstract: A small vertical seismometer whose inertial mass is supported by a leaf spring has been developed as a replacement for conventional long-period (LP) seismometers. The mechanical sensor has a virtually infinite natural period and is operated in a force-balance feedback configuration with an overall response identical to that of a 20-sec LP seismometer. Main considerations in the design were economic production and efficient shielding against environmental disturbances. The sensor is thermally coupled to the ground and protected from atmospheric pressure variations by a vacuum bell. This allows increasing the useful gain at very long periods by two orders of magnitude compared to a standard LP seismograph. The instruments resolve ground noise at least from a 0.3- to 300-sec period (typically, from about 0.1 to 3000 sec) and have a dynamic range of 140 dB. Leaf-spring seismometers have been tested since 1976 as part of wideband, LP, and very LP seismographs. Matching horizontal sensors are also available. This paper discusses the design principles and the initial calibration, and presents test results and typical seismograms.

Effect of surface topography on the diffraction of P, SV, and Rayleigh waves

Abstract: A generalized inverse method for approximate boundary conditions is adapted for boundary value problems in elastic wave propagation. The diffraction of P, SV , and Rayleigh waves at the vicinity of a semi-elliptical canyon is considered. The effects of mode conversion from compressional to shear waves, or vice versa, are examined in detail. The maximum amplification for each plane wave is also studied.

The energy release in earthquakes

Abstract: Energy calculations are generally made through an empirical application of the familiar Gutenberg-Richter energy-magnitude relationships. The precise physical significance of these relationships is somewhat uncertain. We make use here of the recent improvements in knowledge about the earthquake source to place energy measurements on a sounder physical basis. For a simple trapezoidal far-field displacement source-time function with a ratio x of rise time to total duration T_0, the seismic energy E is proportional to [1/ x(1 - x)^2] M_0^2/T_0^3, where M_0 is seismic moment. As long as x is greater than 0.1 or so, the effect of rise time is not important. The dynamic energies thus calculated for shallow events are in reasonable agreement with the estimate E ≅ (5 × 10^(−5))M_0 based on elastostatic considerations. Deep events, despite their possibly different seismological character, yield dynamic energies which are compatible with a static prediction similar to that for shallow events. Studies of strong-motion velocity traces obtained near the sources of the 1971 San Fernando, 1966 Parkfield, and 1979 Imperial Valley earthquakes suggest that, even in the distance range of 1 to 5 km, most of the radiated energy is below 1 to 2 Hz in frequency. Far-field energy determinations using long-period WWSSN instruments are probably not in gross error despite their band-limited nature. The strong-motion record for the intermediate depth Bucharest earthquake of 1977 also suggests little teleseismic energy outside the pass-band of a long-period WWSSN instrument.

Tidal triggering of earthquakes

Abstract: Analysis of the tidal stress tensor at the time of moderate to large earthquakes strongly suggests that shallow (< 30 km) larger magnitude oblique-slip and dip-slip earthquakes are triggered by tidal stresses. No corresponding triggering effect is seen for shallow strike-slip earthquakes or for any type of intermediate or deep focus earthquakes which have been studied. Tidal triggering is also discussed from the viewpoint of the ‘dilatancy-diffusion’ model. Specifically, the model as usually stated, excludes the possibility of small earthquakes being tidally triggered.

The 1971 San Fernando earthquake: A double event?

Abstract: Evidence is presented which suggest that the 1971 San Fernando earthquake may have been a double event that occurred on two separate, subparallel thrust faults. It is postulated that the initial event took place at depth on the Sierra Madre fault zone which runs along the base of the San Gabriel Mountains. Rupture is postulated to have occurred from a depth of about 15 km to a depth of about 3 km. A second event is thought to have initiated about 4 sec later on another steeply dipping thrust fault which is located about 4 km south of the Sierra Madre fault zone. The surface trace of this fault coincides with the San Fernando fault zone which was the principal fault associated with surface rupture. It is postulated that rupture propagated from a depth of 8 km to the free surface. The moments of the first and second events are approximately 0.7 × 10^(26) dyne-cm and 1.0 × 10^(26) dyne-cm, respectively. This model is found to explain the combined data sets of strong ground motions, teleseismic P and S waveforms, and static offsets better than previous models, which consist of either a single fault plane or a plane having a dip angle which shallows with decreasing depth. Nevertheless, many features of the observed motions remain unexplained, and considerable uncertainty still exists regarding the faulting history of the San Fernando earthquake.

Spectral attenuation of SH waves along the Imperial fault

Abstract: Spectral attenuation of SH waves has been studied to infer Q along the Imperial fault. The data set consists of six aftershocks of the Imperial Valley earthquake (15 October 1979, M L = 6.6) digitally recorded up to a distance of 51 km. Although there is large variance in Q −1 due to scatter in the data, Q below 3.75 km appears to be a function of frequency (increasing from about 60 at 3 Hz to 500 at 25 Hz). High Q values obtained at high frequencies strongly suggest that scattering has not removed a significant amount of energy from the signals and thus, the observed result, Q varying with frequency, is not due to scattering. For sources below 4 km the observed average SH -wave spectral amplitudes, A ( f, R ) along the fault can be fit by A ( f , R ) = S ( f ) R e − π f t * e − π f t / Q ( f ) where f is frequency, R is hypocentral distance, S(f) is source factor, Q ( f ) is quality factor below about 3.75 km, and t is travel time up to 3.75 km below the surface. The value of t * for the upper 3.75 km is probably between 0.027 and 0.047 (average Q between 100 and 60) depending upon the falloff of S ( f ) with f ( f −3 or f −2 ) beyond the corner frequency.

Dynamic faulting studied by a finite difference method

Abstract: We have developed a finite difference method that is especially adapted to the study of dynamic shear cracks. We studied a number of simple earthquake source models in two and three dimensions with special emphasis on the modeling of the stress field. We compared our numerical results for semi-infinite and self-similar shear cracks with the few exact solutions that are available in the literature. We then studied spontaneous rupture propagation with the help of a maximum stress criterion. From dimensional arguments and a few simple examples, we showed that the maximum stress criterion depended on the physical dimensions of the fault. For a given maximum stress intensity, the finer the numerical mesh, the higher the maximum stress that had to be adopted. A study of in-plane cracks showed that at high rupture velocities, the numerical results did not resolve the stress concentration due to the rupture front from the stress peak associated with the shear wave propagating in front of the crack. We suggest that this is the reason why transonic rupture velocities are found in the numerical solutions of in-plane faulting when the rupture resistance is rather low. Finally, we studied the spontaneous propagation of an initially circular rupture. Two distinct modes of nucleation of the rupture were studied. In the first, a plane circular shear crack was formed instantaneously in a uniformly prestressed medium. After a while, once stress concentrations had developed around the crack edge, the rupture started to grow. In the second type of nucleation, a preexisting circular crack became unstable at time t = 0 and started to grow. The latter model appeared to us as a more realistic simulation of earthquake triggering. In this case, the initial stress was nonuniform and was the static field of the preexisting fault.

Strain, tilt, and rotation associated with strong ground motion in the vicinity of earthquake faults

Abstract: In the absence of near-field records of differential ground motion induced by earthquakes, we simulate the time histories of strain, tilt, and rotation in the vicinity of earthquake faults embedded in layered media. We consider the case of both strike-slip and dip-slip fault models and study the effect of different crustal structures. The maximum rotational motion produced by a buried 30-km-long strike-slip fault with slip of 1 m is of the order of 3 × 10 −4 rad while the corresponding rotational velocity is about 1.5 × 10 −3 rad/sec. A simulation of the San Fernando earthquake yields maximum longitudinal strain and tilt a few kilometers from the fault of the order of 8 × 10 −4 and 7 × 10 −4 rad. These values being small compared to the amplitude of ground displacement, the results suggest that most of the damage occurring in earthquakes is caused by translation motions. We also show that strain and tilt are closely related to ground velocity and that the phase velocities associated with strong ground motions are controlled by the rupture velocity and the basement rock shearwave velocity.

The empirical prediction of ground motion

Abstract: Recent additions to the strong-motion data set, primarily from earthquakes in California and Italy, are responsible for a large number of papers examining the prediction of ground-motion measures using regression methods. Peak acceleration is still the most common measure being considered, but increasing attention is being given to peak velocity and spectral amplitudes. Although direct comparisons among the studies are hampered by differing definitions of distance and magnitude, in general the various studies give similar answers for peak acceleration in the region of distance and magnitude space in which most of the data are concentrated. As might be expected, the differences are most pronouced for large magnitudes and distances close to the fault, where data are few. Even so, widely differing assumptions about the form of the regression equation and differences in the composition and weighting of the data set can give similar answers. This was true in recent studies by Campbell (1981b) and Joyner and Boore (1981), where the predicted accelerations for large earthquakes at close distances differed by less than 40 per cent. This seemingly large uncertainty is small compared to the scatter in the data about the regression lines. A Monte Carlo study shows that the question of whether the shape of the attenuation curves is magnitude-dependent cannot be resolved by existing data.

Test ban treaty verification with regional data—A review

Abstract: This paper summarizes the use of regional (Δ ≦ 30°) seismic data in a test ban context for detecting, locating, identifying, and determining the yield of underground nuclear explosions. In many areas of the world (Eastern North America, Africa, Eastern USSR), Lg is the largest amplitude wave recorded on standard seismograph systems and thus is the most appropriate phase for monitoring small magnitude events. Excellent location capability for near-regional events has been demonstrated at the Norwegian small aperture array (NORESS) using Lg and P waves. Lg and other regional phases may contain information on source depth, but such information has not been exploited to date. Fifteen classes of regional discriminants have been identified including 1. 1. First Motion 2. 2. Ms : mb 3. 3. P2 / P1 Ratio 4. 4. Excitation of Short-Period SH Waves 5. 5. Lg/Rg Amplitude Ratios 6. 6. Pn/Lg, Pg/Lg , and Pmax/Lg Amplitude Ratios 7. 7. Lg Group Velocity and Energy Ratios in Lg 8. 8. Excitation of Sn 9. 9. Third Moment of Frequency 10. 10. Generation of Higher Mode Surface Waves 11. 11. Peak Amplitudes of Love and Rayleigh Waves and Long-Period Surface Wave Energy Density 12. 12. Prevailing Period of Long-Period Love Waves 13. 13. Spectral Ratio—Long-Period S Waves to Rayleigh Waves 14. 14. Spectral Ratio—Long-Period Love Waves to Rayleigh Waves 15. 15. Frequency of the Peak Spectral Amplitudes and Spectral Ratios in Pn, Pg, S , and Lg . Each of these proposed discriminants has, with differing degrees of success, separated some explosions from some earthquakes. However, most have been tested only on limited data, usually from one geographic region and only one or two recording stations. No systematic analyses have been done to determine the best individual discriminant or combination of them. Preliminary evaluation of the use of Lg for yield determination suggests that regional waves hold promise in this application. Theoretical studies have contributed significantly to the understanding of propagation characteristics of regional waves but further studies are required emphasizing modeling for realistic anisotropic sources. The major conclusion of this study is that a systematic and comparative evaluation of all the proposed regional discriminants is now required, utilizing a common data base derived from all present-day test sites. This evaluation would suggest the optimal discrimination procedure using regional waves, and would also define areas of needed research. Without such an integrated evaluation, it is still possible to speculate, using existing results, on the most promising regional discriminants.

Strong-motion modeling of the imperial valley earthquake of 1979

Abstract: Twelve three-component strong-motion displacement records are modeled for the 1979 Imperial Valley earthquake to recover the distribution of slip on the Imperial fault plane. The final model, for which point source responses are calculated by a discrete wavenumber/finite element technique, uses a structure with gradients in material properties rather than layers. The effects of a velocity gradient are investigated by comparing synthetics with a layer-over-a-half-space model using generalized rays. It is shown that a uniform fault rupture model on a rectangular fault plane does not explain the data. The preferred fault model has slip concentrated below 5 km (in the basement material) and between the epicenter (5 km south of the international border) and Highway 80. Within this region, there appears to be two localized areas of larger dislocations; one just north of the border near Bonds Corner and a second under Interstate 8 at Meloland Overpass. A major arrival associated with large amplitude vertical accelerations (up to 1.7 g) is identified in the El Centro array records. This arrival has an S-P time of approximately 2.3 sec at many of the array stations and is modeled as originating from a localized source 8 km to the south of the array. The moment is estimated to be 5.0 × 10^(25) dyne-cm from the strong-motion records, which is consistent with teleseismic body-wave estimates. The preferred fault model is strike-slip with a 90° dip. The average strike is 143°. However to explain vertical waveforms near the fault trace, a corrugated or wiggly fault plane is introduced. The average rupture velocity is in the range 2.5 to 2.7 km-sec (0.8 to 0.9 times the basement shear-wave velocity). The preferred model has unilateral rupture propagation to the north, although the data would allow a small amount of propagation to the south. The estimated stress drop for the entire fault plane is only 5 to 10 bars; however, the stress drop over the more localized sources is about 200 bars. The fault model is consistent with the pattern of seismicity and observations of aseismic creep in the Imperial Valley and suggests that the southern half of the Imperial fault acts as a locked section which breaks periodically.

The effect of attenuation on seismic body waves

Abstract: Both spectral and time domain studies indicate that the frequency dependence and regional variation of the attenuation of P waves parallels that of S waves with t * β = 4 t * α . Scattering Q cannot be generally separated from intrinsic Q in the mantle. Forward scattering can generate time-dependent variations in the frequency content and complexity of body waves that affect the measurement of t * . Assuming that lateral heterogeneity biases the apparent Q of surface waves, the frequency dependence of Q can be explained by a relaxation model of intrinsic Q . In this model, Q is constant with frequency up to a cutoff frequency 1/(2πτ m ) Hz, where τ m = 0.1 to 0.2 sec. Regional variations in mantle attenuation are consistent with radiometric or magnetic age and tectonic activity, regions of higher relative attenuation coincident with younger, tectonically active crust. Continental cratons are underlain by mantle having small attenuation at all depths. High attenuation usually correlates with slow travel times, lower Pn velocity, and inefficient Pn and Sn propagation. Measures of differential frequency content (δt * and δ Q ) generally correlate better with differential travel time than measures of differential amplitude and m b . The regional pattern and intensity of both travel-time anomalies and t * measurements suggest that both share a common origin due to the regional variation of the thermal structure of the upper 200 to 400 km of the mantle.

The effects of attenuation and site response on the spectra of microearthquakes in the northeastern Caribbean

Abstract: The spectra of microearthquakes recorded by a seismic network in the northeastern Caribbean were analyzed to determine the effects of attenuation and site response on these spectra. The ratios of the spectral amplitudes at 5 and 20 Hz were measured for several earthquakes at different distances from a fixed receiver to estimate Q for P and S waves in the crust and upper mantle. The average Q p determined from three stations was 380 for epicentral distances between 40 and 200 km. The average Q s determined from two stations was estimated at 400. Spectra of earthquakes closer than 40 km to one station indicate that a high Q path ( Q > 800) exists for these short distances in the island arc platform. The near equivalence of Q p and Q s observed in this study of the upper lithosphere contrasts with estimates of Anderson et al. (1965) that Q p = 9/4 Q s in the asthenosphere. This finding that Q p is approximately equal to Q s suggests that the attenuation mechanism in the upper lithosphere differs from that in the asthenosphere. The spectra of nearby microearthquakes unaffected by crustal attenuation display corner frequencies which are uniform despite large differences in the seismic moments of the events. The corner frequencies of these spectra appear to be characteristic of the receiver site and insensitive to the location and moment of the earthquakes. At one station, the S -wave corner frequency of a nearby blast was identical to the corner frequency of a magnitude 4.8 earthquake derived from the record of a strong motion accelerograph at the same site.

A boundary method for elastic wave diffraction: Application to scattering of SH waves by surface irregularities

Abstract: A boundary method developed by Herrera is briefly explained in connection with wave scattering. The method is based on the use of complete systems of solutions of the homogeneous equations. A convenient criterion of completeness is the notion of c -completeness. The general method grants convergence of the approximating sequence when a least-squares fitting of the boundary conditions is used. As an illustration, the scattering and diffraction of SH waves by surface irregularities is treated here. It is shown that plane waves are c -complete in a bounded region of arbitrary shape. Scattering is formulated as a problem of connecting solutions in such a region with solutions in an unbounded one where Hankel functions are used. Numerical results for specific cases are reported.

A dynamic model for far-field acceleration

Abstract: A model for the far-field acceleration radiated by an incoherent rupture is constructed by combining Madariaga9s (1977) theory for the high-frequency radiation from crack models of faulting with a simple statistical source model. By extending Madariaga9s results to acceleration pulses with finite durations, the peak acceleration of a pulse radiated by a single stop or start of a crack tip is shown to depend on the dynamic stress drop of the subevent, the total change in rupture velocity, and the ratio of the subevent radius to the acceleration pulse width. An incoherent rupture is approximated by a sample from a self-similar distribution of coherent subevents. Assuming the subevents fit together without overlapping, the high-frequency level of the acceleration spectra depends linearly on the rms dynamic stress drop, the average change in rupture velocity, and the square root of the overall rupture area. The high-frequency level is independent, to first order, of the rupture complexity. Following Hanks (1979), simple approximations are derived for the relation between the rms dynamic stress drop and the rms acceleration, averaged over the pulse duration. This relation necessarily depends on the shape of the body-wave spectra. The body waves radiated by 10 small earthquakes near Monticello Dam, South Carolina, are analyzed to test these results. The average change of rupture velocity of Δ v = 0.8 β associated with the radiation of the acceleration pulses is estimated by comparing the rms acceleration contained in the P waves to that in the S waves. The rms dynamic stress drops of the 10 events, estimated from the rms accelerations, range from 0.4 to 1.9 bars and are strongly correlated with estimates of the apparent stress.

Statistical characterization of strong ground motions using power spectral density function

Abstract: The spectral content and duration of some 140 strong-motion accelerograms are studied with an aim of quantifying the uncertainty of ground motion representation. Ground motions are characterized by the parameters of the Kanai-Tajimi spectral density function and by the strong-motion duration. Parameters are estimated for each record based on the method of spectral moments. The statistics and dependencies of the parameters are evaluated, and in particular, correlations between the Kanai-Tajimi parameters, peak ground acceleration, epicentral distance, and local magnitude are investigated. The findings constitute the basis for characterizing seismic input for the purpose of safety assessment of constructed facilities.

Crustal structure of the Diablo and Gabilan Ranges, central California: A reinterpretation of existing data

Abstract: The compressional-wave velocity structure of the crust of the Coast Ranges of central California was modeled from seismic refraction data reported previously. For both the Diablo Range (east of the San Andreas fault) and the Gabilan Range (west of the fault), two alternative velocity models were derived for each range by iterative two-dimensional ray tracing. Each pair of models shows a sedimentary layer and an underlying crust composed of three or four layers. For the Diablo Range, the velocities in the sediments range from 2.9 to 4.8 km/sec, and the depth to basement varies from 0.2 km within the central Diablo Range to a maximum of 3.4 km north of the Livermore Valley. In the Gabilan Range, the velocities in the sediments overlying the granitic basement are higher north of the Gabilan Range (3.6 to 4.6 km/sec) than to the south (2.2 to 3.8 km/sec), and the depth to basement both north and south of the range is less than 2 km. Below the sediments and fractured near-surface material, a resolvable difference in the crustal velocity structure on opposite sides of the San Andreas fault indicates compositional differences at depth. The upper crust has an average velocity of 5.7 km/sec at depths between 3 and 16 ± 3 km in the Diablo Range and an average velocity of 6.1 km/sec at depths between 2 and 9 ± 1 km in the Gabilan Range. The lower crust has an average velocity of 6.9 km/sec at depths between 16 ± 3 and 30 km in the Diablo Range and an average velocity of 6.5 km/sec at depths between 10 and 24 km in the Gabilan Range. The models also show that the depth to Moho differs by several kilometers between the two ranges. In the Diablo Range models, the crust-mantle boundary becomes shallower from south to north, rising from a depth of 30 to 26 km. In the Gabilan Range models, the Moho is at a depth of 24 to 26 km, depending on the velocity assumed at the base of the crust. Laboratory measurements of rock velocities and the mapped surface geology allow us to interpret the velocity models in terms of crustal composition. We conclude that the Diablo Range probably consists largely of metagraywacke to a depth of 16 ± 3 km, and gabbroic material below this depth. The crust of the Gabilan Range probably consists of granitic material to a depth of 9 ± 1 km and gneissic material below this depth. Franciscan rocks are not regionally present in the crust of the Gabilan Range. If the gneissic lower crust consists of the same rocks as are found at the surface in the Gabilan Range, then the presumed large-scale lateral motion of the Salinian block has taken place at or below the crust-mantle boundary, rather than along a mid-crustal slip plane.

Crustal structure of Mauna Loa Volcano, Hawaii, from seismic refraction and gravity data

Abstract: In October 1978, the U.S. Geological Survey established a 100-km-long seismic refraction profile normal to the Kona coast of Hawaii Island. Analysis of these data along with available gravity data suggest that the oceanic crust dips about 3° landward under the submerged flank of the island increasing to 8.5° under the Kona coast. Maximum vertical deflection of the base of crust from beneath the deep ocean to a point beneath the summit of Mauna Loa is about 9 km. High-velocity, high-density rocks ( Vp about 7.1 km/sec, density about 2.9 gm/cm 3 ) comprise the bulk of the volcanic edifice and reach to within a few kilometers of the surface beneath the north flank of Mauna Loa. The data also suggest that an elongate high-velocity, high-density body lies parallel to the Kona coast just below the surface; this body probably represents an extinct, buried rift zone.

Analysis of near-source static and dynamic measurements from the 1979 Imperial Valley earthquake

Abstract: Gross features of the rupture mechanism of the 1979 Imperial Valley earthquake ( ML = 6.6) are inferred from qualitative analysis of near-source ground motion data and observed surface rupture. A lower bound on the event's seismic moment of 2.5 × 1025 dyne-cm is obtained by assuming that the average slip over the whole fault plane equals the average surface rupture, 40.5 cm. Far-field estimates of moment suggest an average slip over the fault plane of 105 cm, from which a static stress drop of 11 bars is obtained. An alternative slip model, consistent with the far-field moment, has 40.5 cm of slip in the upper 5 km of the fault and 120 cm of slip in the lower 5 km. This model suggests a static stress drop of 39 bars. From the lower estimate of 11 bars, an average strain drop of 32 µstrain is derived. This strain drop is four times greater than the strain that could have accumulated since the 1940 El Centro earthquake based on measured strain rates for the region. Hence, a major portion of the strain released in the 1979 main shock had been accumulated prior to 1940. Unusually large amplitude (500 to 600 cm/sec2) vertical accelerations were recorded at stations E05, E06, E07, E08, EDA of the EI Centro array, and the five stations of the differential array near EDA. Although the peak acceleration of 1705 cm/sec2 at E06 is probably amplified by a factor of 3 due to local site conditions, these large amplitude vertical accelerations are unusual in that they are evident on only a few stations, all of which are near the fault trace and at about the same epicentral range. Two possible explanations are considered: first, that they are due to a direct P wave generated from a region about 17 km north of the hypocenter, or second, that they are due to a PP phase that is unusually strong in the Imperial Valley due to the large P -wave velocity gradient in the upper 5 km of the Imperial Valley. Based on the distribution of both the horizontal and vertical offsets, it is likely that the rupture went beyond stations E06 and E07 during the main shock. By exploiting the antisymmetry of the parallel components of particle velocity between E06 and E07 and by examining polarization diagrams of the particle velocity at E06 and E07, an average rupture velocity in the basement of 2.5 to 2.6 km/sec between the hypocenter and station E06 is obtained. In addition, several lines of evidence suggest that the Imperial fault dips about 75° to the NE.