Showing papers in "Bulletin of the Seismological Society of America in 2001"

Faster, Better: Shear-Wave Velocity to 100 Meters Depth From Refraction Microtremor Arrays

Abstract: Current techniques of estimating shallow shear velocities for assessment of earthquake site response are too costly for use at most construction sites. They require large sources to be effective in noisy urban settings or specialized independent recorders laid out in an extensive array. This work shows that microtremor noise recordings made on 200-m-long lines of seismic refraction equipment can estimate shear velocity with 20% accuracy, often to 100-m depths. The combination of commonly available equipment, simple recording with no source, a wavefield transformation data processing technique, and an interactive Rayleigh-wave dispersion modeling tool exploits the most effective aspects of the microtremor, spectral analysis of surface wave (SASW) and multichannel analysis of surface wave (MASW) techniques. The slowness-frequency wavefield transformation is particularly effective in allowing accurate picking of Rayleigh-wave phase-velocity dispersion curves despite the presence of waves propagating across the linear array at high apparent velocities, higher-mode Rayleigh waves, body waves, air waves, and incoherent noise. Two locations illustrate the application of this technique in detail: coincident with a large accelerometer microtremor array in Reno, Nevada; and atop a borehole logged for shear velocity in Newhall, California. Refraction equipment could duplicate microtremor results above 3 Hz but could not estimate velocities deeper than 100 m. Refraction microtremor cannot duplicate the detail in the velocity profile yielded by a suspension logger but can match the average velocity of 10- to 20-m depth intervals and suggest structure below the 100-m logged depth of the hole. Eight additional examples from southern California and New Zealand demonstrate that the refraction microtremor technique quickly produces good results from a wide range of hard and soft sites.

Characteristics of Deformation and Past Seismicity Associated with the 1819 Kutch Earthquake, Northwestern India

Abstract: The 1819 earthquake in Kutch, northwestern India, is one of the most significant events to have occurred in a plate-interior setting. Despite being the second largest among the stable continental region (SCR) earthquakes, this event has not been analyzed within the context of present-day understanding of earthquake seismology. Coseismic changes related to this earthquake include massive ground deformation in a wide low-lying tidal-flat area. Although detailed historic accounts of this earthquake exist, many questions regarding the mode of deformation and the seismic history of the region remain unresolved. We explored the region nearly 180 years after the earthquake, and the information gathered adds to our understanding of this event and provides a fresh perspective on this unique intraplate seismogenic zone. A 90-km-long tract of elevated land with a peak height of 4.3 m is the most visible surface expression of this earthquake. We surveyed and analyzed the morphological features of this scarp and also carried out exploratory trenching in this region. The scarp morphology is suggestive of a growing fold related to a buried north-dipping thrust rather than a discrete fault that could have resulted from a surface rupture. The extensive liquefaction field associated with the earthquake offered an ideal setting to explore the paleoearthquake history. Age data of liquefaction features suggest that a previous event of comparable size must have occurred 800–1000 years ago. Seismic activity appears to be related to the reactivation of an ancient rift in a stress regime that is dominated by nearly north–south compression.

Observations of Earthquake Source Parameters at 2 km Depth in the Long Valley Caldera, Eastern California

Abstract: To investigate seismic source parameter scaling and seismic efficiency in the Long Valley caldera, California, we measured source parameters for 41 earthquakes ( M 0.5 to M 5) recorded at 2 km depth in the Long Valley Exploratory Well. Borehole recordings provide a wide frequency bandwidth, typically 1 to 200–300 Hz, and greatly reduce seismic noise and path effects compared to surface recordings. We calculated source parameters in both the time and frequency domains for P and S waves. At frequencies above the corner frequency, spectra decay faster than ω3, indicating that attenuation plays an important role in shaping the spectra (path averaged Q p = 100–400, Q s = 200–800). Source parameters are corrected for attenuation and radiation pattern. Both static stress drops and apparent stresses range from approximately 0.01 to 30 MPa. Although static stress drops do not vary with seismic moment for these data, our analyses are consistent with apparent stress increasing with increasing moment. To estimate tectonic driving stress and seismic efficiencies in the region, we combined source parameter measurements with knowledge of the stress field and a Coulomb failure criterion to infer a driving stress of 40–70 MPa. Subsequent seismic efficiencies are consistent with McGarr's (1999) hypothesis of a maximum seismic efficiency of 6%.

Differences Between Site Characteristics Obtained From Microtremors, S-waves, P-waves, and Codas

Abstract: We examine differences of empirical site characteristics among S waves, P waves, coda, and microtremors using records at 20 sites in and around the Sendai basin, Japan, and interpret the differences theoretically. At soft soil sites the horizontal-to-vertical spectral ratios (HVRs) for early P coda become different from HVRs for a P wave with increasing time and eventually converge on HVRs for microtremors. The HVRs for an S coda become similar to HVRs for microtremors with increasing time in the frequency range lower than 3 Hz at soft soil sites. By contrast, at a rock site and two hard soil sites, HVRs for S coda agree well with HVRs for an S wave. The soil-to-rock spectral ratios for horizontal (HHRs) and vertical (VVRs) components for early S coda are larger than those for an S wave at soft soil sites. When we use the deep sedimentary structures above the bedrock before Tertiary age, theoretical HVR for the fundamental mode of Rayleigh waves is consistent with observed HVR for microtremors and theoretical HVR for an obliquely incident SV wave is consistent with observed HVR for an S wave. Theoretical S -wave site amplification factor explains well observed HHR for S wave but does not coincide with HVR for microtremors. In general the frequencies of maximum peaks of HVRs for microtremors do not coincide with those of HVRs and HHRs for S wave. However, if we select HVRs with peak frequencies lower than 1 Hz and peak amplitudes larger than three, the peak frequencies of HVRs for microtremors roughly coincide with those of HVRs and HHRs for S wave. Even under these constraints, their amplitudes do not coincide with each other. Concerning coda, we conclude that the Rayleigh wave contamination in coda is significant in the frequency range lower than 3 Hz at soft soil sites.

A Simple Stick-Slip and Creep-Slip Model for Repeating Earthquakes and its Implication for Microearthquakes at Parkfield

Abstract: If repeating earthquakes are represented by circular ruptures, have constant stress drops, and experience no aseismic slip, then their recurrence times should vary with seismic moment as \batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} \(t\_{\mathrm{r}}{\propto}M\_{0}^{1{/}3}\) \end{document}. In contrast, the observed variation for small, characteristic repeating earthquakes along a creeping segment of the San Andreas fault at Parkfield (Nadeau and Johnson, 1998) is much weaker. Also, the Parkfield repeating earthquakes have much longer recurrence intervals than expected if the static stress drop is 10 MPa and if the loading velocity V L is assumed equal to the geodetically inferred slip rate of the fault V f. To resolve these discrepancies, previous studies have assumed no aseismic slip during the interseismic period, implying either high stress drop or V L ≠ V f. In this study, we show that a model that includes aseismic slip provides a plausible alternative explanation for the Parkfield repeating earthquakes. Our model of a repeating earthquake is a fixed-area fault patch that is allowed to continuously creep and strain harden until reaching a failure threshold stress. The strain hardening is represented by a linear coefficient C , which when much greater than the elastic loading stiffness k leads to relatively small interseismic slip (stick-slip). When C and k are of similar size creep-slip occurs, in which relatively large aseismic slip accrues prior to failure. Because fault-patch stiffness varies with patch radius, if C is independent of radius, then the model predicts that the relative amount of seismic to total slip increases with increasing radius or M , consistent with variations in slip required to explain the Parkfield data. The model predicts a weak variation in t r with M similar to the Parkfield data.

Memory-Efficient Simulation of Anelastic Wave Propagation

Abstract: Realistic anelastic attenuation can be incorporated rigorously into finite difference and other numerical wave propagation methods using internal or memory variables. The main impediment to the realistic treatment of anelastic attenuation in 3D is the very large computational storage requirement imposed by the additional variables. We previously proposed an alternative to the conventional memory-variable formulation, the method of coarse-grain memory variables, and demonstrated its effectiveness in acoustic problems. We generalize this memory-efficient formulation to 3D anelasticity and describe a fourth-order, staggered-grid finite-difference implementation. The anelastic coarse-grain method applied to plane wave propagation successfully simulates frequency-independent Q p and Q s . Apparent Q values are constant to within 4% tolerance over approximately two decades in frequency and biased less than 4% from specified target values. This performance is comparable to that achieved previously for acoustic-wave propagation, and accuracy could be further improved by optimizing the memory-variable relaxation times and weights. For a given assignment of relaxation times and weights, the coarse-grain method provides an eight-fold reduction in the storage requirement for memory variables, relative to the conventional approach. The method closely approximates the wavenumber-integration solution for the response of an anelastic half-space to a shallow dislocation source, accurately calculating all phases including the surface-diffracted SP phase and the Rayleigh wave. The half-space test demonstrates that the wave field-averaging concept underlying the coarse-grain method is effective near boundaries and in the presence of evanescent waves. We anticipate that this method will also be applicable to unstructured grid methods, such as the finite-element method and the spectral-element method, although additional numerical testing will be required to establish accuracy in the presence of grid irregularity. The method is not effective at wavelengths equal to and shorter than 4 grid cell dimensions, where it produces anomalous scattering effects. This limitation could be significant for very high-order numerical schemes under some circumstances (i.e., whenever wave-lengths as short as 4 grids are otherwise within the usable bandwidth of the scheme), but it is of no practical importance in our fourth-order finite-difference implementation.

Repeating Earthquakes as Low-Stress-Drop Events at a Border between Locked and Creeping Fault Patches

Abstract: The source of repeating earthquakes on creeping faults is modeled as a weak asperity at a border between much larger locked and creeping patches on the fault plane. The x –1/2 decrease in stress concentration with distance x from the boundary is shown to lead directly to the observed scaling 〈 T 〉∞〈 M 〉1/6 between the average repeat time and average scalar moment for a repeating sequence. The stress drop in such small events at the border depends on the size of the large locked patch. For a circular patch of radius R and representative fault parameters, Δσ = 7.6( m / R )3/5 MPa, which yields stress drops between 0.08 and 0.5 MPa (0.8–5 bars) for R between 2 km and 100 m. These low stress drops are consistent with estimates of stress drop for small earthquakes based on their seismic spectra. However, they are orders of magnitude smaller than stress drops calculated under the assumption that repeating sources are isolated stuck asperities on an otherwise creeping fault plane, whose seismic slips keep pace with the surrounding creep rate. Linear streaks of microearthquakes observed on creeping fault planes are trivially explained by the present model as alignments on the boundaries between locked and creeping patches.

Comparison of Site Response Characteristics Inferred from Microtremors and Earthquake Shear Waves

Abstract: We investigated the validity of seismic site response characteristics es- timated from microtremors by comparing them with those of earthquake motions. For this purpose we observed microtremors as well as earthquake motions using large (5-km diameter) and small (0.5-km diameter) arrays deployed on soft sedi- ments. Specifically, we examined four estimates from microtremors: relative site amplification factors to incident shear waves, site amplification factors by the Naka- mura method, resonance frequency in horizontal-to-vertical spectral ratios, and horizontal-to-vertical spectral ratios. As a result of the comparisons, we obtained the following conclusions. The relative amplification factors can be inferred from horizontal-component ratios of microtremors to a reference site within a small area of several hundred meters. The horizontal-to-vertical spectral ratios inferred by the Nakamura method partly reflect site amplification factors, but do not agree with site amplification factors. A sharp-peak frequency in the horizontal-to-vertical spectral ratios is possibly the resonance frequency. The horizontal-to-vertical spectral ratios of microtremors either agree with those of earthquake motions at some array sites or are slightly smaller at the other sites.

Stress Orientations Obtained from Earthquake Focal Mechanisms: What Are Appropriate Uncertainty Estimates?

Abstract: Crustal stress orientations provide important information about the mechanics of regional deformation. Numerous methods exist for inverting earthquake focal mechanisms for stress orientation, and the more widely used methods usually obtain similar results for similar data sets. However, error estimates are highly variable, complicating the interpretation of results. The southern California stress field, for example, contains much statistically significant spatial and temporal variability according to the error estimates of one method (Michael, 1984, 1987b), but very little according to those of another (Gephart and Forsyth, 1984). To resolve whether the southern California stress field is generally homogeneous or heterogeneous, we must determine which of the error estimates best reflects the true inversion uncertainty. To do this, we tested both methods on a suite of synthetic focal mechanism data sets containing random errors. The method of Gephart and Forsyth (1984) usually provides more accurate estimates of stress orientation, especially for high-quality data sets, but its confidence regions are in most cases too large. The method of Michael (1984, 1987b) is more accurate for very noisy data sets and provides a more appropriate estimate of uncertainty, implying that the stress field in southern California is probably heterogeneous.

Sinking Mafic Body in a Reactivated Lower Crust: A Mechanism for Stress Concentration at the New Madrid Seismic Zone

Abstract: We propose a geodynamic model for stress concentration in the New Madrid seismic zone (NMSZ). The model postulates that a high-density (mafic) body situated in the deep crust directly beneath the most seismically active part of the NMSZ began sinking several thousands of years ago when the lower crust was suddenly weakened. Based on the fact that deformation rates in the NMSZ have accelerated over the past 9 k.y., we envision the source of this perturbation to be related to the last North American deglaciation. Excess mass of the mafic body exerts a downward pull on the elastic upper crust, leading to a cycle of primary thrust faulting with secondary strike-slip faulting, after which continued sinking of the mafic body reloads the upper crust and renews the process. This model is consistent with the youth of activity, the generation of a sequence of earthquakes, and the velocity evolution during interseismic periods, which depend upon the density contrast of the mafic body with respect to the surrounding crust, its volume, and the viscosity of the lower crust.

Discontinuous-Grid Finite-Difference Seismic Modeling Including Surface Topography

Abstract: We have developed a two-dimensional P - SV viscoelastic finite-difference modeling technique for complex surface topography and subsurface structures. Realistic modeling of seismic wave propagation in the near surface region is complicated by many factors, such as strong heterogeneity, topographic relief, and large attenuation. In order to account for these complications, we use an O(2,4) accurate viscoelastic velocity-stress staggered-grid finite-difference scheme. The implementation includes an irregular free surface condition for topographic relief and a discontinuous grid technique in the shallow parts of the model. Several methods of free surface condition are bench marked, and an accurate and simple condition is proposed. In the proposed free surface condition, stresses are calculated so that the normal stresses perpendicular to the boundary and shear stresses on the free surface are zero. The calculation of particle velocities at the free surface does not involve any specific calculations, and the particle velocities are set to zero above the free surface. A discontinuous-grid method is introduced, where we use a 3 times finer grid in the near surface or low velocity region compared to the rest of the model. In order to reduce instability, we apply averaging or weighting to the replacement of the coarse-grid components within the fine grid field. The method allows us to avoid any limitation of the shape of the grid-spacing boundary. Numerical tests indicate that approximately 10 grid points per shortest wavelength, counted in coarse-grid spacing, with the discontinuous grid method results in accurate calculations as long as a small number of time steps is concerned.

Attenuation of High-Frequency P and S Waves in the Crust of Southeastern South Korea

Abstract: The seismicity of the Yangsan fault in southeastern S. Korea has received increasing attention recently because the fault lies in an industrial area. For this fault region, we first measured \batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} \(Q_{P}^{-1}\) \end{document} and \batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} \(Q_{S}^{-1}\) \end{document} simultaneously by applying the extended coda-normalization method to seismograms at nine stations of a network deployed by the Korea Institute of Geology, Mining, and Materials. We analyzed 707 seismograms of local earthquakes that occurred between December 1994 and February 2000. From velocity seismograms, bandpass-filtered traces were made by applying a phaseless four-pole butterworth filter with five octave-width frequency bands, 1–2, 2–4, 4–8, 8–16, and 16–32 Hz. Estimated \batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} \(Q_{P}^{-1}\) \end{document} and \batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} \(Q_{S}^{-1}\) \end{document} values decrease from (7 ± 2) × 10–3 and (5 ± 4) × 10–3 at 1.5 Hz to (5 ± 4) × 10–4 and (5 ± 2) × 10–4 at 24 Hz, respectively. By fitting power-law frequency dependence to the estimated values over the whole stations, we obtained 0.009 f –1.05 for \batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} \(Q_{P}^{-1}\) \end{document} and 0.004 f –0.70 for \batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} \(Q_{S}^{-1}\) \end{document}, where f is frequency in Hz. These results indicate that \batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} \(Q_{P}^{-1}\) \end{document} and \batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} \(Q_{S}^{-1}\) \end{document} in the crust of southeastern S. Korea are the lowermost of the reported values in the world, although the exponent values agree well with those in the other areas.

Dynamic Earthquake Ruptures in the Presence of Lithostatic Normal Stresses: Implications for Friction Models and Heat Production

Abstract: We simulate dynamic ruptures on a strike-slip fault in homogeneous and layered half-spaces and on a thrust fault in a layered half-space. With traditional friction models, sliding friction exceeds 50% of the fault normal compressive stress, and unless the pore pressures approach the lithostatic stress, the rupture characteristics depend strongly on the depth, and sliding generates large amounts of heat. Under application of reasonable stress distributions with depth, variation of the effective coefficient of friction with the square root of the shear modulus and the inverse of the depth creates distributions of stress drop and fracture energy that produce realistic rupture behavior. This ad hoc friction model results in (1) low-sliding friction at all depths and (2) fracture energy that is relatively independent of depth. Additionally, friction models with rate-weakening behavior (which form pulselike ruptures) appear to generate heterogeneity in the distributions of final slip and shear stress more effectively than those without such behavior (which form cracklike ruptures). For surface rupture on a thrust fault, the simple slip-weakening friction model, which lacks rate-weakening behavior, accentuates the dynamic interactions between the seismic waves and the rupture and leads to excessively large ground motions on the hanging wall. Waveforms below the center of the fault (which are associated with waves radiated to teleseismic distances) indicate that source inversions of thrust events may slightly underestimate the slip at shallow depths.

Estimation of S-Wave Velocity Structures in and around the Sendai Basin, Japan, Using Array Records of Microtremors

Abstract: We conducted array measurements of microtremors at six sites in and around the Sendai basin to estimate deep S -wave velocity structures above the seismological bedrock (pre-Tertiary bedrock). After estimating phase velocities of microtremors in the frequency range from about 0.5 to 3 Hz, we succeeded to estimate the deep structures above the pre-Tertiary bedrock at four soil sites (KATA, OKIN, ARAH, and MYG15) and only the upper part just beneath the Pliocene layer at the other soil site (TRMA) using a Rayleigh-wave inversion technique. At TRMA and a rock site TAMA, we roughly estimate the deep S -wave velocity structures using empirical site amplification factors derived from strong-motion records. The deepest bedrock depth is 1 km, and the shallowest depth is 200 m among these six sites. The difference of the bedrock depth between the eastern side and the western side of an active thrust fault, the Nagamachi-Rifu line, is only 120 m. The difference of the bedrock depth between two sites in the east of the basin reaches about 500 m, although any geological boundaries or buried faults have not been mapped. Since the deep S -wave velocity structure of the Sendai basin had been basically unknown, we delineate it for the first time in this article using array measurement of microtremors.

Northwestern Turkey Earthquakes and the Crustal Structure Inferred from Surface Waves Observed in Western Greece

Abstract: Records of several earthquakes occurring in Turkey in 1999 obtained at broadband seismic stations in western Greece have been used to study the dispersion of surface waves, mainly Love waves. The observed group-velocity dispersion curves have been inverted into horizontally layered models of the Earth's crust by a modified method of the single-parameter variation. As compared with a previous model for the territory of Greece, the dispersion data require significantly lower velocities in the uppermost crust and smaller crustal thickness. In particular, the resulting model displays S -wave velocities between 1.3 and 2.4 km/sec in the upper 2 km and a crustal thickness of about 33 km. Manuscript received 31 July 2000.

The Vertical Component P-Wave Receiver Function

Abstract: The vertical component P -wave receiver function is an important source of data in studies of the crust/mantle transfer function for determining Earth structure under isolated receivers or under receiver arrays. This waveform illuminates a missing aspect of the wave propagation in receiver function studies that employ only the horizontal components of motion, and yields complementary constraints on near-receiver heterogeneity and P -wave propagation. The vertical component P -wave receiver function is formed using an array estimate for the effective teleseismic source function that is then deconvolved from all the vertical and horizontal components of ground motion at each station in the array. One-dimensional, three-dimensional, and stochastic wave-propagation models are used to test the robustness of the technique. Breakdown of single-station receiver function deconvolution occurs because of high levels of noncorrelated noise between the ground-motion components. Receiver functions for stations of the southern California TERRAscope array are investigated using the array technique. Vertical receiver functions for stations in the Los Angeles Basin and Long Valley Caldera show high-amplitude secondary arrivals that cannot be explained by simple 1D structures but probably reflect wave propagation in 3D basin structures. Three-component receiver functions from the station at Mammoth Lakes, California, show pathological behavior where the horizontal components of ground motion exceed the amplitude of the vertical components, suggesting extreme topographic and 3D velocity heterogeneity. Use of all three components of the receiver function in modern passive array experiments is encouraged to reduce the problems of nonuniqueness in determining Earth models.

Detection of Space and Time Heterogeneity in the Completeness of a Seismic Catalog by a Statistical Approach: An Application to the Italian Area

Abstract: A new statistical approach is proposed for the definition of the time interval characterized by a seismicity data set representative of the actual seismicity (completeness). The proposed approach does not require stringent assumptions about statistical features of local seismicity, nor does it require preprocessing procedures (e.g., aftershock removal), a potential source of statistical biases. In order to validate this procedure, the Italian seismic catalog NT4.1 has been studied, which is probably the one with the best historical background in the world, and for which it is possible to make hypotheses about data set completeness in the light of historiographical considerations. The results obtained indicate that the proposed statistical procedure is effective for a first order completeness estimate of parametric seismic catalogs.

Stress Drop, Slip Type, Earthquake Magnitude, and Seismic Hazard

Abstract: Care must be taken to provide reliable antiseismic protection in earthquake-prone areas where the impact of a large earthquake in megacities with industrial facilities as well as in ordinary buildings is liable to cause massive loss of human life and to cripple the nation's economy. This protection needs to take into account not only vibratory ground motion but also permanent ground failure, and notably surface-faulting hazard, a fact tragically illustrated during the recent events of Turkey and Taiwan. The purpose of this contribution is to conduct a survey of our current state of knowledge concerning theoretical relationships between earthquake source parameters, such as moment magnitude (M, M w), surface wave magnitude ( M S), seismic moment ( M O), stress drop (Δσ), rupture length ( L ), and displacement on the fault ( D ). A relationship is proposed that links M S to L and Δσ: M S = 2 log L + 1.33 log Δσ + 1.66, using a simple rupture model. Earthquake data from all over the world for which the parameters of rupture length, fault width ( W ), fault displacement, and surface-wave magnitude are available have enabled stress drop values to be computed for each event using both geological observation (Δσ1) and the previously proposed equation (Δσ2). The results obtained tend to indicate that stress drop values increase versus fault width (depth) up to approximately 15 km (corresponding perhaps to the brittle-ductile boundary). This increase is more pronounced in the case of reverse faults than it is for those with strike-slip or normal mechanisms. An equation of the type Δσ = kW n has been used to fit the data, and preliminary values for k and n have been supplied for the three slip types. For depths in excess of 15 km the data do not display significant variation (Δσ < 100 bars). These results are in agreement with certain laboratory models of the continental lithosphere. Although more data, particularly in the large-magnitude range, are needed to ascertain whether it is the W or the L model that better describes earthquake scaling laws, stress drop does not appear to be fault-length dependent, thus being supportive of the L model. The risk of surface faulting is dependent on the dynamic environment of the fault, that is, the stress drop, the rupture length, and the fault width. Although statistics show that surface faulting appears in most instances at magnitudes of at least 6.1, data from certain regions indicate that seismicity at superficial depths is under certain conditions accompanied by significant surface faulting even for magnitudes as small as 5.5, suggesting a change in scaling law. The threshold magnitude for surface faulting is accordingly seen to depend on the rheology of materials in the fault area and on the stress environment. Manuscript received 31 May 2000.

Earthquake Doublet in Kagoshima, Japan: Rupture of Asperities in a Stress Shadow

Abstract: Two shallow moderate ( M ∼ 6) earthquakes occurred in the northwestern part of Kagoshima Prefecture, Kyushu, southern Japan. I discuss the effect of the stress change due to the first earthquake (26 March 1997) on the occurrence of the second earthquake (13 May 1997). The rupture characteristics of the two earthquakes are inferred in two steps to form the basis of the discussion. I first invert strong ground motion data to construct kinematic source models and then estimate the distribution of static stress drop from the derived dislocation distributions. The rupture process of the March event is simple and well described with rupture of a single asperity (patch of high stress drop). On the other hand, multiple asperities on conjugate faults ruptured during the May event. The maximum value of static stress drop for both earthquakes is about 4 MPa, and seems lower than those of other Japanese intraplate earthquakes. The hypocenter and the largest asperity of the May earthquake are located in a stress shadow caused by the March earthquake. Thus the rupture history of the May earthquake is difficult to explain with a static stress change model. Other mechanisms such as fluid migration and dynamic stresses were also investigated, but failed to explain the triggering. I propose the coupled effect of static change in shear stress and normal stress under the rate- and state-dependent friction law as a possible mechanism.

Simulation of Tsunami Induced by Dynamic Displacement of Seabed due to Seismic Faulting

Abstract: In conventional tsunami-simulation techniques, simplifications have been employed by neglecting the dynamic seabed displacement resulting from fracturing of a seismic fault and considering only the static contribution. The water layer is also assumed to be incompressible, regardless of its acoustic effects. They should be reconsidered in light of the state-of-the-art technology because considerable discrepancies between numerical simulations and actual observation have been pointed out regarding, for example, arrival time and wave height. In the present study, tsunami simulation is conducted without using these kinds of simplification, taking into account both the dynamic displacement and acoustic effects. As a result, thus simulated tsunamis are found to be remarkably larger in the wave height especially in the near-fault area where these two effects are superposed. In far-field, however, tsunamis thus simulated are likely to show little difference in the wave height, but show considerable difference in the arrival time. In addition, the present dynamic analysis is capable of simulating the water wave induced by the Rayleigh wave propagated along the seabed.

Accuracy of the Explicit Planar Free-Surface Boundary Condition Implemented in a Fourth-Order Staggered-Grid Velocity-Stress Finite-Difference Scheme

Abstract: We compute the accuracy of two implementations of the explicit planar free-surface boundary condition for 3D fourth-order velocity-stress staggered-grid finite differences, 1/2 grid apart vertically, in a uniform half-space. Due to the stag- gered grid, the closest distance between the free surface and some wave-field com- ponents for both implementations is 1/2-grid spacing. Overall, the differences in accuracy of the two implementations are small. When compared to a reflectivity solution computed at the staggered positions closest to the surface, the total misfit for all three components of the wave field is generally found to be larger for the free surface colocated with the normal stresses, compared to that for the free surface colocated with the xz and yz stresses. However, this trend is reversed when compared to the reflectivity solution exactly at the free surface (the misfit encountered in staggered-grid modeling). When the wave field is averaged across the free surface, thereby centering thestaggered wave field exactly on the freesurface,thefree-surface condition colocated with the xz and yz stresses generates the smallest total misfit for increasing epicentral distance. For an epicentral distance/hypocentral depth of 10, the total misfit of this condition is about 15% smaller than that for the condition colocated with the normal stresses, mainly controlled by the misfit on the Rayleigh wave.

Correlation of Ground Motion and Intensity for the 17 January 1994 Northridge, California, Earthquake

Abstract: We analyze the correlations between intensity and a set of ground-motion parameters obtained from 66 free-field stations in Los Angeles County that recorded the 1994 Northridge earthquake. We use the tagging intensities from Thywissen and Boatwright (1998) because these intensities are determined independently on census tracts, rather than interpolated from zip codes, as are the modified Mercalli isoseismals from Dewey et al. (1995). The ground-motion parameters we consider are the peak ground acceleration (PGA), the peak ground velocity (PGV), the 5%-damped pseudovelocity response spectral (PSV) ordinates at 14 periods from 0.1 to 7.5 sec, and the rms average of these spectral ordinates from 0.3 to 3 sec. Visual comparisons of the distribution of tagging intensity with contours of PGA, PGV, and the average PSV suggest that PGV and the average PSV are better correlated with the intensity than PGA. The correlation coefficients between the intensity and the ground-motion parameters bear this out: r = 0.75 for PGA, 0.85 for PGV, and 0.85 for the average PSV. Correlations between the intensity and the PSV ordinates, as a function of period, are strongest at 1.5 sec ( r = 0.83) and weakest at 0.2 sec ( r = 0.66). Regressing the intensity on the logarithms of these ground-motion parameters yields relations I ∝ m logθ with 3.0 ≤ m ≤ 5.2 for the parameters analyzed, where m = 4.4 ± 0.7 for PGA, 3.4 ± 0.4 for PGV, and 3.6 ± 0.5 for the average PSV. Manuscript received 15 April 1999.

Spatial Correlation of Probabilistic Earthquake Ground Motion and Loss

Abstract: Spatial correlation of annual earthquake ground motions and losses can be used to estimate the variance of annual losses to a portfolio of properties exposed to earthquakes. A direct method is described for the calculation of the spatial correlation of earthquake ground motions and losses. Calculations for the direct method can be carried out using either numerical quadrature or a discrete, matrix-based approach. Numerical results for this method are compared with those calculated from a simple Monte Carlo simulation. Spatial correlation of ground motion and loss is induced by the systematic attenuation of ground motion with distance from the source, by common site conditions, and by the finite length of fault ruptures. Spatial correlation is also strongly dependent on the partitioning of the variability, given an event, into interevent and intraevent components. Intraevent variability reduces the spatial correlation of losses. Interevent variability increases spatial correlation of losses. The higher the spatial correlation, the larger the variance in losses to a portfolio, and the more likely extreme values become. This result underscores the importance of accurately determining the relative magnitudes of intraevent and interevent variability in ground-motion studies, because of the strong impact in estimating earthquake losses to a portfolio. The direct method offers an alternative to simulation for calculating the variance of losses to a portfolio, which may reduce the amount of calculation required.

Edge-Diffracted 1-Sec Surface Waves Observed in a Small-Size Intramountain Basin (Colfiorito, Central Italy)

Abstract: During the Umbria-Marche, central Italy seismic sequence a small-aperture (≈200 m), four-station array was operating in the Colfiorito plain, a few kilometers away from the epicenters of the ML 5.6 and 5.8 mainshocks of 26 September 1997. The array was deployed approximately 500 m from the eastern edge of the basin. We analyze the three-component seismograms of 12 aftershocks, in a magnitude range of 2.5 to 4.1. Amplitudes of the horizontal components are systematically higher than those of the vertical component, with an average horizontal-to-vertical spectral ratio of about 3 at 1 Hz. In this frequency band, earthquake-induced ground shaking is highly coherent across the array. A 1-sec running-window zero-lag cross-correlation algorithm is used to compute apparent velocity and backazimuth of coherent wave trains in the frequency band 0.5 to 2 Hz. Apparent velocity and backazimuth show a different behavior in the first part of the seismograms compared to the late coda. The largest amplitude waves, that is, S waves and early coda, are characterized by low apparent velocities, mostly between 400 and 1200 m/sec. This suggests that, near the rock edge, the most significant part of seismic energy propagates horizontally in the basin. Backazimuth of these low-frequency, coherent wavetrains never coincides with the array-to-source direction. The predominant backazimuth is peaked around N110°, corresponding to the nearest, steep outcrop of the basin edge. The observed 1-sec coherent wave trains are interpreted as locally generated surface waves that are persistently diffracted from the nearby basin edge as long as a significant level of seismic radiation is incident to the bedrock. When the bedrock excitation decreases a much larger variability of both apparent velocity and backazimuth is observed, suggesting that, in the coda, randomly scattered waves within the basin and late arrivals of deeper origin become more important. Multipathing from the source to the site as well as multipathing within the basin are therefore interpreted as the main causes of the observed long-duration, coherent low-frequency basin shaking.

Geographic Deaggregation of Seismic Hazard in the United States

Abstract: The seismic hazard calculations for the 1996 national seismic hazard maps have been geographically deaggregated to assist in the understanding of the relative contributions of sources. These deaggregations are exhibited as maps with vertical bars whose heights are proportional to the contribution that each geographical cell makes to the ground-motion exceedance hazard. Bar colors correspond to average source magnitudes. We also extend the deaggregation analysis reported in Harmsen et al. (1999) to the western conterminous United States. In contrast to the central and eastern United States (CEUS); the influence of specific faults or characteristic events can be clearly identified. Geographic deaggregation for 0.2-sec and 1.0-sec pseudo spectral acceleration (SA) is performed for 10% probability of exceedance (PE) in 50 yr (475-yr mean return period) and 2% PE in 50 yr (2475-yr mean return period) for four western U.S. cities, Los Angeles, Salt Lake City, San Francisco, and Seattle, and for three central and eastern U.S. cities, Atlanta, Boston, and Saint Louis. In general, as the PE is lowered, the sources of hazard closer to the site dominate. Larger, more distant earthquakes contribute more significantly to hazard for 1.0-sec SA than for 0.2-sec SA. Additional maps of geographically deaggregated seismic hazard are available on the Internet for 120 cities in the conterminous United States ( ) for 1-sec SA and for 0.2-sec SA with a 2% PE in 50 yr. Examination of these maps of hazard contributions enables the investigator to determine the distance and azimuth to predominant sources, and their magnitudes. This information can be used to generate scenario earthquakes and corresponding time histories for seismic design and retrofit. Where fault density is lower than deaggregation cell dimensions, we can identify specific faults that contribute significantly to the seismic hazard at a given site. Detailed fault information enables investigators to include rupture information such as source directivity, radiation pattern, and basin-edge effects into their scenario earthquakes used in engineering analyses.

The Attenuation of Seismic Intensity in Italy: A Bilinear Shape Indicates the Dominance of Deep Phases at Epicentral Distances Longer than 45 km

Abstract: The attenuation of seismic intensity with distance in Italy is analyzed by using felt intensity report data obtained from two comprehensive historical databases recently made available. The observed attenuation pattern that in the past was interpreted as a logarithmic or root (square or cubic) attenuation law shows quite clearly two different linear trends in the near and in the far field. At distances shorter than 45 km, the decrease of the intensity with distance is about one degree per 20 km, while at longer distances the slope is about one degree per 50 km. This is in agreement with some recent findings of realistic modeling of seismic ground motion that has been explained as the transition from upper-crust direct Sg phases to waves reflected at the Moho controlling the energy main release. The slope of the curve in the far field shows a regional dependence in agreement with recent works on the attenuation of Pn and Sn phases in Italy. If effective, this correlation might allow us to discriminate the contribution of crustal and subcrustal paths in seismic intensity attenuation studies. Manuscript received 31 May 2000.

Viscoelastic wave simulation in basins by a variable-grid finite-difference method

Abstract: A variable-grid finite-difference (FD) scheme is introduced for efficiently modeling viscoelastic wave propagation in 3D basins. The basin model includes a near-surface unconsolidated layer that is modeled with a fine grid and a deep part that is modeled by a coarse grid. The FD method changes the grid spacing in all three dimensions at a certain depth to provide a significant reduction in computational cost. It is an improvement on other variable-grid FD methods in that it can accommodate both 2× and 3× grid-spacing changes and a possible instability problem is overcome by a 3D interpolation scheme in the wavenumber domain. As an example, the variable-grid method is used to simulate the 3D viscoelastic response of a Salt Lake basin model. Simulation results show that the 3D basin features and the shallow layer significantly affect the amplitude and duration time of the ground motion. A basin model without a shallow low-velocity layer underestimates the ground-motion duration and cumulative kinetic energy by 50% or more. In this case, the variable-grid method requires 5 times less CPU time (and physical memory) compared to a standard FD method.

How Accurate Can Strong Ground Motion Attenuation Relations Be

Abstract: This article gives the results of a study using 1484 strong-motion records, which tried to find an upper limit on the accuracy that attenuation relations can achieve independently of the functional form adopted and the methods used for the construction of the equation. It is found that the current data do not allow a significant improvement in the uncertainty over what has been found for previous attenuation relations. Also, we find evidence for significant nonuniform scatter with respect to magnitude and that the scatter is not dependent on the amplitude of ground motion.

Location and Magnitude from Seismic Intensity Data of Recent and Historic Earthquakes in the Northern Rhine Area, Central Europe

Abstract: By adapting and calibrating Bakun and Wentworth's (1997) solution strategy for seismic intensity observations for the Northern and Middle Rhine Area (NRA), Central Europe, local magnitudes with objective confidence-level uncertainties are estimated for 23 test-set earthquakes that occurred between 1692 and 1963. Analysis of 4375 Medvedev Sponheuer Karnik intensity (MSKI) observations for 14 instrumentally recorded and located training-set events suggests that an intensity magnitude, M LI, corresponding to local magnitude, M L, can be determined from the mean of M LIi = (MSKIi + 0.7374 + 0.0184 * Δi)/1.2673. Δi is the distance in km of observation MSKIi. In a grid of 81 × 51 trial epicenters, 5-km grid-point distance, contours of rms [ M LI], where rms is the root mean square, bound the epicentral region. A total of 3628 intensity observations was used for the test-set earthquakes, seven of which showed M LI ≥ 5.5. The strongest historical events are the Verviers 1692 and the Duren 1756 events with M LI values of 6.8 and 6.4, respectively.

What We Can and Cannot Learn about Earthquake Sources from the Spectra of Seismic Waves

Abstract: Earthquake sources are commonly viewed as shear dislocations. This imposes distinct limitations on what source parameters can be realistically determined from radiated shear-wave spectra. First, the slip velocity on the fault is the real parameter that controls the strength of the high-frequency radiation; it can be directly determined from acceleration spectra by fitting their high-frequency level. Second, the relationship between corner frequency of the spectrum and the radius of the source is fundamentally unclear. As a result, the source dimensions cannot be accurately determined from the spectra; such an estimate would be as accurate as any other informed guess. Third, the stress drop only serves as a proxy for the source radius in the relationship between the radius and the corner frequency; it thus cannot be reliably determined from the spectra. The quantity usually obtained from the spectra and referred to as the stress drop is a poorly defined parameter that may bear little relevance to the actual stresses acting on faults. This parameter has little meaning unless converted to the maximum slip velocity, which is the only quantity that can be accurately determined from the spectra. The typical value of stress drop of 100 bars, established from the spectra of California events, may imply that the typical slip velocities have been on the order of 0.5 m/sec, although it is more accurate to determine slip velocities directly from the spectra.