Discrete Wavenumber Representation Research Articles

Simulation of strong ground motion from the 1995 Mw 6.5 Kozani-Grevena, Greece, earthquake using a hybrid deterministic-stochastic approach

The 1995 Mw 6.5 Kozani-Grevena earthquake struck an area in northwestern Greece characterized by relatively low seismicity based on historical information and instrumental data. The ground shaking in the near-fault region was recorded by a strong-motion accelerograph in the city of Kozani, at a distance of about 23 km from the epicenter. In this article, broadband ground motions are generated at selected locations and at a dense grid of observation points extending over the causative fault of the 1995 Kozani-Grevena earthquake using a hybrid deterministic-stochastic method. Based on a multi-segment fault model with curved geometry proposed in the literature, the low-frequency components of the synthetic ground motion are simulated using the discrete wavenumber representation method and the generalized transmission and reflection coefficient technique. The high-frequency components of the synthetic ground motion are generated using the stochastic modeling approach and the specific barrier model. The two independently derived ground-motion components are then combined using matched filtering at a crossover frequency of 1.2 Hz to generate broadband ground-motion time histories and response spectra. The simulation results are validated by comparing the synthetic ground motions with the recorded ones in the city of Kozani and with estimates of peak ground-motion quantities inferred from ground-motion prediction equations.

Finite-Fault Simulation of Broadband Strong Ground Motion from the 2010 Mw 7.0 Haiti Earthquake

Abstract Because of the socioeconomic environment in the small island nation of Haiti, no seismic recording stations were operating in the source region at the time of the 2010 M w 7.0 earthquake. The lack of strong motion instruments has hindered the estimation of the amplitude, duration, and frequency content of the ground shaking caused by the seismic event. In this study, synthetic broadband strong ground motions are generated in the vicinity of the 2010 Haiti earthquake. The low‐frequency components of the synthetic motions are simulated using a slip model compatible with seismological observations, geologic field data, and space geodetic measurements. The computations are carried out using the discrete wavenumber representation method and the generalized transmission and reflection coefficient technique. The high‐frequency ground‐motion components are generated using the stochastic modeling approach and the specific barrier model. The two independently derived ground‐motion components are subsequently combined using matched filtering at a crossover frequency of 1 Hz to generate broadband ground‐motion time histories and response spectra for the city of Port‐au‐Prince and other sites in the vicinity of the earthquake. Finally, the synthetic strong ground motions are compared against peak ground‐motion estimates inferred from the U.S. Geologic Survey ShakeMap of peak ground accelerations, ground‐motion prediction equations, and observed structural damage. The synthetic time histories and response spectra generated in this study should be seen as plausible, but not necessarily unique, ground motions that capture the primary features of the 2010 Haiti earthquake.

Effect of Fault Rupture Characteristics on Near-Fault Strong Ground Motions

The effect of fault rupture characteristics on near-fault strong ground motions is investigated using a kinematic modeling approach in an attempt to identify physical processes that lead to specific ground-motion patterns. The shear-stress distribution on the causative fault plane of four well-documented seismic events (i.e., 1979 Imperial Valley, 1985 Michoacan, 1989 Loma Prieta, and 1999 Izmit) is calculated based on fault slip models available in the literature using the methodology proposed by Bouchon (1997) for stress field computations. In order to associate the fault rupture characteristics (i.e., slip, rupture velocity, state of stress) of the investigated earthquakes with near-fault ground motions generated by the events, forward ground-motion simulations are performed using the discrete wavenumber representation method and the concept of the S -wave isochrones is exploited. The results indicate that the seismic energy radiated from the high-isochrone-velocity region of the fault arrives at the receiver within a time interval that coincides with the time window of the long-period ground-motion pulse recorded at the site. Furthermore, the near-fault ground-motion pulses are strongly correlated with large slip on the fault plane locally driven by high stress drop. In addition, the local rupture velocity seems to be inversely correlated to the spatial distribution of the strength excess over the fault plane confirming findings of previous studies. For various events the area of the fault that contributes to the formation of the near-fault pulse encompasses more than one patch of significant moment release (subevent) (e.g., 1979 Imperial Valley, 1989 Loma Prieta). This observation explains why a dislocation model with average properties (i.e., slip, rise time, etc.) reproduces successfully near-fault ground motions for strike-slip faults and for dip-slip faults with intermediate-to-large earthquake magnitudes (Aki, 1979). However, for very large earthquakes, such as megathrust events on subduction zones (e.g., 1985 Michoacan), the fault region that contributes to the pulse formation encompasses individual subevents and, consequently, cracklike slip functions (rather than dislocation models) may be more appropriate for the simulation of the near-fault ground motions.

Estimation of Strong Ground Motion from the Great 1964 Mw 9.2 Prince William Sound, Alaska, Earthquake

We are generating physically plausible near-field synthetic ground motions for the great 1964 Prince William Sound, Alaska, earthquake compatible with available seismological data, tectonic information, and eyewitness accounts. The first objective of this study is the simulation of the low-frequency (i.e., f <0.03 Hz) strong ground motions on selected locations and on a dense grid of observation points extending over the shallow dipping causative fault of the 1964 Alaska earthquake. In order to accomplish this task, we are utilizing the slip model proposed by Johnson et al. (1996) based on a joint inversion of tsunami waveforms and geodetic data. The calculations are carried out using the discrete wavenumber representation method (Bouchon and Aki, 1977; Bouchon, 1979) and the generalized transmission and reflection coefficient technique (Luco and Apsel, 1983). The second objective of this study is the reconstruction of the strong ground motion time histories and response spectra that the city of Anchorage experienced during the 1964 Alaska earthquake. The low-frequency (i.e., f <0.03 Hz) ground motions are generated using the methodology described previously. The intermediate-frequency (i.e., 0.03< f <0.50 Hz) ground motions are simulated by convolving Green’s functions generated by the discrete wavenumber representation method with far-field radiation pulses of circular cracks (Sato and Hirasawa, 1973; Dong and Papageorgiou, 2002a). The high-frequency (i.e., 0.5< f <8.0 Hz) ground motions are simulated using the stochastic modeling approach. The three independently derived ground-motion components are then properly combined to generate synthetic broadband ground-motion time histories and response spectra for the city of Anchorage due to the 1964 Prince William Sound earthquake. The third objective of this study is the validation of the synthetic strong ground motions for the 1964 Alaska earthquake against observed tectonic deformation, ground-motion estimates inferred from descriptions of structural damage, and eyewitness accounts. In summary, the analysis presented in this study contributes to a better understanding of the seismological aspects of the 1964 Alaska earthquake and provides synthetic time histories and response spectra for engineering applications compatible with all available information (i.e., seismological, tectonic, and eyewitness accounts). It should be noted however that the generated strong ground motions are not necessarily unique, nor do they reflect the entire uncertainty that characterizes the problem under investigation.

A reflection/transmission matrix formulation for seismoacoustic scattering by an irregular fluid--solid interface

The seismoacoustic scattering due to an irregular fluid—solid interface (i.e. the ocean bottom) must be considered when modelling seismic wave propagation in oceanic regions. In this paper, we present an accurate method to treat this problem. The method is an extension of the reflection/transmission matrix approach that was developed to model scattering due to an irregular interface between two elastic solids. This approach uses the discrete wavenumber representation of the wavefield and the Rayleigh ansatz; the wavefield is decomposed into a set of plane waves, and we assume that the scattered wavefield due to an incident plane wave can be expanded in terms of only the waves moving away from the interface. The plane waves at both sides of the interface are then connected to each other based on this hypothesis and proper boundary conditions. The elements of the reflection/transmission matrices describe these connection coefficients. As the fluid—solid interface, the direct application of the above method is difficult because the tangential displacement at the interface is not necessarily continuous. To avoid this problem, we use pressure as the variable inside the fluid layer. The reflection/transmission matrices between the pressure wave (i.e. the acoustic wave) and the elastic waves are then developed by using the standard boundary conditions at the fluid—solid interface (i.e. normal stress continuity, zero tangential stress, and normal displacement continuity) and the Rayleigh ansatz. To demonstrate the validity and feasibility of our method, we compare the results of our method with those of other methods. First, we examine the reflection of plane elastic waves by a periodic sinusoidal interface for a single frequency. The interface profile is characterized by its periodicity or wavelength (D) and peak to trough height (h). The behaviour of the reflection calculated by our method shows almost complete agreement with that calculated by a boundary element method (BEM) up to a relatively steep interface whose height to wavelength ratio (h/D) is 0.5. Second, we calculate the synthetic time domain waveforms for a plane vertically incident P wave into basin-like fluid layers. We compare the waveforms calculated by the present method with those calculated by the finite difference method (FDM). In general, the waveforms calculated by the two methods match well. A quantitative study shows that the degree of agreement indicated by the RMS residuals between the waveforms of the two methods becomes better when we use a smaller grid interval in the FDM calculation. For the models treated here, the cases of 30 grid-points per wavelength results in RMS residuals less than about 10–15 per cent. This grid interval is smaller than that usually applied (more than 5–10 grid-points per wavelength). Since, in general, the accuracy of the FDM calculation becomes better as the grid interval decreases, these results indicate the validity of the present method.

Exact Near-Field SH Motion at the Surface of an Elastic Solid Layer Lying over Fluid-Saturated Porous Solid Half-Space.

A method based on the discrete wavenumber representation of seismic source wave-fields is applied to discuss the SH motion in the near-field of a seismic source. The seismic source is assumed to be a concentrated horizontal line force embedded in a fluid saturated porous solid half-space lying under an elastic solid layer. Analytical expressions in the form of converging infinite series are obtained for the exact evaluation of displacement and acceleration at the free surface of the elastic layer. Corresponding expressions are also derived for the point source response in a three-dimensional cylindrically symmetric medium. To analyze the effects of porosity, anelasticity of the solid, and viscosity of the interstitial fluid on the near-field SH motion, synthetic seismograms for the displacement and the acceleration are computed for particular models. The decrease in velocity of the SH wave because of pores saturated by viscous fluid and attenuation due to anelastic nature of solid frame is also discussed.

Constraints on the shallow crustal model of the Northern Apennines (Italy) from the analysis of microearthquake seismic records

SUMMARY A joint study of microearthquake source and medium parameters was carried out by analysing a seismic sequence that occurred in the Tuscan Emilian Apenninic region. Signal processing and graphic techniques were applied to study the amplitude and polarization of wave motion and thus identify the main and secondary body-wave arrivals on the seismic records. The evidence for similar waveforms (denoted as 'similar events') in a microearthquake subset allowed application of a non-linear technique, which provided the accurate relative location of the events. Microearthquakes occurred within the shallow sediments (average depth of 3.5 km), and all appeared to be concentrated in a small volume of about 1 km3. The composite fault mechanism of the 'similar events' was computed by non-linear inversion of P-polarity readings. The maximumlikelihood solution appeared to be well constrained, and indicated a normal-faulting mechanism with the Taxis approximately oriented in a northerly direction. Interpretation of several secondary arrivals was performed by direct modelling of traveltimes and wave-motion amplitudes using a double-couple point-source model. Green's functions in a layered medium were computed using two different methods, based on ray theory (Farra 1990) and discrete wavenumber representation of the wavefield (Bouchon 1981). The study of secondary arrivals indicates a depth of 11-12 km for the top of the crystalline pre-Tertiary basement. This estimate concerns a region located at around 3-6km from the epicentres of the 'similar events', along the N290E direction. The modelling of arrival times for an S-to-P converted phase at the basement discontinuity suggests an increase of about 10 per cent in the basement seismic-wave velocity (V, = 6.9 km SKI), or, equivalently, an increase of the V, to V, ratio in the upper sediments. The increments were defined with respect to an existing reference model by AGIP (Italian Petroleum Agency). Recordings at the Minerbio station (MIN) (located about 40 km SE of the epicentral area) show converted/reflected phases at shallow crustal discontinuities and waveresonance phenomena. These path effects appear repeatedly on seismic records independently of the size of earthquakes within the magnitude range considered. Waveform and traveltime modelling of these secondary arrivals provide further constraints on the depth and velocity of main-structure discontinuities.

Ground motion on stratified alluvial deposits for incident SH waves

A boundary method is applied to study the response of a two-dimensional horizontally stratified deposit of arbitrary shape under the incidence of SH waves. The procedure combines the line source method with a discrete wavenumber representation for the stratified part in terms of propagator matrix. Comparison of results for a circular, nonhomogeneous deposit with those obtained with the finite element method shows excellent agreement . The response of a basin with two strata is analyzed. Variation of results as a function of incidence angle is presented for several frequencies. Transfer functions at several points on the surface of the deposit are obtained for vertical incidence and comparison with results from a one-dimensional analysis show significant differences. Time response for an incident Ricker wavelet clearly shows important effects due to lateral heterogeneity .

The rupture mechanism of the Coyote Lake earthquake of 6 August 1979 inferred from near-field data

abstractThe Coyote Lake earthquake (ML = 5.7) occurred within the dense network of seismic instruments of central California and was recorded by numerous accelerograph stations. Two of these stations, located within the fault zone itself, provide particularly remarkable records of the rupture process. We use these data obtained in the immediate vicinity of the fault and the broadband seismograms recorded at Berkeley, about 100 km away from the epicenter, to infer the velocity of propagation of the rupture, the extent of the fractured area, the rupture front geometry, and other characteristics of the fracture mechanism. In order to extract this information from the data, we model the earthquake as a propagating dislocation starting at the hypocenter and spreading radially. We compute the resulting ground motion at the receiver sites using the discrete wavenumber representation of Green's functions (Bouchon, 1981). The results yield a rupture velocity of 2.6 km/sec, a fault length of about 14 km and a fault slip of 15 to 20 cm. They also show that the fault extends to shallower depth than indicated by the aftershocks. The most important result is the finding that slip, at any given location on the fault, takes place in a very short time span and that simple uniform dislocation models give a good description of the rupture process.

Simulation of long-period, near-field motion for the great California earthquake of 1857

abstractUsing the fault slip determined by Sieh (1978a), the great 1857 California earthquake is modeled as a propagating fault buried in a realistic medium consisting of a two-layer crust overlying the mantle. The computation is carried out by the discrete wavenumber representation method (Bouchon, 1979). The resulting motion is almost purely horizontal throughout central and southern California, and, at most of the locations, the direction of severe ground shaking is oriented NE-SW. In the Los Angeles area, the peak displacement is about 30 cm, and the duration of severe ground motion is about 75 sec. Since our model does not include the effect of incoherent rupture propagation, our estimate should be considered as a lower bound. The simulated seismic motions are presented in the form of three-dimensional snapshots as well as in the usual form of time series at selected locations. The resultant near-field seismograms show a great diversity in the characteristic of motion as pointed out for actual near-field accelerograms by Hudson (1976). Our simulated motions appear to be in harmony with the description of the effect of the 1857 earthquake by contemporary accounts compiled by Agnew and Sieh (1978).

Calculation of complete seismograms for an explosive source in a layered medium

We apply the method of discrete wavenumber representation of elastic wave fields of Bouchon and Aki (1977) to the computation of synthetic seismograms for an explosive source in a layered medium. The method is based on the representation of the source radiation by a superposition of plane waves propagating in discrete directions. This discretization is exact and results from a periodic arrangement of sources. The two‐dimensional (2-D) and three‐dimensional (3-D) problems are described, and some examples of calculation are presented. They show that very complex seismograms can be obtained for rather simple geologic structures.

Near-field of a seismic source in a layered medium with irregular interfaces

Summary A method based on a discrete wavenumber representation of elastic wave fields is developed and applied to the study of the radiation and scattering in the vicinity of a seismic source located in an irregularly layered medium. The discretization results from a periodicity assumption in the description of the source and of the medium. The problem is two-dimensional but the source can be quite general and is represented by its body force equivalents. The method is an extension of the Aki-Larner technique originally developed to study the scattering of plane waves at irregular boundaries. It is applicable to wavelengths which are either longer than, or of the order of, the dimensions of the irregularities. A study of the strong motion response of a sedimentary basin to a nearby earthquake is presented, for which the main result is a large amplification of horizontal motions.

Discrete wave-number representation of seismic-source wave fields

AbstractA method based on a discrete horizontal wave-number representation of seismic-source wave fields is developed and applied to the study of the near-field of a seismic source embedded in a layered medium. The discretization results from a periodicity assumption in the description of the source. The problem is basically two-dimensional but its extension to three dimensions is sometimes feasible. The source is quite general and is represented through its body-force equivalents. Tests of the accuracy of the method are made against Garvin's (1956) analytical solution (a buried line source in a half-space) and against Niazy's (1973) results for a propagating fault in an infinite medium. In both cases, a remarkably good agreement is found. The method is applied to the modeling of the San Fernando earthquake, and to the computation of synthetic seismograms at short distance from a complex source in a layered medium. In particular, we show that the high acceleration-high frequency phase of the Pacoima Dam records is due to the Rayleigh wave from the point of ground breakage. Other high-acceleration phases, predicted by our model, are associated with the shear-wave arrival from the hypocenter or result from changes in the fault orientation.