Elastic Finite-Difference Modelling and Imaging for Earthquake Sources

Hu, Liang-Zie; McMechan, George A.

doi:10.1111/j.1365-246x.1988.tb00469.x

Cited by 30 publications

(20 citation statements)

References 19 publications

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“…In this study the pseudospectral elastic modeling method is used to solve the wave equation in 2-D (Kosloff et al, 1984) and in 3-D (Reshef et al, 1988). With the time-reversed seismograms, the RTI method maps the seismic sources based on the constructive and destructive interferences of back-propagated wavefields (Gajewski and Tessmer, 2005;Hu and McMechan, 1988;McMechan, 1982). As shown in Fig.…”

Section: The Reverse-time Imaging Methodsmentioning

confidence: 99%

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An evaluation of reverse-time imaging of clustering earthquakes

et al. 2015

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Clustering earthquakes refer to the seismic events that occur closely with each other in time and space. Because their overlapping waveform records make it difficult to pick the first arrivals, the hypocenters of clustering earthquakes cannot be determined accurately by traveltime location methods. Here we apply a reverse-time imaging (RTI) method to map clustering earthquakes. Taking the advantage of directly using waveforms, the RTI method is capable to map either a single small earthquake or some densely distributed clustering earthquakes beneath a 2-D seismic array. In 3-D case the RTI method is successfully applied to locate the long-offset doublet earthquakes using the data from a set of sparsely distributed surface stations. However, for the same acquisition geometry, the RTI encounters challenges in mapping densely distributed clustering earthquakes. While it is obvious that improving the mapping of clustering earthquakes requires a denser receiver network with wider range of illumination angles, it is necessary to verify the actual resolution of the RTI method with synthetic data. In our study area in the Three Gorges region, our tests in 3-D case suggest that some events beneath the linear aligned sub-arrays have reasonable resolution.

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Section: The Reverse-time Imaging Methodsmentioning

confidence: 99%

“…In mathematical point of view, RTI is to solve the boundary condition of wave equation (Hu and McMechan, 1988). In this study the pseudospectral elastic modeling method is used to solve the wave equation in 2-D (Kosloff et al, 1984) and in 3-D (Reshef et al, 1988).…”

Section: The Reverse-time Imaging Methodsmentioning

confidence: 99%

An evaluation of reverse-time imaging of clustering earthquakes

et al. 2015

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“…This is an excellent method, however, it cannot be applied to realistic problems in which the ground surface and the heterogeneity of the crust are taken into account, although the mirror image technique can be applied to a strike slip fault in elastic half space (AOCHI and FUKUYAMA, 2002). Finitedifference method (FDM) is a practical tool in seismology (e.g., HU and MCMECHAN, 1988;OLSEN et al, 1977). Two types of FDM are used for solving the elasto-dynamic equations of motion; displacement-based FDM and staggered grid FDM.…”

Section: Introductionmentioning

confidence: 99%

Improvement in the Fault Boundary Conditions for a Staggered Grid Finite-difference Method

Miyatake

Kimura

2006

Pure appl. geophys.

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The staggered grid finite-difference method is a powerful tool in seismology and is commonly used to study earthquake source dynamics. In the staggered grid finite-difference method stress and particle velocity components are calculated at different grid points, and a faulting problem is a mixed boundary problem, therefore different implementations of fault boundary conditions have been proposed. VIRIUEX and MADARIAGA (1982) chose the shear stress grid as the fault surface, however, this method has several problems: (1) Fault slip leakage outside the fault, and (2) the stress bump beyond the crack tip caused by S waves is not well resolved. MADARIAGA et al. (1998) solved the latter problem via thick fault implementation, but the former problem remains and causes a new issue; displacement discontinuity across the slip is not well modeled because of the artificial thickness of the fault. In the present study we improve the implementation of the fault boundary conditions in the staggered grid finite-difference method by using a fictitious surface to satisfy the fault boundary conditions. In our implementation, velocity (or displacement) grids are set on the fault plane, stress grids are shifted half grid spacing from the fault and stress on the fictitious surface in the rupture zone is given such that the interpolated stress on the fault is equal to the frictional stress. Within the area which does not rupture, stress on the fictitious surface is given a condition of no discontinuity of the velocity (or displacement). Fault normal displacement (or velocity) is given such that the normal stress on the fault is continuous across the fault. Artificial viscous damping is introduced on the fault to avoid vibration caused by onset of the slip. Our implementation has five advantages over previous versions: (1) No leakage of the slip prior to rupture and (2) a zero thickness fault, (3) stress on the fault is reliably calculated, (4) our implementation is suitable for the study of fault constitutive laws, as slip is defined as the difference between displacement on the plane of z = + 0 and that of z = ) 0, and (5) cessation of slip is achieved correctly.

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“…One is to determine the source parameters of the earthquake (source length, rupture velocity, radiation pattern, etc.) using the records obtained by an array spreading near the epicenter Hu and McMechan, 1988). In this case, the direct wave is reverse-time extrapolated until it focuses best.…”

Section: Methodsmentioning

confidence: 99%

Estimation of the Subsurface Reflection Coefficient Using the Prestack Reverse-Time Depth Migration.

Kawasaki¹

1995

J,Phys,Earth

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The prestack reverse-time depth migration is developed to estimate the reflection coefficient of the subsurface. To examine the capability of this method, a numerical experiment is implemented and it is shown that this method gives proper reflection coefficients even for a structure with 45-degree dips. It is also applied to real data of land survey. A distribution map of the reflection coefficient can be obtained after compensating the amplitude from the 3D to 2D wavefield including consideration for the Q value. However, extracting the velocity perturbation from the estimated reflection coefficient is hard due to inaccuracy of the estimated source strength, oscillatory behavior of the image, and lack of information about the density. The waveform inversion method is compared with the present method and it is found that the first iteration of the former method is nearly identical to the present method. Problems which are inherent in these methods are discussed.

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Elastic Finite-Difference Modelling and Imaging for Earthquake Sources

Cited by 30 publications

References 19 publications

An evaluation of reverse-time imaging of clustering earthquakes

An evaluation of reverse-time imaging of clustering earthquakes

Improvement in the Fault Boundary Conditions for a Staggered Grid Finite-difference Method

Estimation of the Subsurface Reflection Coefficient Using the Prestack Reverse-Time Depth Migration.

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