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[1] A new two-step hybrid technique (hybrid) has been developed to estimate the earthquake ground motion in three-dimensional (3-D) local models excited by external sources. The main use of the technique is fast evaluation of site effects and seismic hazard because our technique needs less computer memory and time than all-in-one source-path-site computational methods. The first step of the hybrid requires an arbitrary 3-D method (e.g., finite difference (FD), discrete wave number, ray, or analytical solution) to compute three-component excitation on a grid box surrounding a site of interest. A particular excitation contains information on the source and path effects and is saved on disk as a time history. Depending on the method used, the first step may also contain nonplanar topography. The second step (3-D FD) employs local structure and topography inside the excitation box and a procedure that exactly couples the first step results with the second step. The speedup of the hybrid method is made possible through the computation of the excitation (saved on disk) in the first step and the use of FD on irregular grids in the second step of the hybrid. The second step computational model can be just a small spatial fraction of the original source-path-site model. A practical parameter study example of a point double-couple source and regional topography model (applied in the first step) with a local low-velocity basin structure and ridge (both applied in the second step only) is presented.

Finite-difference (FD) modeling of complicated structures requires simple algorithms. This paper presents a new elastic FD method for spatially irregular grids that is simple and, at the same time, saves considerable memory and computing time. Features like faults, low-velocity layers, cavities, and/or nonplanar surfaces are treated on a fine grid, while the remaining parts of the model are, with equal accuracy, represented on a coarse grid. No interpolation is needed between the fine and coarse parts due to the rectangular grid cells. Relatively abrupt transitions between the small and large grid steps produce no numerical artifacts in the present method. Planar or nonplanar free surfaces, including underground cavities, are treated in a way similar to internal grid points but with consideration of the zero-valued elastic parameters and density outside the free surface (vacuum formalism). A theoretical proof that vacuum formalism fullfills the free-surface conditions is given. Numerical validation is performed through comparison with independent methods, comparing FD with explicitly prescribed boundary conditions and finite elements. Memory and computing time needed in the studied models was only about 10 to 40% of that employing regular square grids of equal accuracy. A practical example of a synthetic seismic section, showing clear signatures of a coal seam and cavity, is presented. The method can be extended to three dimensions.

Direct seismic waves (P- or S-waves) are used to locate and further characterize microseismic events. The resolution of information obtained from direct waves depends on the peak frequencies of the waveforms. The peak frequency results from combination of the source, propagation, and the receiver effects. For frequencies below the corner frequency, propagation effects control the peak frequency in observed seismograms of microseismic events. The frequency dependence of direct body waves can be modeled by attenuation, specifically the global attenuation factor. This model is consistent with observed data along surface profiles explaining the difference between the peak frequencies of P- and S-waves. In addition, the model is consistent with the peak frequencies observed on downhole monitoring arrays. This can be used to invert effective attenuation providing additional unique measurement from microseismic events. The corner frequency can be estimated from the average stress drop and analytical source models such as a circular crack model. Typical stress drops for various magnitude ranges are discussed. The peak frequencies are usually below the corner frequencies of microseismic events smaller than moment magnitude 0.7 for surface monitoring and moment magnitude −0.5 for downhole monitoring. Understanding of the frequency dependence of the direct waves allows us to optimally design monitoring networks and mainly invert effective attenuation providing unique measurement from microseismic monitoring.