Abstract
Seismic modeling in heterogeneous media is accomplished by using either approximate or fully numerical methods. A popular approximate method is ray-Born modeling, which requires the computation of 3D integrals. We have developed an integration technique for accurate and, under certain circumstances, efficient evaluation of the ray-Born integrals in the time domain. The 3D integrals are split into several 2D integrals, each of which gives the wavefield at a certain time, so that the waveform at each time step is computed independently of all other times. We compute seismograms for 3D heterogeneous acoustic media using this technique and compare these seismograms with seismograms computed using two other modeling methods: frequency-domain ray-Born modeling and finite-difference modeling of the acoustic wave equation. Our method can also be applied to elastic ray-Born modeling. Velocity models with smooth scatterers and the SEG/EAGE overthrust model are used for comparison. The ray-Born seismograms computed using the time- and frequency-domain ray-Born modeling methods are identical, as expected. The comparison between the ray-Born modeling and the finite-difference-modeling method indicates that the waveforms are similar for both types of velocity models. We evaluate the discrepancies in terms of multiple scattering and multipathing.
Highlights
Modeling of seismic waves is very important for studying the Earth’s structure
More work needs to be done on the interpolation of results for integration with, for example, the imaging integrals in Sarajaervi and Keers (2019). If this integration is achieved, an advantage to the approach is that the need to transfer data between graphics processing units (GPUs) and central processing units (CPUs) memory is eliminated as all ray data is contained in the GPU memory
The seismograms computed over surface integrals in the time domain are identical to ray-Born seismograms computed over volumes in the frequency domain
Summary
The Born integral 13 requires knowledge of g0. In the case of a homogeneous background medium, g0 is known explicitly. In preparation for ray-Born modeling using equation 36, the quantities Trs, ∇Trs, and Ars are computed using ray tracing They are found by first computing Tðs; xÞ, ∇Tðs; xÞ, and Aðs; xÞ from the source s to all points x in the scattering region D. With the two-point ray tracing completed for the source-receiver pair, we compute the traveltime function Trs using equation 19 and the amplitude function Ars using equation 20. We have computed Trs using the ray-tracing procedure described above, and we have used the marching cubes algorithm (Lorensen and Cline, 1987) to extract surfaces In this case, Sτ is defined on a triangular grid with vertex positions x1 1⁄4 x1ðnÞ, x2 1⁄4 x2ðnÞ, and x3 1⁄4 x3ðnÞ, where n 1⁄4 1; : : : ; ntr and ntr is the number of triangles. To avoid edge effects within the time window of interest, all velocity models are extended beyond the area of interest
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