Computation of ray-Born seismograms using isochrons

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.

Ray-based inversion accounting for scattering for biomedical ultrasound tomography

“…Inversions exploiting the Born-approximation. A common approach to incorporating first-order scattered waves in simulations and inversions is to turn to the Born approximation [16,22,48], and in particular the ray-Born approximation [60,67]. The Born approximation suggests an efficient way for approximating the wavefield using an assumption that the sound speed model can be decomposed into a homogeneous or slowly varying background and a rapidly varying scatterer [68].…”

“…The Born approximation suggests an efficient way for approximating the wavefield using an assumption that the sound speed model can be decomposed into a homogeneous or slowly varying background and a rapidly varying scatterer [68]. It has been studied extensively from both theoretical [65,66] and numerical points of view [32,67].…”

Ray-based inversion accounting for scattering for biomedical ultrasound computed tomography

“…Inversions exploiting the Born-approximation. A common approach to incorporating firstorder scattered waves in simulations and inversions is to turn to the Born approximation, and in particular the ray-Born approximation [73,57,81]. The Born approximation suggests an efficient way for approximating the wavefield using an assumption that the sound speed model can be decomposed into a slowly varying background and a rapidly varying scatterer [82].…”

“…The Born approximation suggests an efficient way for approximating the wavefield using an assumption that the sound speed model can be decomposed into a slowly varying background and a rapidly varying scatterer [82]. It has been studied extensively from both theoretical [79,80] and numerical points of view [35,81].…”