Approximate solution of nonlinear double-scattering inversion for true amplitude imaging

Abstract

Linearized inversion algorithms are the main techniques in seismic imaging that apply the single-scattering (Born) approximation to the scattered field, and therefore, have difficulty handling the strong perturbation of model parameters and nonlinear multiple-scattering effects. To theoretically overcome these drawbacks in the linearization of the inverse scattering problem, we have developed an approach to deal with nonlinear double-scattering inversion. We first used an integral equation formulation associated with the scattered field consisting of single and double scattering in an acoustic earth model based on the second-order Born approximation, and we found that the approximation of the scattered field can be naturally related to the generalized Radon transform (GRT). We then adopted the inverse GRT to obtain the corresponding quadratic approximate inversion solution. Our inversion scheme can appropriately handle the first-order transmission effects from double scattering in a local area, which gives a significant amplitude correction for the inversion results and ultimately results in a more accurate image with true amplitude. We conducted numerical experiments that showed the conventional single-scattering inversion was good in amplitude only for perturbation up to 10% of the background medium, but our approach can work for up to 40% or more. Test results indicated that our inversion scheme can effectively relax the requirement of the weak perturbation of the model parameter in the Born approximation and can deal with the complex model directly. The computational complexity of our new scheme is almost the same as conventional linear scattering inversion processing. Therefore, the cost of our approach is at a similar level to that of linear scattering inversion.

A joint imaging method of vertical seismic profiling data by generalized radon transform migration

“…where is the amplitude weighting function, whose calculation is related to amplitude propagation, geometrical spreading and scattering angle at the image point (see Ouyang et al ., 2014, for more details). is the total travel time function calculated by the paraxial dynamic ray tracing.…”

“…Another important point is that most of these methods focus more on structural imaging and seldom involve amplitude‐preserved consideration. Since Beylkin (1984) first introduces the generalized Radon transform (GRT) to solve the linearized inverse scattering problem mathematically, the GRT migration/inversion method has been extensively researched and developed (Beylkin and Burridge, 1990; Thierry et al ., 1998; Ursin, 2004; Ouyang et al ., 2014; Li et al ., 2018; Liang et al ., 2020). This is a classical, efficient and direct inversion method for inverse scattering problems based on the perturbation theory and high‐frequency approximation.…”

Imaging of vertical seismic profiling data using weighted generalized radon transform migration in dip-angle domain

“…The linearized integral equation relates the scattered wavefield to the subsurface medium parameters under the Born approximation. The asymptotic solutions of the integral equation have been derived using the inversion theory of the GRT (Beylkin, 1985;Miller et al, 1987;Ouyang et al, 2015). For an arbitrary observation system, the GRT inverse operator on a scattered field at imaging point x is given by…”