Finite-frequency traveltime inversion offers higher accuracy for velocity model building than ray-based traveltime inversion. The adjoint force is the key for the computation of inversion kernels. Starting at the definition of inversion kernels for the acoustic wave equation, we have derived the explicit formula for the spectral distribution density function used in the adjoint force computation. Two formulations are developed for the computation of adjoint forces for receiver-side extrapolation, frequency-domain representation, and time-domain representation. The accuracy of finite-frequency traveltime inversion kernels is benchmarked with the analytical solutions for homogeneous isotropic media. We use wavefront construction to compute the first Fresnel zones for kernel conditioning. Based on dynamic ray tracing, we design a processing procedure guided by synthetic data tests to extract the desired events for wavefield backward extrapolation from the data. Unlike ray-based velocity tomography, finite-frequency inversion can resolve the velocity structures comparable with the size of Fresnel zones as we demonstrate on a marine salt model using ocean-bottom node acquisition geometry. Despite the fact that the inversion kernels are based on Born approximation, velocities with errors up to 20% can be well-resolved. For practical purposes, a simple formulation is given for the determination of the shot spacing. Our workflow for finite-frequency inversion is efficient and converges in only very few iterations.

Reverse Time Migration (RTM) is a preferred depth migration method for imaging complex structures. It solves the complete wave equation and can model all types of complex wave propagation with no dip limitation. Reverse time migration using the inverse scattering imaging condition produces structural images with an amplitude approximate to the reflectivity, which is a composite effect of the impedance and velocity changes in the acoustic media with variable velocity and density. In this study, we present a modified inverse scattering imaging condition to separate the effect of the impedance and velocity perturbations from the reflectivity. The proposed imaging condition is designed to predict the relative impedance perturbation by selecting near-angle reflections during common-shot RTM. We validate our approach on synthetic models and show that the proposed method can estimate reliable impedance perturbation.

Correlation- and convolution-based internal multiple prediction is one of the most common methods to predict and subsequently attenuate internal multiples. This technique requires the convolution of two seismic events from the deep section followed by the correlation with an event from the shallow part section to satisfy the so-called deep-shallow-deep (late-early-late) condition; otherwise, nonphysical seismic events can be predicted. To comply with this condition, seismic data are separated into shallow and deep portions according to a given phantom horizon. Internal multiples whose raypaths pass through the phantom horizon four times are predicted for one trial. In this way, only a portion of internal multiples are predicted. To address this limitation, a novel algorithm called the generalized internal multiple prediction (GIMP) algorithm is proposed. This algorithm is founded upon the adaptation of the deep-shallow correlation and deep-deep convolution techniques, constrained by specific integration boundaries. The GIMP method effectively accommodates the deep-shallow-deep (late-early-late) mode, without necessitating the segmentation of the seismic data set into shallow and deep segments via a user-defined phantom horizon. Notably, this approach is comprehensive in nature and has the capability to predict all potential internal multiples concurrently. Considering the computational cost, the current implementation focus of GIMP is primarily on 1D or 1.5D; however, GIMP is applicable to 2D and 3D scenarios.

This study discusses the properties and decompositions of the traveltime sensitivity kernels in elastic isotopic and transversely isotropic media. Analytical solutions in homogeneous isotropic elastic media are derived and help better understand their properties. One key component is the kernel phase function which determines the frequency components of the sensitivity kernels, the geometrical setting of the Fresnel zones, and the resolving ability for velocity inversion. For the purpose of exploration seismology, the sensitivity kernels for finite-frequency traveltime inversion in transversely isotropic elastic media are expressed in terms of Thomsen’s anisotropic parameters. The sensitivity kernels in anisotropic media can be decomposed into the summation of the isotropic terms constructed by the elastic properties in the symmetry direction and the correction terms due to the presence of anisotropy. Sensitivity kernels computed from different types of acquisitions contain information for different parameters. We compare the kernels computed using finite-difference with those by dynamic ray tracing. We conclude that the full wave numerical method is able to provide high-resolution kernels, which form the basis for 3D finite-frequency traveltime inversion for velocity and anisotropic parameters.