Efficient extended least-squares reverse time migration based on excitation amplitude imaging condition

Abstract

Least-squares reverse time migration (LSRTM), a linearized inversion problem, can provide optimal migration image with high-resolution by minimizing a misfit function that is defined as difference between predicted and observed data. However, because LSRTM commonly become over-determined linear inverse problem, LSRTM has slow convergence speed and provide inaccurate migration image if inaccurate migration velocity is utilized for LSRTM. To mitigate sensitivity to accuracy of the migration velocity, extended LSRTM (ELSRTM) can be adopted to extend a dimension of model space. Introducing an extra dimension to model space can help to accelerate the convergence and find the optimal migration image by increasing degrees of freedom in model space. However, huge computational costs in assembling migration image volume, proportional to the number of bins in the extra dimension, hinder practical application of ELSRTM. Furthermore, there is another computational issue for ELSRTM as well as LSRTM, which is considerable memory burden for storing forward source wavefield into computer memory directly. In this dissertation, to alleviate these computational issues for construction of the migration image volume and storage of the forward source wavefield, I propose an efficient ELSRTM strategy based on an excitation amplitude (ExA) imaging condition, which is called as ELSRTM-ExA. By computational advantage of ExA imaging condition, computation for assembling the migration image volume in ELSRTM-ExA is only performed if current propagation time equals to arrival time of ExA (ExT). It leads to reduce the computation times for assembling the migration image volume. Furthermore, since the forward source wavefield can be saved as ExA and ExT, whose size is identical to that of velocity model, memory consumption for storing the forward source wavefield can be dramatically reduced. From dot-product test on forward and adjoint operators of ELSRTM-ExA, I verified that these operators have numerically adjoint relationship. And feasibility of ELSRTM-ExA is verified by comparing the forward source wavefields, Born modeled data and gradient vectors computed by conventional and ExA imaging condition. Numerical examples that are implemented with graben, modified marmousi-2, and modified pluto 1.5 models demonstrate that ELSRTM-ExA can provide fast convergence speed and high-quality migration results with significant computational efficiency in performance time and memory consumption, even if inaccurate migration velocity is utilized. Furthermore, for real dataset application, it is verified that ELSRTM-ExA can enhance resolution and quality of the migration image.