Effective Q-compensated reverse time migration using new decoupled fractional Laplacian viscoacoustic wave equation

Abstract

Seismic waves are attenuated and distorted during propagation because of the conversion of acoustic energy to heat energy. We focus on intrinsic attenuation, which is caused by [Formula: see text], which is the portion of energy lost during each cycle or wavelength. Amplitude attenuation can decrease the energy of the wavefields, and dispersion effects distort the phase of seismic waves. Attenuation and dispersion effects can reduce the resolution of image, and they can especially distort the real position of interfaces. On the basis of the viscoacoustic wave equation consisting of a single standard linear solid, we have derived a new viscoacoustic wave equation with decoupled amplitude attenuation and phase dispersion. Subsequently, we adopt a theoretical framework of viscoacoustic reverse time migration that can compensate the amplitude loss and the phase dispersion. Compared with the other variable fractional Laplacian viscoacoustic wave equations with decoupled amplitude attenuation and phase dispersion terms, the order of the Laplacian operator in our equation is a constant. The amplitude attenuation term is solved by pseudospectral method, and only one fast Fourier transform is required in each time step. The phase dispersion term can be computed using a finite-difference method. Numerical examples prove that our equation can accurately simulate the attenuation effects very well. Simulation of the new viscoacoustic equation indicates high efficiency because only one constant fractional Laplacian operator exists in this new viscoacoustic wave equation, which can reduce the number of inverse Fourier transforms to improve the computation efficiency of forward modeling and [Formula: see text]-compensated reverse time migration ([Formula: see text]-RTM). We tested the [Formula: see text]-RTM by using Marmousi and BP gas models and compared the [Formula: see text]-RTM images with those without compensation and attenuation (the reference image). [Formula: see text]-RTM results match well with the reference images. We also compared the field data migration images with and without compensation. Results demonstrate the accuracy and efficiency of the presented new viscoacoustic wave equation.