Fractional Time Derivative Seismic Wave Equation Modeling for Natural Gas Hydrate

Yanfei Wang,Yaxin Ning,Yibo Wang

doi:10.3390/en13225901

Abstract

Simulation of the seismic wave propagation in natural gas hydrate (NGH) is of great importance. To finely portray the propagation of seismic wave in NGH, attenuation properties of the earth’s medium which causes reduced amplitude and dispersion need to be considered. The traditional viscoacoustic wave equations described by integer-order derivatives can only nearly describe the seismic attenuation. Differently, the fractional time derivative seismic wave-equation, which was rigorously derived from the Kjartansson’s constant-Q model, could be used to accurately describe the attenuation behavior in realistic media. We propose a new fractional finite-difference method, which is more accurate and faster with the short memory length. Numerical experiments are performed to show the feasibility of the proposed simulation scheme for NGH, which will be useful for next stage of seismic imaging of NGH.

Highlights

Seismic exploration is a main technique in natural gas hydrate (NGH) survey
We focus on the finite difference discretization of the fractional time derivative for 1 < β < 2
We have introduced a more rigorous form of definition of fractional derivative to calculate the fractional time derivative of the viscoasoustic wave equation, which is more accurate and simpler than the other nearly constant-Q methods for describing the propagation of viscoasoustic wave

Summary

Introduction

Seismic exploration is a main technique in natural gas hydrate (NGH) survey. To gain a better estimation of the NGH content, we need to understand the characteristics of the seismic wave propagation in NGH. Traditional seismic modeling and inversion techniques are usually built on perfectly elastic medium model. The real underground medium usually has attenuation properties, which will cause amplitude loss and phase distortion of seismic waves. Ignoring the attenuation of the medium will make the numerical simulation and inversion results different from the real situation [1,2,3], which will result in the inability to obtain the true and accurate structural features of the underground. Studying the numerical simulation method of viscoacoustic seismic wave will help to obtain the actual propagation of underground seismic wave. Using the viscoacoustic wave equation for migration and inversion can effectively compensate the loss of amplitude, accelerate the convergence rate, and make the inversion results closer to the actual underground geological characteristics [4]

Methods

Results

Discussion

Conclusion