Linearized Frequency-Dependent Reflection Coefficient and Attenuated Anisotropic Characteristics of Q-VTI Model

Yahua Yang,Gang Gao,Danping Cao,Xingyao Yin,Bo Zhang

doi:10.3390/en14248506

Abstract

Seismic wave exhibits the characteristics of anisotropy and attenuation while propagating through the fluid-bearing fractured or layered reservoirs, such as fractured carbonate and shale bearing oil or gas. We derive a linearized reflection coefficient that simultaneously considers the effects of anisotropy and attenuation caused by fractures and fluids. Focusing on the low attenuated transversely isotropic medium with a vertical symmetry axis (Q-VTI) medium, we first express the complex stiffness tensors based on the perturbation theory and the linear constant Q model at an arbitrary reference frequency, and then we derive the linearized approximate reflection coefficient of P to P wave. It decouples the P- and S-wave inverse quality factors, and Thomsen-style attenuation-anisotropic parameters from complex P- and S-wave velocity and complex Thomsen anisotropic parameters. By evaluating the reflection coefficients around the solution point of the interface of two models, we analyze the characteristics of reflection coefficient vary with the incident angle and frequency and the effects of different Thomsen anisotropic parameters and attenuation factors. Moreover, we realize the simultaneous inversion of all parameters in the equation using an actual well log as a model. We conclude that the derived reflection coefficient may provide a theoretical tool for the seismic wave forward modeling, and again it can be implemented to predict the reservoir properties of fractures and fluids based on diverse inversion methods of seismic data.

Highlights

Development of seismic acquisition and processing technology makes it possible to sufficiently employ useful information embedded in seismic data, e.g., amplitude variation with offset, azimuth and frequency (AVO, AVAz, AVF), to estimate fluids and fractures
We focus on the case of Q-VTI medium with low-loss attenuation and weak anisotropy, which means we neglect the term proportional to higher orders of the attenuation factors and Thomsen anisotropic parameters, and we let P-wave, SV-wave and SH-wave propagate in the linear constant Q attenuation reference media
Under the assumption of low-loss attenuation and weak anisotropy of velocities, we derive the linearized approximate frequency-dependent reflection coefficient based on the linear constant Q-VTI model

Summary

Introduction

Development of seismic acquisition and processing technology makes it possible to sufficiently employ useful information embedded in seismic data, e.g., amplitude variation with offset, azimuth and frequency (AVO, AVAz, AVF), to estimate fluids and fractures. The modeling of frequency-dependent attenuation and anisotropy of seismic waves, and the inversion for attenuation factors and anisotropic parameters using frequency-dependent seismic amplitude data, may help improve the reliability of the detection of fractured reservoirs and infilling fluids [10,11]. Dynamic equivalent medium models are proposed to describe how seismic wave propagates in fractured rocks in the case of considering the effect of frequency variation [2,3,4,5,6,7,8,9]. Schematic of of seismic seismic wave wave propagate propagate in in an an attenuation attenuation anisotropy anisotropy medium medium based based on on the the Figure perturbation theory. ItItisischaracterized characterizedbybythree three elastic parameters α, S-wave veβ and β density ρ; two viscoelastic parameters P-wave quality

Objectives

Methods

Discussion

Conclusion