Linearized formulations and approximate solutions for the complex eikonal equation in orthorhombic media and applications of complex seismic traveltime

Author:

Huang Xingguo1ORCID,Greenhalgh Stewart2

Affiliation:

1. Formerly Chinese Academy of Geological Sciences (CAGS), Institute of Geophysical and Geochemical Exploration (IGGE), Langfang, China; presently University of Bergen, Department of Earth Science, Bergen, Norway..

2. King Fahd University of Petroleum and Minerals, Department of Geosciences, Dhahran, Saudi Arabia..

Abstract

We have developed linearized complex eikonal equations for orthorhombic media and the analytic solution for homogeneous acoustic media. The linearized formulations are developed from the highly nonlinear complex eikonal equation using a perturbation analysis. The analytic solution is obtained by expanding the complex traveltime in a Taylor series and constructing its coefficients. A critical factor for deriving this analytic expression is to apply the complex point-source method to the analytic expression for the background anisotropic medium. The analytic expressions show that the complex traveltime is a function of the anisotropic parameters, wave velocity, and spatial coordinates. We give the numerical results of the complex traveltime for different anisotropic parameters and initial beam widths. Furthermore, numerical examples are investigated for various coefficients as a function of the coordinates.

Publisher

Society of Exploration Geophysicists

Subject

Geochemistry and Petrology,Geophysics

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