Anisotropic Mean Traveltime Curves: A Method to Estimate Anisotropic Parameters from 2D Transmission Tomographic Data

Abstract

We present the mathematical deduction and properties of the mean traveltime curves for homogeneous elliptical anisotropic media. These curves generalize their isotropic counterparts which have been introduced in the past as a simple data quality analysis technique at the pre-inversion stage for 2D transmission experiments, allowing the inference of prior velocity models to gain stability at the tomographic inversion. Also, the anisotropy parameters (maximum velocity, anisotropic direction and ratio) are shown to affect the shape of these curves. The degree of asymmetry of the anisotropic mean traveltime curves (displacement of the mean time and standard deviation minima from the middle of the gathering line) is related to the direction of anisotropy which can then be visually estimated. Least squares’ fitting of the anisotropic theoretical models to their experimental counterparts is an effective method to estimate at the pre-inversion stage a macroscopic elliptical anisotropic velocity model, valid at the scale of the experiment, and able to match the experimental mean traveltime distribution.