ABSTRACT

We have developed a derivation of a system of equations for acoustic waves in a medium with transverse isotropy (TI) in velocity and attenuation. The equations are derived from Cauchy’s equation of motion, and the constitutive law is Hooke’s generalized law. The anisotropic anelasticity is introduced by combining Thomsen’s parameters with standard linear solids. The convolutional term in the constitutive law is eliminated by the method of memory variables. The resulting system of partial differential equations is second order in time for the pseudopressure fields and for the memory variables. We determine the numerical implementation of this system with the finite-difference method, with second-order accuracy in time and fourth-order accuracy in space. Comparison with analytical solutions, and modeling examples, demonstrates that our modeling approach is capable of capturing TI effects in intrinsic attenuation. We compared our modeling approach against an alternative method that implements the constitutive law of an anisotropic visco-acoustic medium, with vertical symmetry, in the frequency domain. Modeling examples using the two methods indicate a good agreement between both implementations, demonstrating a good accuracy of the method introduced herein. We develop a modeling example with realistic geologic complexity demonstrating the usefulness of this system of equations for applications in seismic imaging and inversion.

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