Moveout approximation for a P-SV wave in a moderately anisotropic homogeneous DTI layer

Abstract

We derive and test the moveout formula for converted P-SV (or SV-P) waves in a homogeneous, weakly or moderately anisotropic, transversely isotropic layer with axis of symmetry perpendicular to a dipping reflector underlying it. Instead of commonly used Taylor series expansion of the squared traveltime with respect to the offset, we use weak-anisotropy approximation of the exact traveltime formula. We replace the exact traveltime along the actual ray of a converted wave by its first-order weak-anisotropy approximation along a ray in a nearby reference isotropic medium. The traveltime formula is derived in the plane defined by the source-receiver line and the normal to the reflector. The source and the receiver may be situated arbitrarily in the model, the flat reflector may have an arbitrary 3D orientation. The accuracy of the proposed moveout formula is tested on models with varying strength of anisotropy for a varying dip of the reflector. In isotropic media, the formula yields highly accurate results with relative traveltime errors not exceeding 0.5%. In anisotropic media of P- and SV-wave anisotropy of about 25% and 12%, respectively, relative traveltime errors do not exceed 2%.