The Interpretation of Shear-Wave Splitting Parameters In the Presence of Two Anisotropic Layers

Abstract

We consider the behaviour of shear-wave splitting parameters that are made under the assumption of a single layer of anisotropic material when in fact two layers of differing anisotropic properties are present. It is shown that the resulting apparent splitting parameters are still meaningful quantities and in fact can (at fixed frequency) be written as trigonometric functions of the splitting parameters of the individual layers. These expressions reveal many properties of the apparent splitting parameters. For example, the apparent fast polarization øa and delay time δta exhibit systematic variations as a function of incoming polarization with π/2 periodicity. The derived expressions can be used to invert for the individual properties of the two layers in many circumstances. We show that several stations along the San Andreas fault system display the properties of two layers, with the top layer being parallel to the local strike of the San Andreas fault. Finally, the derived expressions for the apparent splitting parameters are shown to be easily generalized to multiple layers.