THE INTERPRETATION OF SHEAR-WAVE SPLITTING PARAMETERS IN THE PRESENCEOF 2 ANISOTROPIC LAYERS

We consider the behaviour of shear-wave splitting parameters that are made under the assumption of a single layer of anisotropic material wh en in fact two layers of differing anisotropic properties are present. It is shown that the resulting apparent splitting parameters are stil l meaningful quantities and in fact can (at fixed frequency) be writte n as trigonometric functions of the splitting parameters of the indivi dual layers. These expressions reveal many properties of the apparent splitting parameters. For example, the apparent fast polarization phi( a) and delay time delta t(a) exhibit systematic variations as a functi on of incoming polarization with pi/2 periodicity. The derived express ions can be used to invert for the individual properties of the two la yers in many circumstances. We show that several stations along the Sa n 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 parameter s are shown to be easily generalized to multiple layers.