We did this by developing a set of utilities for calculating the elastic properties of equivalent media. The toolkit enables the user to derive the elastic properties of layered and fractured media using S&M theory.

The calculation of equivalent media is based on the parameterisation of a layer by its thickness, density, and (compressed subscript notation) stiffness tensor. The symmetric matrix is rearranged to give three submatrices. We call the form the ``parameter'' form and the three matrix form the ``model'' form. This change is merely a reordering of elements, no arrithmetic is performed.

Layers are combined in a ``group domain'' by simple addition of group elements. In the group domain the parameterisation takes the form of two scalars and three matrices. The mapping from the layer to group is computed using only matrix operations as is the inverse mapping from group to layer.

The other operation we wish to perform is rotation of the coordinate frame of the elastic constants of a layer. This is done by expanding the stiffness matrix to its full tensor form and then multiplying by a transformation operator.

To find the elastic constants for the boundary grid cell, we add the two bounding media in the appropriate ratio, and then rotate the result so the layer dips the right amount.

Figure 2

Figure 3

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