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Converting the Roughness of Model Interfacies into the Statistical Distribution of Elastic Parameters of the Layered Medium

In the paper, the effect of interface roughness on the elastic parameters of a layered medium is studied. Three-dimensional models of a layered medium with different material inside and outside the layer are considered. Initially, the first class of models is statistically generated with rough interfaces between the layers and fixed elastic parameters of the inner layers. Then the effective stiffness tensor is estimated for the equivalent homogeneous model. After that, new elasticity parameters of the inner layer are reconstructed for second class of models with flat interfacies. Thus, the roughness of the model interfacies is mapped into a statistical distribution of the stiffness tensor components for a fixed model geometry. In addition, an algorithm for extending the results of reconstructing the elastic tensors for arbitrary interface roughness parameters using bilinear regression of covariance matrices is proposed. The algorithm verification shows that the error in restoring the covariance matrix does not exceed 7%; i.e., one can use it in statistical modeling the second class of models with flat interfacies for the arbitrary interface roughness values and given physical parameters of layers in the first class of models.