The inertia tensor in elastic wave modeling

Francis Muir

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ABSTRACT

The homogeneous equivalent to a fine-layered, heterogeneous elastic medium may need a frequency-dependent, anisotropic inertia tensor if it is to be dynamically equivalent in a useful sense. The elastic and inertial matrices that make up this equation would likely not commute, and there would be no Christoffel-like equation. This difficulty is resolved by a local transformation of the field variable from displacement to an energy form. This inertia tensor is shown, by analogy, to be physically reasonable.