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I believe it is useful to extend the visco-elastic equation in two directions:
- Replace the scalar mass density, , with a 3-by-3 matrix
representation,
*R*, of a (generally anisotropic) 2nd order inertia tensor.
- Allow frequency-dependence in the elements of the matrix
*R*.

Why do I want to do this? A simple, one-dimensional answer is that
velocity and impedance can only be independently controlled by access
to both elasticity and density. This is certainly true at the frequency
origin, and may also be true just away from the origin.
So, the scalar density in equation (2) is replaced by an inertia matrix, *R*,

| |
(3) |

and then this inertia matrix is made frequency dependent:
| |
(4) |

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Stanford Exploration Project

11/17/1997