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Using the definitions of the Thomsen parameters, we can also rewrite the
terms appearing in (33) in order to make connection with
this related point of view. Recalling (5) and the fact that *b* = *a* - 2*m*, we have

| |
(34) |

with some higher order corrections involving powers of and products of with and that we have
neglected here. We have added and subtracted equally
some terms proportional to , and others proportional to
, in order to emphasize
the similarities between the form
(34)
and that found previously in (33). In particular, the
difference is known (Postma, 1955; Berryman, 1979)
to be non-negative and its deviations from zero depend on fluctuations
in from layer to layer, behavior similar to that of
the final term in (33). Since the formula
(34) is only approximate and its interpretation
requires the use of various other results we derive later for other
purposes, we will for now delay further discussion of this point
to the end of the paper.

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** Up:** SINGULAR VALUE DECOMPOSITION
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Stanford Exploration Project

10/16/2003