New approximations are developed for R PP and R PS that are optimal in the sense that they preserve as much accuracy as possible with as much simplicity as possible. In particular, they are expressed in a form that is pseudo-linear after the form of the Aki- Richards approximation. Thus they would be very simple to apply in an essentially exact non-linear inversion. Accurate analogues of the two-term Shuey equation are also given for both R PP and R PS .
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