Shuey (1985) has rewritten the Aki-Richards Rpp in a useful form consisting of three terms. The first is the zero-offset reflection coefficient, the second depends on the square of the sine of the average P-wave angle, and the third essentially depends on fourth and higher even-order powers of the sine. The full three-term expression is equivalent to Aki-Richards, but the 2-term approximation is commonly used and is normally considered accurate up to an angle of about 30 degrees. This allows one to invert to only two variables, the two variables being combinations of the four Aki-Richards variables.
In the case of Rps, one obtains an odd-power series of sine functions and Rps is sometimes approximated as a function linear in the sine. Rss, like Rpp, has an even-power expansion and can be expressed by a 2-term approximation.
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