*The scattering equation for compressional (longitudinal) acoustic waves in rock analogous to the radar equation for lossy media is:

Pr = [PT/(4p)3][(l2G2s)/R4]e-4bR

where
    Pr = Received acoustic power, watts
    PT = Transmitted power, watts
    l = Wavelength in the medium, m
    R = Distance to target, m
    G = Gain of receiving and transmitting transducers
    b = Absorptive attenuation factor of the medium, pre meter
    s = Equivalent cross-sectional area of target, m2

the absorptive attenuation factors we have measured to date do not appear to follow the e-4bR term, the reason for which is yet to be determined. We have found that for radar, attenuation generally increases with frequency raised to the power of 0.5, whereas for acoustic waves in rock the attenuation more commonly increases with frequency raised to the power of 0.9.