Amplitude-variation-with-angle (AVA) methods establish the seismic properties of material either side of a reflective interface, and their use is growing in glaciology. The AVA response of an interface is defined by the complex Knott-Zoeppritz (K-Z) equations, numerous approximations to which we typically assume weak interface contrasts and isotropic propagation, inconsistent with the strong contrasts at glacier beds and the vertically transverse isotropic (VTI) fabrics were associated with englacial reflectivity. We considered the validity of a suite of approximate K-Z equations for the exact P-wave reflectivity RP of ice overlying bedrock, sediment and water, and englacial interfaces between isotropic and VTI ice. We found that the approximations of Aki-Richards, Shuey, and Fatti match exact glacier bed reflectivity to within RP±0.05, smaller than the uncertainty in typical glaciological AVA analyses, but only for maximum incident angle θi limited to 30°. A stricter limit of θi20° offered comparable accuracy to a hydrocarbon benchmark case of shale overlying gas-charged sand. The VTI-compliant Rüger approximation accurately described englacial reflectivity, to within RP±0.01, and it can be modified to give a quadratic expression in sin2(θi) suitable for curve-matching operations. Having shown the circumstances under which AVA approximations were valid for glaciological applications, we have suggested that their interpretative advantages can be exploited in the future AVA interpretations.

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