The accuracy of approximating P-wave traveltimes in orthotropic media using VTI equations

Abstract

SUMMARY Analysis of azimuthally varying non-hyperbolic moveout of P-wave traveltimes in orthotropic media can provide valuable information for reservoir fracture characterization and seismic data processing. Moveout velocities and azimuthal orientation of the two vertical symmetry planes plus anellipticity parameters defined for the three symmetry planes of an orthotropic medium can be estimated from the inversion of P-wave traveltimes measured in long-spread, wide-azimuth seismic surveys. Several orthotropic moveout equations have been developed to this date that can be used in the traveltime data inversion. The accuracy of the inversion results is primarily determined by the complexity of the equation and the assumptions (i.e. elastic or acoustic) made to derive it. Here, we show that often simpler moveout equations derived for transverse isotropy media with vertical axis of symmetry (VTI) can be used to estimate anellipticity parameters of the orthotropic media with high accuracy. We make an accuracy comparison analysis between non-hyperbolic moveout equations that are widely used in modelling P-wave traveltimes in VTI media. Our comparison analysis is based on the accuracy of estimating anellipticity parameters defined for two vertical [η(1) and η(2)] and one horizontal [η(3)] symmetry planes of a wide range of orthotropic media. The anellipticity parameters are estimated from the inversion of numerical traveltimes that are generated for a single and horizontal orthotropic layer. We show that for the survey geometry used in this analysis, most of the moveout equations can produce reliable estimates of the anellipticity parameters η(1) and η(2). Despite the availability of traveltime data from wide-azimuths and long source–receiver offsets, none of the moveout equations can estimate η(3) as accurate as η(1) and η(2) estimations. We show that while all the equations produce mostly accurate estimates of η(1) and η(2), generalized moveout approximation (GMA) provides the greatest accuracy. We also assess the validity of using GMA to invert P-wave traveltimes for three anellipticity parameters in terms of anisotropy in the background medium, fracture weakness, source–receiver offset (group angle) and traveltime data coverage in both the vertical (dip) and horizontal (azimuthal) planes. We show that, for a reasonable offset range, GMA can be reliably used to estimate anellipticity parameters η(1) and η(2) for an orthotropic medium that is constructed by intensive fracturing of a host medium with strong VTI anisotropy.