A simplified form for nonhyperbolic equation in a TIM

Abstract

According to Dix?s formula, for the isotropic and short spread case, the moveout curves of a common shotpoint (CSP) gather or a common midpoint (CMP) gather can be approximated by a hyperbola. As a matter of fact, the spread of the field survey may not always meet the requirement of Dix?s assumption and the real earth does not behave as a perfect isotropic medium. Releasing the limitation of spread length and considering the anisotropy the real earth, Byun et al (1989) derived the formula for nonhyperbolic analysis for horizontally layered, transversely isotropic, media. The formula is called skewed hyperbolic moveout formula and involves three measurement parameters: the average vertical velocity and horizontal and skew moveout velocities. Carry on Byun?s skewed hyperbolic moveout formula; Sena (1991) derived analytical expressions giving traveltime-offset curves for multilayered weakly azimuthally isotropic and anisotropic media on terms of the elastic properties of each layer. Inheriting to the idea of skewed hyperbola moveout that has been proposed, we assumed that the seismic ray follows an imaginary rectilinear path. Based on the fundamental concept of vector analysis, we decomposed the velocity of seismic wave into two components: vertical and horizontal components. Compare to Byun?s moveout formula, the velocity parameters had been reduced from three to two. We named the new formula as a simplified nonhyperbolic moveout formula. To ascertain our ideology, the new formula is tested by laboratory data. Laboratory walk away transmission experiments were done on both Plexiglas and phenolite that were homogenous and commonly adopted to stand for isotropic and anisotropic materials, respectively. A semblance analysis is adopted to process the observed data. Scanning the recorded gather using the new formula we proposed, laboratory works show the moveout velocity that was computed from reflection seismology could be decomposed into vertical and horizontal components with reasons. In the process of time-to-depth conversion, one can always estimate the depth or layer thickness by multiplying one-way traveltime to vertical velocity of the new moveout formula, and the horizontal velocity that can be used to diagnose the anisotropy of the explored area and to explore the lithology of the subsurface strata.