Plane waves, spherical waves and angle‐dependent P‐wave reflectivity in elastic VTI‐models

Abstract

The AVA-response of VTI-models for AVO-Classes 1 to 4 and two special cases is computed utilizing plane-wave reflection coefficients and the Weyl-integral. It is found that below 30° of angle, in most cases, the spherical VTI-response departs more from an isotropic plane-wave comparison than isotropic spherical responses. Depth dependence of isotropic spherical responses is strongest near critical angles, exactly where important information resides. VTI-type anisotropy shifts this point of maximum sensitivity towards larger angles.

Spatial patterns of regeneration in managed uneven-aged ponderosa pine/Douglas-fir forests of Western Montana, USA

“…In this study, we computed 99% confidence bands for L(t) by running 99 simulations at intervals of 1 m from 1 to 16 m (half the length of the shortest side of the plot). The Cramer-von-Mises test was used to test for significance (Haase, 2002). Since edge effects become a concern at greater distances, we used the weighted edge correction factor proposed by Ripley (1981) to account for this effect (Haase, 1995).…”

“…A value ofL 1:2 ðtÞ significantly larger or smaller than 0 indicates spatial attraction or repulsion, respectively, between the two size-classes at range t. Monte Carlo simulations were used to evaluate the statistical evidence of a departure from zero, where each simulation consisted of randomly assigning new coordinates to only one size-class, while the coordinates of the other size-class remain unchanged (Goreaud and Pélissier, 2003;Haase, 2002). The spatial statistics program SPPA.EXE (Haase, 2002) was used for the computations of both univariate and bivariate analyses.…”

Improved Modelling of Spherical-Wave AVO

“…This new approach is admittedly not as exible as the numerical approach of Haase (2002Haase ( , 2003Haase ( , 2004a, which can not only be easily extended to other wavelets, but to converted waves Haase (2004a), viscoelastic media (Haase, 2004b), and anisotropic media (Haase and Ursenbach, 2005) as well. However the case of PP-re ections in isotropic, elastic media is central to exploration seismology.…”

“…One way to obtain AVO information from this trace is to extract the maximum of the trace envelope. This method has been implemented by Haase (2002Haase ( , 2003Haase ( , 2004a, and we refer to it as the numerical method, to distinguish it from the method of this paper.…”

AVO Analysis of Spherical Reflected P Waves

“…(16), the displacement U of a particle can be calculated. Then, in terms of the reflective coefficient of the particle displacement from Zoeppritz equation, we compute the reflective coefficient of the elastic interface [14,18] . In this calculation, the reflective coefficient is normalized by the maximum particle displacement to determine the reflective coefficient of reflective PP waves.…”