SEISMIC REFLECTION AMPLITUDES¹

Abstract

URSIN, B. and DAHL, T. 1992. Seismic reflection amplitudes. Geophysical Prospecting 40,483-512.Seismic amplitude variations with offset contain information about the elastic parameters. Prestack amplitude analysis seeks to extract this information by using the variations of the reflection coefficients as functions of angle of incidence. Normally, an approximate formula is used for the reflection coefficients, and variations with offset of the geometrical spreading and the anelastic attenuation are often ignored. Using angle of incidence as the dependent variable is also computationally inefficient since the data are recorded as a function of offset.Improved approximations have been derived for the elastic reflection and transmission coefficients, the geometrical spreading and the complex travel-time (including anelastic attenuation). For a 1 D medium, these approximations are combined to produce seismic reflection amplitudes (P-wave, S-wave or converted wave) as a Taylor series in the offset coordinate. The coefficients of the Taylor series are computed directly from the parameters of the medium, without using the ray parameter.For primary reflected P-waves, dynamic ray tracing has been used to compute the offset variations of the transmission coefficients, the reflection coefficient, the geometrical spreading and the anelastic attenuation. The offset variation of the transmission factor is small, while the variations in the geometrical spreading, absorption and reflection coefficient are all significant.The new approximations have been used for seismic modelling without ray tracing. The amplitude was approximated by a fourth-order polynomial in offset, the traveltime by the normal square-root approximation and the absorption factor by a similar expression. This approximate modelling was compared to dynamic ray tracing, and the results are the same for zero offset and very close for offsets less than the reflector depth.

Decoupled elastic prestack depth migration

“…with the angle-independent coefficients K n (lm) expressed in terms of the elastic parameters q( Q) and C( Q) (for stratified isotropic media, see Ursin and Dahl, 1992). Substituting Eq.…”

Support Vector Machine (SVM) based prestack AVO inversion and its applications

“…Based on the classical work on geophysical probabilistic inverse theory (e.g., Tarantola, 1987;Menke, 1989), they employ the Bayesian statistical method to formulate the AVO inversion problem successfully (Gouveia, 1996;Sen and Stoffa, 1996;Gouveia and Scales, 1998;Buland and Omre, 2003;Riedel et al, 2003;Downton, 2005;Rabben et al, 2008;Karimi et al, 2010;Theune et al, 2010;Alemie and Sacchi, 2011;Zong et al, 2013). In the literature listed above, some are using the linearized approximations (see Aki and Richards, 1980;Shuey, 1985;Smith and Gidlow, 1987;Gray et al, 1999;Ursin and Dahl, 1992;Wang, 1999;Ursenbach, 2002) and some are employing the accurate Zeoppritz equations (Simmons and Backus, 1996). Through various parameterizations and approximations of the accurate Zeoppritz equations, they are popular in the AVO inversion problems.…”

2.5-D Geometrical Spreading in a Layered Isotropic Medium Under Deep-Water Condition

“…It is a convenient and simple method, which has found wide applications in real life, but its compensation accuracy is limited. Ursin et al (1978Ursin et al ( , 1990Ursin et al ( , 1992Ursin et al ( , 2003Ursin et al ( , 2006) systematically studied the relationship among seismic ray tracing, travel time and amplitude compensation. Several approximate formulas to calculate the layered medium under the condition of non-zero shot-offset.…”