SEISMIC REFLECTION AMPLITUDES 1

A bstract 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.