Reflections on Amplitudes*

Abstract

Modern seismic recording instruments allow precise measurements of the amplitude of reflected signals. Intuitively we would expect that this amplitude information could be used to increase our knowledge of the physical properties of the reflecting earth. The relevant factors defining the amplitude of a reflection signal are: spherical divergence, absorption, the reflection coefficient of the reflecting interface, the cumulative transmission loss at all interfaces above this, and the effect of multiple reflections. Of these factors, three—spherical divergence, the reflection coefficient and the transmission loss—are reasonably clear concepts (though the estimation of transmission loss from acoustic logs caused some difficulties in the hey‐day of synthetic seismograms). Absorption still presents considerable problems of detail, but our understanding has increased significantly in recent years. The factor least well understood is undoubtedly the effect of multiple reflections. Multiple paths having an even number of bounces can have the effect of delaying, shaping and magnifying the pulse transmitted through a layered sequence. Simple demonstations of this phenomenon can be made using elementary thin plates, and these can be presented for various synthetic and real sequences of layers. Such demonstrations lead one to explore the relation between the spectrum of the transmitted pulse and the spectrum of the reflection coefficient series. If it were possible to isolate the amplitude and shape variations imposed by absorption within a layer, there would be a chance that this measure of absorption would be useful as a correlatable or diagnostic indication of rock properties. If it were possible to isolate the amplitude and shape variations imposed by multiple reflections, there would be a chance that this measure would be useful as an indication of cyclic sedimentation and of the dominant durations of the sedimentary cycles. However, the separation of these two effects constitutes a formidable challenge. The very difficulty of this separation suggests that it may be opportune to review the quantitative estimates of absorption made by field experiments.

On the role of multiples in Marchenko imaging

“…Note that G þ ðz ϵ 4 ; z 0 ; tÞ is (apart from the transmission coefficient of the last interface) equal to the transmission response of the layered medium; hence, it is a causal minimum-phase signal, delayed by t d (Anstey and O'Doherty, 1971;Robinson and Treitel, 1976). The inverse of a minimum-phase signal is causal and minimum phase as well (Robinson, 1954;Berkhout, 1974); hence, G þ inv ðz ϵ 4 ; z 0 ; tÞ is a causal signal, advanced by t d .…”

Understanding the Physics of Kappa (Κ0): Insights From the Euroseistest Network

“…In the field of exploration seismology, it is well known that wave propagation through fine layering can filter out high frequencies and may increase the apparent attenuation through short period multiples (O' Doherty and Anstey, 1971), an effect referred to as stratigraphic filtering. However, current discussions on the nature of κ0 do not explicitly include the contribution of scattering.…”

Influence of Scattering on Seismic Waves

“…However, several special cases have been studied (O'Doherty and Anstey, 1971;Kopnichev, 1977;Toks6z, 1977, 1981;Richards and Menke, 1983;and Gao et al, 1983a, b). Wu (1984Wu ( , 1985 formulated the multiple scattering problem in the frequency domain using radiative transfer theory.…”