Apparent attenuation associated with seismic wave interference in two-component cyclic stratification

Abstract

Interference effects and dissipation produce frequency selective attenuation. In a one-dimensional stratified medium the observed attenuation is a composite of the apparent attenuation arising from interference effects and dissipation. An understanding of the interference effects and its relation to the parameters of the medium can lead to better estimates of dissipation. Depth intervals in the earth are modeled as two-component cyclic zones. Synthetic seismograms are used to generate the response which include the interference effects. Interference effects for both nondissipative and dissipative zones are analyzed. The layer thicknesses are generated from a uniform distribution with specified minimum and maximum values. Apparent attenuation values depend not only on the parameters of the layers but also on their arrangement. To obtain results that depend only on the model parameters, the apparent attenuation for a particular layer arrangement is treated as a random variable. The apparent attenuation corresponding to all the possible permutations constitute the population. Estimates of the population mean based on attenuation values form 15 or 20 layer arrangements, are used in analyzing the effect of varying the model parameters on the apparent attenuation. In a system with nondissipative layers, the apparent attenuation is negligible (< .1 dB/wavelength) in frequency band of 20 - 125 Hz, when the reflection coefficients in the cyclic system are less than 0.06. When the layer thicknesses are small (< 3.10 m) the reflection coefficients have to be large (> .15) before apparent attenuation becomes significant. For reflection coefficients normally encountered the apparent attenuation is not significant. Interference effects for a system with dissipative layers have been analyzed in connection with the measurement of dissipation in the field by the method of amplitude ration. It is shown that the method of amplitude ratios is extremely sensitive to noise. Ion the field, signal-to-noise ratio considerations limit the method to the direct wave. The direct wave in contaminated by inferring event. The dominant source of contamination changes from primaries, when the number of layer is small (small receiver separation), to multiples when the number of layers is large...