Scale dependence of reflection and transmission coefficients

摘要

Well logs show that heterogeneities occur at many different depth scales. This study examines the effects of these heterogeneities on the propagation of seismic waves, and specifically the dependence of reflection and transmission on the spatial scale content of the medium. Wavelet transformations are used to filter certain spatial scales from an acoustic sonic log. The scale-filtered logs are used to construct layerstack models for which reflection and transmission seismograms are computed. The modified logs are also used to calculate frequency dependent reflection and transmission coefficients as functions of scale content. It is observed that features shorter than one-fourth of the dominant wavelength have little effect on the reflection and transmission of seismic waves. Features larger than the dominant wavelength affect arrival times of individual packets within the wavetrain, but often these features hardly alter the overall appearance of individual wave packets. Reflection and transmission coda are primarily governed by heterogeneity at spatial scales similar to half the propagating wavelength. These scales appear to control the presence and shape of the events within the coda. The study also shows that the arrival times of packets at 1 kHz approach the theoretically expected value obtained from the harmonic velocity average, and the arrival times of packets below 1 Hz approach the theoretical value expected for the Backus average of the velocities.