Seismic attenuation due to wave‐induced flow

Abstract

Three P wave attenuation models for sedimentary rocks are given a unified theoretical treatment. Two of the models concern wave‐induced flow due to heterogeneity in the elastic moduli at “mesoscopic” scales (scales greater than grain sizes but smaller than wavelengths). In the first model, the heterogeneity is due to lithological variations (e.g., mixtures of sands and clays) with a single fluid saturating all the pores. In the second model, a single uniform lithology is saturated in mesoscopic “patches” by two immiscible fluids (e.g., air and water). In the third model, the heterogeneity is at “microscopic” grain scales (broken grain contacts and/or microcracks in the grains), and the associated fluid response corresponds to “squirt flow.” The model of squirt flow derived here reduces to proper limits as any of the fluid bulk modulus, crack porosity, and/or frequency is reduced to zero. It is shown that squirt flow is incapable of explaining the measured level of loss (10 −2 < Q −1 < 10 −1 ) within the seismic band of frequencies (1–10 4 Hz); however, either of the two mesoscopic scale models easily produces enough attenuation to explain the field data.