The study of thin-bed seismic response is an important part in lithologic and methane reservoir modeling, critical for predicting their physical attributes and/or elastic parameters. The complex propagator matrix for the exact reflections and transmissions of thin beds limits their application in thin-bed inversion. Therefore, approximation formulas with a high accuracy and a relatively simple form are needed for thin-bed seismic analysis and inversion. We have derived thin-bed reflection and transmission coefficients, defined in terms of displacements, and approximated them to be in a quasi-Zoeppritz matrix form under the assumption that the middle layer has a very thin thickness. We have verified the approximation accuracy through numerical calculation and concluded that the errors in PP-wave reflection coefficients [Formula: see text] are generally smaller than 10% when the thin-bed thicknesses are smaller than one-eighth of the PP-wavelength. The PS-wave reflection coefficients [Formula: see text] have lower approximation accuracy than [Formula: see text] for the same ratios of thicknesses to their respective wavelengths, and the [Formula: see text] approximation is not acceptable for incident angles approaching the critical angles (when they exist) except in the case of extremely strong impedance difference. Errors in phase for the [Formula: see text] and [Formula: see text] approximation are less than 10% for the cases of thicknesses less than one-tenth of the wavelengths. As expected, a thinner middle layer and a weaker impedance difference would result in higher approximation accuracy.
Reflection and transmission coefficients of a thin bed
