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 RPP are generally smaller
than 10% when the thin-bed thicknesses are smaller than
one-eighth of the PP-wavelength. The PS-wave reflection coefficients
RPS have lower approximation accuracy than RPP for
the same ratios of thicknesses to their respective wavelengths,
and the RPS 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 RPP and RPS 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.