Abstract
The study of thin-bed seismic phenomena is important in crustal, exploration and engineering seismology. Presently, seismic reflectivity theories based on single-interface assumption are widely used though they are only suitable for thick deposits. Thin-bed reflectivity theories are established on complex propagator matrices and are difficult to be applied to reveal thin-bed properties directly. Therefore, an approximation of thin-bed PP-wave reflection coefficients (RPP) is derived in this paper. First, the relationship between thin-bed RPP and incidence angles is analyzed through series expansion method. For PP-wave, its reflection coefficients are even power series functions of sine incidence angles. Then, for small incidence, RPP of the thin bed is further simplified into a second-order series approximation with respect to the sine incidence angles. Simulations and accuracy analyses of the approximate formula show that approximation errors are smaller than 5% as the incidence angles smaller than 20 degrees. Based on this approximate formula, an approach is given for estimating thin-bed properties including P-wave impedance ratios and thickness. The estimation approach is applied in properties estimation of a thin bed model. Perfect performances of the model example show the future potentiality of the approximate formula in thin-bed Amplitude-Versus-Offset (AVO) analysis and inversion.
Highlights
Seismic wave propagation in thin-bed models has been a hot topic of interest to crustal, exploration and engineering seismologists for many years [1,2,3]
For some sedimentary basins, such as Williston Basin in America [5,6,7], Alberta Basin in Canada [8,9], SongLiao and Tarim Basins in China [10,11], lithologic reservoirs are composed of thin beds with the thicknesses below the vertical resolution limits [12]
Under the small-incidence assumption, P-wave reflection coefficients are simplified into the second-order series approximation of sine incidence angles
Summary
Seismic wave propagation in thin-bed models has been a hot topic of interest to crustal, exploration and engineering seismologists for many years [1,2,3]. Yang et al gave approximate formulas of thin-bed reflections in elastic media under the assumptions of small incidence angles and weak impedance contrasts [22] These approximations show as relatively compact forms, but all ignore the contributions of interbed multiples and converted waves. Singh et al gave reflection and transmission matrix equations of P-wave at the interfaces of the layered sandwiched model comprised of a water layer between an upper ice half-space and a lower isotropic elastic half-space [34] These matrix formulas considered all wave modes including interbed multiple waves and converted waves. To solve Equation (1) approximately, the trigonometric function parameters are rewritten as complicated matrix calculations prevent its application in thin-bed AVO analysis and a series expansion of sine incidence angle (see Appendix B). N 0 where A and B are coefficients of series functions
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