A Low-Order Series Approximation of Thin-Bed PP-Wave Reflections

• Main Authors: Chun Yang, Yun Wang, Jun Lu, Benchi Chen, Lei Shi
• Format: Article
• Language: English
• Published: MDPI AG 2019-02-01
• Series: Applied Sciences
• Subjects: thin bed; PP-wave reflection coefficients; approximate formula; series expansion method
• Online Access: https://www.mdpi.com/2076-3417/9/4/709

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 (<i>R_PP</i>) is derived in this paper. First, the relationship between thin-bed <i>R_PP</i> 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, <i>R_PP</i> 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.