Reflection and transmission coefficients of a thin bed Chun Yang 1 , Yun Wang 1 , and Yanghua Wang 2 ABSTRACT The study of thin-bed seismic response is an important part in lithologic and methane reservoir modeling, critical for pre- dicting their physical attributes and/or elastic parameters. The complex propagator matrix for the exact reflections and trans- missions of thin beds limits their application in thin-bed inver- sion. 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 displace- ments, and approximated them to be in a quasi-Zoeppritz ma- trix 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 R PP are generally smaller than 10% when the thin-bed thicknesses are smaller than one-eighth of the PP-wavelength. The PS-wave reflection co- efficients R PS have lower approximation accuracy than R PP for the same ratios of thicknesses to their respective wavelengths, and the R PS 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 R PP and R PS approximation are less than 10% for the cases of thicknesses less than one-tenth of the wave- lengths. As expected, a thinner middle layer and a weaker impedance difference would result in higher approximation accuracy. INTRODUCTION As exploration targets have been expanded in scope from struc- tural traps to lithologic and stratigraphic traps, more attention has been paid to thin-bed reservoirs that require higher resolution to be recognized (Zhang and Zheng, 2007). However, mature industrial amplitude variation with offset (AVO) inversion methods, which are based on the Zoeppritz equations and their approximation formulas, for describing reflection and transmission of plane waves across a single interface, are not suitable for thin-bed problems (Pan and Kristopher, 2013). Thin-bed seismic responses are composed of the superposition of all reflecting waveforms and multiples, includ- ing converted waves, which is different from a single-interface case (Chen and Liu, 2006). Thin-bed reflections depend not only upon the elastic parameters of layered media, but also upon the thin-bed thickness and the fre- quency of incident waves. Brekhovskikh (1960) studies reflections and transmissions of plane waves propagating in layered media by elastic dynamic theory and derives accurate equations with dis- placement potential function. However, the complex propagator matrix limited their application in seismic inversion. Meissner and Meixner (1969) present the time delayed transmission/reflec- tion method and deduce thin-bed reflection coefficients by multi- plying the reflecting and transmitting coefficients of the top and bottom interfaces. Widess (1973) studies the normal pulse reflec- tions from the top and bottom of a thin bed under the assumptions of equal amplitudes and opposite polarities and tries to predict thin- bed thickness by amplitude information. Chung and Lawton (1995) extend Widess (1973) study into a thin bed, which has equal am- plitudes and identical polarities in the bottom and top interfaces and analyze the influence of different wavelets on thin-bed reflections. Liu and Schmitt (2003) present an acoustic reflectance spectrum formula of a thin bed in the frequency domain and discuss the impact of thickness and Poisson’s ratio on thin-bed seismic AVO Manuscript received by the Editor 3 July 2015; revised manuscript received 22 March 2016; published online 27 July 2016. 1 China University of Geosciences, School of Geophysics and Information Technology, Beijing, China. E-mail: yangchunanhui@163.com; yunwang@mail. iggcas.ac.cn. 2 Imperial College London, Department of Earth Science and Engineering, Centre for Reservoir Geophysics, London, UK. E-mail: yanghua.wang@imperial. ac.uk. © 2016 Society of Exploration Geophysicists. All rights reserved. N31 GEOPHYSICS, VOL. 81, NO. 5 (SEPTEMBER-OCTOBER 2016); P. N31–N39, 9 FIGS., 3 TABLES. 10.1190/GEO2015-0360.1