True amplitude wave equation migration arising from true amplitude one-way wave equations

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	True amplitude wave equation migration arising from true amplitude one-way wave equations
	Zhang, Y ; Zhang, GQ ; Bleistein, N
	2003-10-01
发表期刊	INVERSE PROBLEMS
ISSN	0266-5611
卷号	19 期号:5 页码:1113-1138
摘要	One-way wave operators are powerful tools for use in forward modelling and inversion. Their implementation, however, involves introduction of the square root of an operator as a pseudo-differential operator. Furthermore, a simple factoring of the wave operator produces one-way wave equations that yield the same travel times as the full wave equation, but do not yield accurate amplitudes except for homogeneous media and for almost all points in heterogeneous media. Here, we present augmented one-way wave equations. We show that these equations yield solutions for which the leading order asymptotic amplitude as well as the travel time satisfy the same differential equations as the corresponding functions for the full wave equation. Exact representations of the square-root operator appearing in these differential equations are elusive, except in cases in which the heterogeneity of the medium is independent of the transverse spatial variables. Here, we address the fully heterogeneous case. Singling out depth as the preferred direction of propagation, we introduce a representation of the square-root operator as an integral in which a rational function of the transverse Laplacian appears in the integrand. This allows us to carry out explicit asymptotic analysis of the resulting one-way wave equations. To do this, we introduce an auxiliary function that satisfies a lower dimensional wave equation in transverse spatial variables only. We prove that ray theory for these one-way wave equations leads to one-way eikonal equations and the correct leading order transport equation for the full wave equation. We then introduce appropriate boundary conditions at z = 0 to generate waves at depth whose quotient leads to a reflector map and an estimate of the ray theoretical reflection coefficient on the reflector. Thus, these true amplitude one-way wave equations lead to a 'true amplitude wave equation migration' (WEM) method. In fact, we prove that applying the WEM imaging condition to these newly defined wavefields in heterogeneous media leads to the Kirchhoff inversion formula for common-shot data when the one-way wavefields are replaced by their ray theoretic approximations. This extension enhances the original WEM method. The objective of that technique was a reflector map, only. The underlying theory did not address amplitude issues. Computer output obtained using numerically generated data confirms the accuracy of this inversion method. However, there are practical limitations. The observed data must be a solution of the wave equation. Therefore, the data over the entire survey area must be collected from a single common-shot experiment. Multi-experiment data, such as common-offset data, cannot be used with this method as currently formulated. Research on extending the method is ongoing at this time.
语种	英语
WOS研究方向	Mathematics ; Physics
WOS类目	Mathematics, Applied ; Physics, Mathematical
WOS记录号	WOS:000186022700007
出版者	IOP PUBLISHING LTD
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/18149
专题	中国科学院数学与系统科学研究院
通讯作者	Zhang, Y
作者单位	1.Veritas DGC Inc, Houston, TX 77072 USA 2.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, Beijing 100080, Peoples R China 3.Colorado Sch Mines, Dept Geophys, Ctr Wave Phenomena, Golden, CO 80401 USA
推荐引用方式 GB/T 7714	Zhang, Y,Zhang, GQ,Bleistein, N. True amplitude wave equation migration arising from true amplitude one-way wave equations[J]. INVERSE PROBLEMS,2003,19(5):1113-1138.
APA	Zhang, Y,Zhang, GQ,&Bleistein, N.(2003).True amplitude wave equation migration arising from true amplitude one-way wave equations.INVERSE PROBLEMS,19(5),1113-1138.
MLA	Zhang, Y,et al."True amplitude wave equation migration arising from true amplitude one-way wave equations".INVERSE PROBLEMS 19.5(2003):1113-1138.