A stable TTI reverse time migration and its implementation

Modeling and reverse time migration based on the tilted transverse isotropic (TTI) acoustic wave equation suffers from instability in media of general inhomogeniety, especially in areas where the tilt abruptly changes. We develop a stable TTI acoustic wave equation implementation based on the original elastic anisotropic wave equation. We, specifically, derive a vertical transversely isotropic wave system of equations that is equivalent to their elastic counterpart and introduce the self-adjoint differential operators in rotated coordinates to stabilize the TTI acoustic wave equations. Compared to the conventional formulations, the new system of equations does not add numerical complexity; a stable solution can be found by either a pseudospectral method or a high-order explicit finite difference scheme. We demonstrate by examples that our method provides stable and high-quality TTI reverse time migration images.

[1]  Paul J. Fowler,et al.  A New Pseudo-acoustic Wave Equation For TI Media , 2008 .

[2]  I. Tsvankin.  P-wave signatures and notation for transversely isotropic media: An overview , 1996 .

[3]  E. Baysal,et al.  Reverse time migration , 1983 .

[4]  Jerry Young,et al.  Subsalt imaging using TTI reverse time migration , 2009 .

[5]  Guanquan Zhang,et al.  An Anisotropic Acoustic Wave Equation For Modeling And Migration In 2D TTI Media , 2006 .

[6]  Paul G. Richards,et al.  Quantitative Seismology: Theory and Methods , 1980 .

[7]  Robin P. Fletcher,et al.  Reverse time migration in tilted transversely isotropic "TTI… media , 2009 .

[8]  A stable TTI reverse time migration , 2011 .

[9]  Tariq Alkhalifah,et al.  Building a 3-D Anisotropic Model: Its Implication to Traveltime Calculation And Velocity Analysis , 2000 .

[10]  L. Thomsen.  Weak elastic anisotropy , 1986 .

[11]  Yu Zhang,et al.  Reverse Time Migration In 3D Heterogeneous TTI Media , 2008 .

[12]  S. Shapiro,et al.  Modeling the propagation of elastic waves using a modified finite-difference grid , 2000 .

[13]  Robin P. Fletcher,et al.  Coupled equations for reverse time migration in transversely isotropic media , 2010 .

[14]  John Etgen,et al.  Wide Azimuth Streamer Imaging of Mad Dog; Have We Solved the Subsalt Imaging Problem? , 2006 .

[15]  G. McMechan.  MIGRATION BY EXTRAPOLATION OF TIME‐DEPENDENT BOUNDARY VALUES* , 1983 .

[16]  Peter M. Bakker,et al.  Stable P-wave modeling for reverse-time migration in tilted TI media , 2011 .

[17]  M. Araya-Polo,et al.  Hybrid Finite Difference-pseudospectral Method for 3D RTM in TTI Media , 2008 .

[18]  J. Virieux.  P-SV wave propagation in heterogeneous media: Velocity‐stress finite‐difference method , 1986 .

[19]  Edip Baysal,et al.  Forward modeling by a Fourier method , 1982 .

[20]  A. Long.  How multi-azimuth and wide-azimuth seismic compare , 2006 .

[21]  Eric Duveneck,et al.  Acoustic VTI Wave Equations And Their Application For Anisotropic Reverse-time Migration , 2008 .

[22]  Linbin Zhang,et al.  Shear waves in acoustic anisotropic media , 2004 .

[23]  Tariq Alkhalifah,et al.  Acoustic approximations for processing in transversely isotropic media , 1998 .

[24]  N. Whitmore.  Iterative Depth Migration By Backward Time Propagation , 1983 .

[25]  H. Zhou,et al.  An Anisotropic Acoustic Wave Equation for VTI Media , 2006 .

[26]  Wei Liu,et al.  On the instability in second-order systems for acoustic VTI and TTI media , 2012 .

[27]  M. V. D. Meulen,et al.  Using dual-azimuth data to image below salt domes , 2006 .

[28]  Daoliu Wang,et al.  Controlled Beam Migration Applications In Gulf of Mexico , 2008 .

[29]  James Sun,et al.  Reverse-time Migration: Amplitude And Implementation Issues , 2007 .

[30]  R. P. Fletcher,et al.  A New Pseudo-acoustic Wave Equation for VTI Media , 2008 .