True-amplitude Gaussian-beam migration

Abstract

Gaussian-beam depth migration and related beam migration methods can image multiple arrivals, so they provide an accurate, flexible alternative to conventional single-arrival Kirchhoff migration. Also, they are not subject to the steep-dip limitations of many (so-called wave-equation) methods that use a one-way wave equation in depth to downward-continue wavefields. Previous presentations of Gaussian-beam migration have emphasized its kinematic imaging capabilities without addressing its amplitude fidelity. We offer two true-amplitude versions of Gaussian-beam migration. The first version combines aspects of the classic derivation of prestack Gaussian-beam migration with recent results on true-amplitude wave-equation migration, yields an expression involving a crosscorrelation imaging condition. To provide amplitude-versus-angle (AVA) information, true-amplitude wave-equation migration requires postmigration mapping from lateral distance (between image location and source location) to subsurface opening angle. However, Gaussian-beam migration does not require postmigration mapping to provide AVA data. Instead, the amplitudes and directions of the Gaussian beams provide information that the migration can use to produce AVA gathers as part of the migration process. The second version of true-amplitude Gaussian-beam migration is an expression involving a deconvolution imaging condition, yielding amplitude-variation-with-offset (AVO) information on migrated shot-domain common-image gathers.

A fast algorithm for prestack Gaussian beam migration adopting the steepest descent approximation

“…Bleistein and Gray (2010) proposed the method for computing the Hessian matrix in the formula of 3D prestack Gaussian beam migration by the steepest descent approximation. Yue et al (2012) extended Gray and Bleistein (2009) method to rugged topography by a phase correction method. Casasanta and Gray (2015) proposed converted-wave Gaussian beam migration, in which the steepest descent approximation was adopted to solve the migration formula.…”

“…Zhu et al (2007) extended Gray (2005) method to the anisotropic media, in which simplified anisotropic ray tracing systems by the weak-anisotropic approximation were used to increase the computational efficiency. Gray and Bleistein (2009) derived true-amplitude prestack Gaussian beam migration formulae based on the cross-correlation imaging condition and the deconvolution imaging condition, respectively, and proposed the method to solve the formulae by the steepest descent approximation. Popov et al (2010) expressed the Green function in the Kirchhoff integral formula by the Gaussian beam summation method to extrapolate the recorded wavefields and proposed a prestack depth migration method which was similar to the reverse time migration.…”

Seismic characterization of fractured reservoirs using 3D double beams

“…) is the windowed data The form of the beams can be taken as Gaussian beams (e.g., Cerveny, 1982;Hill, 1990;Hale, 1992;Hill, 2001;Nowack, 2003;Gray and Bleistein, 2009). If the beam widths are infinite, then we have plane wave extrapolation such as the double-square-root operator, plane wave migration, offset plane waves etc.…”

An amplitude-preserved adaptive focused beam seismic migration method

“…(5). According to the true-amplitude GBM formula presented by Gray and Bleistein (2009), the up-going and down-going wave-fields can be written as P U ðx P ;x S ;xÞ ¼ À2ix Z dr cos/ R v R G Ã ðx P ;x R ;xÞP U ðx R ;x S ;xÞ P D ðx P ;x S ;xÞ ¼ À2ix cos/ S v S Gðx P ;x S ;xÞ; ð24Þ where x S , x R ; and x P are the Cartesian coordinates of source, receiver, and imaging point, respectively, / S and / R are the ray emergence angles from surface at source and receiver (see Fig. 5), P U ðx R ; x S ; xÞ is the recorded wavefield, v S and v R are the velocity at source and receiver separately, ''*'' denotes the complex conjugate.…”

“…Ever since the basic framework of GBM was presented by Hill (1990Hill ( , 2001, it has been extended to irregular topographic conditions (Gray 2005;Yue et al 2012;Yang et al 2014) and trueamplitude migration (Gray and Bleistein 2009). In addition, many new seismic beam imaging methods have been developed, such as fast beam migration (Gao et al 2006(Gao et al , 2007, focused beam migration (Nowack 2008), and laser beam migration (Xiao et al 2014), which expand the members of the beam migration family.…”