Elastic 3D PS converted-wave Gaussian beam migration

Abstract

Elastic-wave migration is a desirable technique because it can image the structure of the earth more accurately. We develop a new elastic Gaussian beam migration method with 3D three component (3D-3C) seismic data that focuses on a complex PS-converted wave. Based on the elastic-wave equations and complete boundary conditions, we derive effective work formulas for an accurate multimode wave downward continuation for the free-space, ocean-bottom, and free-surface models. We separate the PS-wave into linear-polarized P-S1 and P-S2 waves to simplify the expression and derivation of the migration. To image the vectorial wave directly and solve the reverse-polarity issue, we use the crosscorrelations of P-wave divergence and PS-wave curl operators as the 3D P- and PS-imaging conditions, and we develop a unit vector to define the rotation direction of the PS-wave. With our approach, 3D-3C multimode waves are automatically decomposed to P- and PS-waves during the migration without the need for prior data separation, which not only reduces the crosstalk noise caused by inaccurate multimode wave decomposition but also decreases the processing cost. Applications of this method to two 3D-3C synthetic examples indicate successful PS-wave migration. Also, confirming that the PS-image can be constructed by summing the P-S1 and P-S2 images and is independent of the choice of the ray-centered local coordinates validates this method.

Least-squares Gaussian beam migration in elastic media

“…Equations 12 and 13 are asymptotically equivalent to the EGBM formulas of Li et al (2018) derived using vector Gaussian beams (their equations 18 through 20, with free-space surface condition A-11), which also confirms our proposed scalar beam approach to extrapolating principal components of elastic waves.…”

“…Gaussian beam migration (GBM) is an elegant imaging method (Hill, 1990(Hill, , 2001Hale, 1992;Gray, 2005;Nowack et al, 2005;Gao et al, 2006;Gray and Bleistein, 2009;Yue et al, 2012Yue et al, , 2019aYue et al, , 2019b because it not only preserves the high efficiency of ray-based migration methods, but it also achieves high level of accuracy by migrating multipath arrivals. Recently, Protasov and Tcheverda (2012), Li et al (2018), and Yang et al (2018a) successfully extend GBM to elastic isotropic media, providing a competitive alternative to imaging elastic waves.…”

“…To provide an efficient approach of ELSM, we propose elastic least-squares Gaussian beam migration (ELSGBM), which can not only produce better illuminated elastic images with enhanced resolution and attenuated crosstalk, but it can also achieve a good balance between computational cost and imaging accuracy. Instead of using vector Gaussian beams to extrapolate the elastic wavefields with Cartesian components (Protasov and Tcheverda 2012;Li et al, 2018;Yang et al, 2018a), we choose an equivalent but simpler approach by extrapolating principal component wavefields using scalar wave propagators (Goertz, 2002;Schleicher et al, 2007;Stolt and Weglein, 2012), which is helpful in constructing the conjugate modeling and migration operators. We dynamically transform multicomponent data to the principal components of different wave modes using the polarization vectors available in the migration process, and then we use scalar Gaussian beams as the wave propagator to construct the forward modeling and the adjoint migration operators.…”

Q-Compensated Gaussian Beam Migration under the Condition of Irregular Surface

“…It has imaging accuracy close to wave equation migration and preserves the flexible and highly efficient advantages of the Kirchhoff migration method, which can effectively address the issue of multi-value traveltime [13]. Since Hill [14,15] proposed the GBM method, researchers have conducted massive studies on the complex-surface, anisotropy, and multi-component GBM [16][17][18][19][20][21][22]. In addition, Wu et al [23] created a viscoacoustic Gaussian beam prestack depth migration (GB-PSDM) method by correcting the complex-value traveltime of the Gaussian beam and then proposed a Q-compensated multi-component GBM method based on wavefield separation.…”

Application of Gaussian Beam Summation Migration in Reflected In‐seam Wave Imaging

“…It inherits the efficiency and flexibility of the ray migration method and has an imaging precision close to that of wave equation migration Han et al, 2020). Over the past few years, many researchers have conducted extensive studies on complex surface, preserved-amplitude, anisotropic and multicomponent Gaussian beam migration methods (Alkhalifah, 1995;Hill, 2001;Gray, 2005;Zhu et al, 2007;Han et al, 2013Han et al, , 2014El Yadari, 2015;Protasov, 2015;Li et al, 2018;. The Gaussian beam migration technique has increasingly matured within oil exploration and has achieved good practical results.…”