In areas with a complex surface, the acquisition and processing of seismic data is a great challenge. Although elevation-static corrections can be used to eliminate the infl uences of topography, the distortions of seismic wavefields caused by simple vertical time shifts still greatly degrade the quality of the migrated images. Ray-based migration methods which can extrapolate and image the wavefi elds directly from the rugged topography are effi cient ways to solve the problems mentioned above. In this paper, we carry out a study of prestack Gaussian beam depth migration under complex surface conditions. We modify the slant stack formula in order to contain the information of surface elevations and get an improved method with more accuracy by compositing local plane-wave components directly from the complex surface. First, we introduce the basic rules and computational procedures of conventional Gaussian beam migration. Then, we give the original method of Gaussian beam migration under complex surface conditions and an improved method in this paper. Finally, we validate the effectiveness of the improved method with trials of model and real data.

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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.

Gaussian beam migration (GBM) is an effective imaging method that has the ability to image multiple arrivals while preserving the advantages of ray-based methods. We have extended this method to linearized least-squares imaging for elastic waves in isotropic media. We have dynamically transformed the multicomponent data to the principal components of different wave modes using the polarization information available in the beam migration process, and then we use Gaussian beams as wavefield propagator to construct the forward modeling and adjoint migration operators. Based on the constructed operators, we formulate a least-squares migration scheme that is iteratively solved using a preconditioned conjugate gradient method. With this method, we can obtain crosstalk-attenuated multiwave images with better subsurface illumination and higher resolution than those of the conventional elastic Gaussian beam migration. This method also allows us to achieve a good balance between computational cost and imaging accuracy, which are both important requirements for iterative least-squares migrations. Numerical tests on two synthetic data sets demonstrate the validity and effectiveness of our proposed method.