Frequency-Domain Common Image Gathers for Quickly Checking the Accuracy of Migration Velocity

The common image gather (CIG) method enables qualitative and quantitative evaluation of the velocity model through the image. The most common such methods are offset-domain common image gather (ODCIG) and angle-domain common image gather (ADCIG). The challenge is that it requires a great deal of additional computation besides migration. We, therefore, introduce a new CIG method that has low computational cost: frequency-domain common image gather (FDCIG). FDCIG simply rearranges data using a gradient (partial image) calculated in the process of obtaining a migration image to represent it in the frequency-depth domain. We apply the FDCIG method to the layered model to show how FDCIGs behave when the velocity model is inaccurate. We also introduced the 3-D SEG/EAGE salt model to show how to apply the FDCIG method in the hybrid domain. Last, we applied 2-D real data. These sample field data also indicate that even in a complex velocity model, deviant behavior by FDCIG appears intuitively if the background velocity is inaccurate.

An improved LTI algorithm for multiphase raytracing in undulating surface model

Based on the linear traveltime interpolation (LTI) algorithm, we propose an improved LTI (referred as ILTI) algorithm for multiphase seismic ray tracing, which uses a velocity node in model parameterization and introduces secondary nodes between adjacent velocity nodes. To better fit the undulating surface model, an irregular velocity node is used in near the irregular interface, and regular velocity nodes are still used in the region far away from the irregular interface. We derive an iterative fixed-point formula for calculating traveltime. By combining multistage computational technology and wavefront narrowband expansion technology, the proposed ILTI algorithm can efficiently trace the multiphase seismic raypath and compute the corresponding traveltime field. Through comparison and analysis with the traditional LTI algorithm, its computational accuracy can be highlighted by at least one order of magnitude. Compared with the popular fast marching method (FMM) and irregular shortest-path (ISPM) algorithms, it also has the advantages in terms of computational accuracy and efficiency. Numerical simulations in the Marmousi model show that the algorithm is also suitable for tracking multiphase seismic rays in the complex velocity model.

Efficient 3D wave-equation migration using virtual planar sources

Full-volume seismic imaging is essential for a sound interpretation of structurally complex geologies. Prestack depth imaging is the most appropriate tool for such imaging, but it requires a precise and often complex velocity model. In such situations, 3D Kirchhoff prestack depth migration can be quite expensive. On the other hand, a wavefield approach, although generally tremendously expensive, is not affected by the complexity of the velocity model. We propose an affordable 3-D wavefield prestack depth-migration technique. It is designed for marine surveys for which the source-receiver azimuth is approximately constant. The technique applies a plane-wave migration algorithm to time-shifted data — quite a surprising approach when we realize that marine surveys do not allow the synthesis of genuine plane-wave data. Additionally, the imaging principle has to be modified to give results consistent with shot-record migration. Our technique also produces image gathers that allow an update of the velocity model by means of migration velocity analysis. Results from synthetics and conventional marine data demonstrate the effectiveness of the method.

Fast and accurate dynamic raytracing in heterogeneous media

We have developed a fast and accurate dynamic raytracing method for 2.5-D heterogeneous media based on the kinematic algorithm proposed by Langan et al. (1985). This algorithm divides the model into cells of constant slowness gradient, and the positions, directions, and travel times of the rays are expressed as polynomials of the travel path length, accurate to the second other in the gradient. This method is efficient because of the use of simple polynomials at each raytracing step. We derived similar polynomial expressions for the dynamic raytracing quantities by integrating the raytracing system and expanding the solutions to the second order in the gradient. This new algorithm efficiently computes the geometrical spreading, amplitude, and wavefront curvature on individual rays. The two-point raytracing problem is solved by the shooting method using the geometrical spreading. Paraxial corrections based on the wavefront curvature improve the accuracy of the travel time and amplitude at a given receiver. The computational results for two simple velocity models are compared with those obtained with the SEIS83 seismic modeling package (Cerveny and Psencik, 1984); this new method is accurate for both travel times and amplitudes while being significantly faster. We present a complex velocity model that shows that the algorithm allows for realistic models and easily computes rays in structures that pose difficulties for conventional methods. The method can be extended to raytracing in 3-D heterogeneous media and can be used as a support for a Gaussian beam algorithm. It is also suitable for computing the Green's function and imaging condition needed for prestack depth migration.