Smoothing Imaging Condition and Handling Lateral Velocity Change in Gaussian Beam Seismic Imaging

Summary An approximation of the reflection coefficient in seismic imaging condition is described by dividing the upgoing wavefield to the downgoing wavefield in the image point. Calculation of the reflection coefficient would be unstable wherever downgoing wave field equals or is close to zero. The imaging conditions will be distorted in the presence of the lateral velocity change. In this study, we have used the strategy of smoothed imaging condition in the Gaussian beam (GB) imaging method. The new operator has been changed in order to handle lateral velocity change. Different imaging points, distributed on a non-circular imaging operator, have been analyzed by coherency analysis. The point that gives the highest coherency would be selected as the final imaging point. The new strategy has been applied on synthetic and real land seismic data. Results of the synthetic data have been promising in the final image. The real data have been processed by three different velocity models. These velocity models have been obtained by different velocity functions to model velocity changes in different levels. The final image has proved that smoothing imaging condition can handle the lateral velocity change in the propagation media.
Introduction Different methods and strategies have been introduced to handle the problem of imaging condition. In one study, the focal surface imaging method has been introduced for imaging in complex media. The imaging condition is evaluated in common offset domain rather than the zero offset domain. By this strategy, the imaging condition would be evaluated in a surface of points instead of a single one. Thus, the errors in these conditions will be distributed in different points and the final imaging point is selected by coherency analysis. In other study, thick rays have been used to reduce errors in imaging condition. The concept of thick rays has also been used to introduce the GB migration method. To better resolve the problem, imaging condition smoothing in wavefield propagation has been used to handle the lateral velocity change. In this study, the smoothing strategy is used in the GB imaging method.
Methodology and Approaches The GB imaging operator is an isochrone that is produced by a set of beams which will be propagated forward for shot wavefield and backward for receiver wavefield. The imaging is located on the isochrones, exactly in the cross point of the shot wavefield and receiver wavefield central beams. By smoothing the imaging condition, the imaging operator is not an exact semicircle, but could have any shape. This iscochrone is created by beams propagated in the media with lateral velocity change. Then, different points are selected as the image point on this operator. By a simple coherency analysis, the point that gives the highest coherency would be selected as the final image point.
Results and Conclusions The smoothing strategy has been applied on synthetic and real land seismic data set. The synthetic data have been created by ray tracing technique on a velocity model having constant velocities on layers. However, complex structure of the model will produce the desired lateral velocity change in the media for wavefield propagation. The results of applying the strategy on free noise data and data contaminated with noise have been promising. To better understand the effect of the lateral velocity change in the media, the real land data set has been imaged by three different velocity models. These velocity models present three different degrees of velocity change, small, mild and high. Imaging with velocity model having small velocity change has been unable to accurately focus the reflectors. The velocity model with high lateral velocity change has also been unable to image minor truncations in the reflectors. It is may be due to the simple coherency analysis used. The final image obtained by the velocity model with mild lateral velocity change, however, has been promising as it contains better image of the faults, reflector truncations and more preserving of the continuity in the reflectors.