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As an approximation of the spherical-wave reflection coefficient (SRC), the plane-wave reflection coefficient does not fully describe the reflection phenomenon of a seismic wave generated by a point source. The applications of SRC to improve analyses of seismic data have also been studied. However, most of the studies focus on the time-domain SRC and its benefit to using the long-offset information instead of the dependency of SRC on frequency. Consequently, we have investigated and accounted for the frequency-dependent spherical-wave reflection coefficient (FSRC) and analyzed the feasibility of this type of inversion. Our inversion strategy requires a single incident angle using reflection data for inverting the density and velocity ratios, which is distinctly different from conventional inversion methods using amplitude variation with offset. Hence, this investigation provides an alternative approach for estimating media properties in some contexts, especially when the range of aperture of the reflection angles is limited. We apply the FSRC theory to the inversion of noisy synthetic and field data using a heuristic algorithm. The multirealization results of the inversion strategy are consistent with the feasibility analysis and demonstrate the potential of the outlined method for practical application.

Detection and identification of subsurface anomalous structures are key objectives in seismic exploration. The coherence technique has been successfully used to identify geologic abnormalities and discontinuities, such as faults and unconformities. Based on the classic third eigenvalue-based coherence ([Formula: see text]) algorithm, we make several improvements and develop a new method to construct covariance matrix using the original and Hilbert transformed seismic traces. This new covariance matrix more readily converges to the main effective signal energy on the largest eigenvalue by decreasing all other eigenvalues. Compared with the conventional coherence algorithms, our algorithm has higher resolution and better noise immunity ability. Next, we incorporate this new eigenvalue-based algorithm with time-lag dip scanning to relieve the dip effect and highlight the discontinuities. Application on 2D synthetic data demonstrates that our coherence algorithm favorably alleviates the low-valued artifacts caused by linear and curved dipping strata and clearly reveals the discontinuities. The coherence results of 3D real field data also commendably suppress noise, eliminate the influence of large dipping strata, and highlight small hidden faults. With the advantages of higher resolution and robustness to random noise, our strategy successfully achieves the goal of detecting the distribution of discontinuities.