Two-dimensional seismic surveys often are conducted along crooked line traverses due to the inaccessibility of rugged terrains, logistical and environmental restrictions, and budget limitations. The crookedness of line traverses, irregular topography, and complex subsurface geology with steeply dipping and curved interfaces could adversely affect the signal-to-noise ratio of the data. The crooked-line geometry violates the assumption of a straight-line survey that is a basic principle behind the 2D multifocusing (MF) method and leads to crossline spread of midpoints. Additionally, the crooked-line geometry can give rise to potential pitfalls and artifacts, thus, leads to difficulties in imaging and velocity-depth model estimation. We develop a novel multifocusing algorithm for crooked-line seismic data and revise the traveltime equation accordingly to achieve better signal alignment before stacking. Specifically, we present a 2.5D multifocusing reflection traveltime equation, which explicitly takes into account the midpoint dispersion and cross-dip effects. The new formulation corrects for normal, inline, and crossline dip moveouts simultaneously, which is significantly more accurate than removing these effects sequentially. Applying NMO, DMO, and CDMO separately tends to result in significant errors, especially for large offsets. The 2.5D multifocusing method can perform automatically with a coherence-based global optimization search on data. We investigated the accuracy of the new formulation by testing it on different synthetic models and a real seismic data set. Applying the proposed approach to the real data led to a high-resolution seismic image with a significant quality improvement compared to the conventional method. Numerical tests show that the new formula can accurately focus the primary reflections at their correct location, remove anomalous dip-dependent velocities, and extract true dips from seismic data for structural interpretation. The proposed method efficiently projects and extracts valuable 3D structural information when applied to crooked-line seismic surveys.
