Continuous 3D Dip Field and Velocity interpolation from sparse 2D Seismic Survey with Sinusoidal Implicit Neural Networks (SIREN)

A 2D reflection seismic survey is a cost-effective method for imaging subsurface structures and estimating dip and velocity fields for applications such as oil/gas/mineral exploration and CO$_2$ sequestration. However, 2D surveys cannot reliably capture out-of-plane structures, while dense 3D acquisition is often constrained by cost, metoceanic conditions, and regulations. Existing production workflows interpolate sparse 2D lines into 3D volumes but can introduce gridding artifacts and reduce lateral continuity. We therefore propose a novel application of SIREN-based Implicit Neural Representation (INR) that learns a continuous coordinate-based representation of velocity and dip fields directly from sparse 2D observations. On a representative 20-line dataset, SIREN outperforms Sigmoid and ReLU activations for dip interpolation, achieving SSIM = 0.9995, Pearson correlation $R=0.9999$, and Normalized Root Mean Squared Error (NRMSE) = 0.44\%. On a large marine dataset from Brazil ($\sim$194,000 km$^2$), SIREN achieves mean SSIMs of 0.9970 and 0.9858 for velocity and dip fields, respectively. We also observe that interpolation quality remains qualitatively consistent despite increasing line sparsity. Compared to legacy methods SIREN produces smoother interpolation with reduced interpolation artifacts.