I introduce a partial differential equation to describe the process of prestack reflection data transformation in the offset, midpoint, and time coordinates. The equation is proved theoretically to provide correct kinematics and amplitudes on the transformed constant-offset sections. Solving an initial-value problem with the proposed equation leads to integral and frequency-domain offset contin...

Standard imaging techniques rely on the single scattering assumption. This requires that the recorded data do not include internal multiples, i.e. waves bouncing multiple times between layers before reaching the receivers at the acquisition surface. When multiple reflections are present in the data, standard imaging algorithms incorrectly image them as ghost reflectors. These artifacts can misl...

I introduce a partial differential equation to describe the process of prestack reflection data transformation in the offset, midpoint, and time coordinates. The equation is proved theoretically to provide correct kinematics and amplitudes on the transformed constant-offset sections. Solving an initial-value problem with the proposed equation leads to integral and frequency-domain offset contin...

Prestack depth migration provides a powerful tool for velocity analysis in complex media. Both prominent approaches to velocity analysis—depth-focusing analysis and residual-curvature analysis, rely on approximate formulas to update velocity. Generally, these formulas are derived under the assumptions of horizontal reflector, lateral velocity homogeneity, or small offset. Therefore, the convent...

In order to produce an accurate depth migration of a seismic line, one needs an accurate velocity model. This model should reflect the lithology and lithostatic load that the rocks have experienced through burial and deformation. If we understand the geometry of these rocks, and their behaviour upon deformation, we can produce a more accurate velocity model. Performing palinspastic restoration ...

With finite capital and logistical means, interpolation is a necessary part of seismic processing, especially for such data-dependent methods as surface-related multiple elimination. One such method is to first estimate a prediction-error filter (PEF) on a training data set, and then use that PEF to estimate missing data, where each step is a least-squares problem. This approach is useful becau...

Single-frequency diffraction tomography, though is well known in the literature, has its inherent problems, such as the limited resolution and image distortion due to the existence of “blind areas” of the object spectrum. The introduction of multi-frequency methods can improve the resolution and partly fill out the “blind areas” of the spectrum. The existing multi-frequency methods, such as the...

the conventional approach to seismic data analysis consists of two main steps: estimating seismic velocities, (the subsurface macro-model), and seismic imaging, (mapping of the reflected seismic energy to the reflector positions). the aim and the major challenge in the seismic data analysis is the construction of the best undistorted image. this challenge would be more problematic when geometri...