Systems, methods, and apparatuses for generating a subsurface image using diffraction energy information are disclosed. The systems, methods, and apparatuses may include converting a shot gather into one or more plane-wave gather using a Radon transform. The plane-wave gathers may be extrapolated into source-side wavefields and receiver-side wavefields and further generate a pseudo dip-angle gather. The diffraction energy information may be extracted from the pseudo dip-angle gather, and an image containing subsurface features may be generated from the extracted diffraction energy information. The receiver-side wavefields may be decomposed using a recursive Radon transform.

Prediction and subtraction of multiple diffractions may include transforming previously acquired seismic data from a time-space domain to a transformed domain using a dictionary of compressive basis functions and separating, within the transformed previously acquired seismic data, a first portion and a second portion of the transformed previously acquired seismic data. Prediction and subtraction of multiple diffractions may also include predicting a plurality of multiple diffractions based on the separated first and second portions and adaptively subtracting the predicted multiple diffractions from the previously acquired seismic data. Prediction and subtraction of multiple diffractions may also include inverse transforming a particular seismic data set from the transformed domain to the time-space domain.

Method for reconstructing seismic data. The method includes receiving at a computing device an input seismic data set d related to plural shots emitted by one or more seismic sources; receiving at the computing device a positional data set d.sub.p relating to recording locations of the receivers that recorded the input seismic data set d; receiving at the computing device a receiver target location; calculating an adjusted receiver location based on (i) the positional data set d.sub.p and (ii) the receiver target location, wherein the adjusted receiver location substantially coincides with a receiver location from the positional data set d.sub.p; calculating reconstructed seismic data d.sub.r at the adjusted receiver location using the input seismic data set d and the positional data set d.sub.p; and correcting the seismic wave paths from the one or more seismic sources to the receivers based on the reconstructed seismic data d.sub.r.

A method of generating geophysical data using at least one source. The method may include the steps of generating a geophysical wavefield with a varying signature using at least one source, wherein the signature is varied in a periodic pattern.

A method of generating geophysical data using at least one source. The method may include the steps of generating a geophysical wavefield with a varying signature using at least one source, wherein the signature is varied in a periodic pattern.

Raw 3D seismic streamer wavefield data is received as a receiver-ghosted shot gather. The received receiver-ghosted shot gather shot gather is processed into a normalized form as normalized data. The normalized data is partitioned into a plurality of user-defined sub-gathers and processed to generate a complete receiver-deghosted shot gather. Output of the complete receiver-deghosted shot gather is initiated.

A system and method for interpolating seismic data collected by a set of geophones arranged in an irregularly spaced grid by: transforming the collected seismic data by a Radon transform; pre-computing a set of basis function correlation factors by geometrically scaling a spatial geometry of each temporal frequency slice of the transformed seismic data independently by its temporal frequency; computing, solely in the transformed domain, an anti-leakage Radon transform of the seismic data by computing each Radon coefficient independently for each temporal frequency slice using the pre-computed basis function correlation factors, until a relative error between the collected seismic data and an approximation of the collected seismic data based on the Radon coefficients is less than a predetermined convergence threshold; and simulating seismic data collected in a regularly spaced grid by interpolating the anti-leakage Radon transform of the collected seismic data in the irregularly spaced grid.

Raw 3D seismic streamer wavefield data is received as a receiver-ghosted shot gather. The received receiver-ghosted shot gather shot gather is processed into a normalized form as normalized data. The normalized data is partitioned into a plurality of user-defined sub-gathers and processed to generate a complete receiver-deghosted shot gather. Output of the complete receiver-deghosted shot gather is initiated.

A method for deblending seismic signals includes entering as input to a computer recorded signals comprising seismic energy from a plurality of actuations of one or more seismic energy sources. A model of deblended seismic data and a blending matrix are initialized. A blending matrix inversion is performed using the initialized model. The inversion includes using a scaled objective function. The inversion is constrained by a thresholding operator. The thresholding operator is arranged to recover coefficients of the model of the deblended seismic data that are substantially nonzero, against a Gaussian white noise background. The thresholded model is projected into data space. Performing the blending matrix inversion is repeated if a data residual exceeds a selected threshold and the inversion is terminated if the data residual is below the selected threshold. At least one of storing and displaying an output of the blending matrix inversion is performed when the blending matrix inversion is terminated.

A method for full-waveform sonic (FWS) wavefield separation includes receiving FWS data; performing an anti-aliasing linear Radon transform on the received FWS data; extracting Radon-transformed FWS data corresponding to a wave component using a slanted window; and determining signals of the wave component by performing an inverse Radon transform on the extracted Radon-transformed FWS data.