A method for computing amplitude independent gradient for seismic velocity inversion in a frequency domain includes receiving seismic data associated with a region. The region comprises one or more earth subsurface layers represented by a plurality of points, and each point is associated with a seismic velocity. Seismic velocities at the plurality of points are determined by iteratively updating the seismic velocities based on a plurality of gradient values, where each gradient value corresponds to a point and is determined by evaluating a gradient of an objective function at a location of the point. A seismic image of the one or more earth subsurface layers is displayed based on the determined seismic velocities.

A method and a system for implementing the method are disclosed wherein the pre-stack seismic input data, an initial anellipticity anisotropy parameter, and a baseline normal moveout velocity from a non-flat surface, are sometimes mild or foothill topography as well as the shot and receiver lines might not necessarily be straight, and often curve to avoid obstacles on the land surface. In particular, the method and system disclosed, allows for updating the anisotropy parameters iteratively and when the stopping criteria is satisfied, the final estimated parameter can be directly used for time migration. This method and system are mainly used for time migration with the purpose of obtaining the high fidelity (accurate amplitude, i.e. not only travel-time correct but also amplitude correct) image gathers which are used for reservoir characterization and interpretation.

Systems and methods for seismic imaging of a subterranean geological formation include receiving parameter data representing one or more parameters of a seismic survey, the seismic data specifying an incident angle and an azimuth angle for each trace of the seismic survey; determining a relationship between the incident angle and the azimuth angle for each trace and a location in a spiral coordinate system, and generating a weighting function for applying a weight value to each trace seismic data based on the incident angle and the azimuth angle associated with each trace; and determining a residual moveout value of the seismic data for each location in the spiral coordinate system by applying the weighting function to each; and generating a seismic image representing the residual moveout value of the seismic data for each location in the spiral coordinate system.

Methods for full waveform inversion (FWI) in the midpoint-offset domain include using a computer system to sort seismic traces into common midpoint-offset bins (XYO bins). For each XYO bin, a linear moveout correction is applied to a collection of seismic traces within the XYO bin. The collection of seismic traces is stacked to form a pilot trace. The computer system determines a surface-consistent residual static correction for each seismic trace. The computer system determines that the surface-consistent residual static correction for each seismic trace is less than a threshold. Responsive to the determining that the surface-consistent residual static correction is less than the threshold, the computer system stacks the collection of seismic traces to provide the pilot trace. The computer system groups the pilot traces for the XYO bins into a set of virtual shot gathers. The computer system performs one-dimensional FWI based on each virtual shot gather.

Seismic data are obtained by recording simultaneously in seismic streamer, acquired by activating approximately simultaneously two or more seismic sources towed at two positions in the vicinity of seismic streamers. A residual is updated iteratively for an inversion solution for the activations of the two or more seismic sources. The iterative updating of the residuals utilizes a sequence of overlapping temporal windows containing reflection events and utilizes normal moveout corrections based on largest reflection events in each temporal window. A final updated residual is added to a final updated model result.

A method includes receiving, via a processor, input data based upon received seismic data, migrating, via the processor, the input data via a pre-stack depth migration technique to generate migrated input data, encoding, via the processor, the input data via an encoding function as a migration attribute to generate encoded input data having a migration function that is non-monotonic versus an attribute related to the input data, migrating, via the processor, the encoded input data via the pre-stack depth migration technique to generate migrated encoded input data, and generating an estimated common image gather based upon the migrated input data and the migrated encoded input data. The method also includes generating a seismic image utilizing the estimated common image gather, wherein the seismic image represents hydrocarbons in a subsurface region of the Earth or subsurface drilling hazards.

Seismic data are obtained by recording simultaneously in seismic streamer, acquired by activating approximately simultaneously two or more seismic sources towed at two positions in the vicinity of seismic streamers. A residual is updated iteratively for an inversion solution for the activations of the two or more seismic sources. The iterative updating of the residuals utilizes a sequence of overlapping temporal windows containing reflection events and utilizes normal moveout corrections based on largest reflection events in each temporal window. A final updated residual is added to a final updated model result.

Methods and systems are presented in this disclosure for semblance-based anisotropy parameter estimation using isotropic depth-migrated common image gathers. Far-offset image gathers can be generated from seismic data associated with a subterranean formation migrated based on an isotropic depth migration that uses an isotropic velocity model. Based on the far-offset image gathers, a plurality of semblance values can be calculated as a function of an anisotropy parameter of the subterranean formation for the different depths and the surface locations. Effective values of the anisotropy parameter of the subterranean formation can be then chosen that result in maxima of the plurality of semblance values for the different depths and the surface locations. Anisotropy model of the subterranean formation can be obtained based on the effective values of the anisotropy parameter.

Methods for seismic exploration of an underground formation including at least one anisotropic layer perform a joint velocity-variation-with-azimuth, VVAz, and amplitude-variation-with-azimuth, AVAz, inversion using the azimuthal angle stacks to obtain a structural representation of the underground formation. The structural representation is used to generate scenarios for exploiting resources in at least one layer of the underground formation.

An apparatus and a method for estimating interval anellipticity parameter by inversing effective anellipticity parameter in the depth domain using a least-squares method. One embodiment of interval anellipticity parameter estimator includes: 1) an interface configured to receive seismic data and borehole information; 2) a depth convertor configured to obtain a function of depth of effective anisotropy parameter based on said borehole information; 3) an inverse transformer configured to set up said function of depth of effective anisotropy parameter as a least-squares fitting problem based on said P-wave data; and 4) an iterative solver configured to use iterative methods to solve said least-squares fitting problem and to obtain an anisotropy model containing interval anellipticity parameter.