A method for determining spatial distribution of proppant incudes using signals detected by seismic sensors disposed proximate a formation treated by pumping fracturing fluid containing the proppant. Origin time and spatial position of seismic events induced by pumping the fracturing fluid are determined. Volume and orientation of at least one fracture in the subsurface formation associated with each induced seismic event are determined. Spatial distribution of a volume of the pumped fracturing fluid is determined using the volume and orientation of each fracture. A length of ellipsoidal axes is selected using a surface defined by a selected fractional amount of the total volume of frac fluid pumped into the formation. Spatial distribution of the proppant is determined using proppant mass, specific gravity and expected proppant porosity in the fractures, and spatially distributing a volume of the fractures within an ellipsoid defined by the ellipsoidal axes.

A system having an unmanned marine vessel and a multi-dimensional seismic sensor array coupled to the unmanned marine vessel. The multi-dimensional seismic sensor array is configured to acquire seismic survey data and calculate pressure gradients in multiple directions. The frame includes members that are configured to rotatably pivot with respect to each other in moveable x-shaped crossing configurations.

Provided in some embodiments are systems and associated methods for regularizing seismic data. Embodiment include obtaining non-uniformly sampled seismic data (e.g., generated by real seismic sensor array having an un-even distribution of real seismic sensors physically positioned proximate a subsurface formation), interpolating the non-uniformly sampled seismic data (e.g., using a Lagrange interpolation or non-linear interpolation) to generate regularized seismic data representing a regular distribution of seismic sensors, and generating, using the regularized seismic data, a seismic image of the subsurface formation.

A system and method for reconstructing an incomplete data subset in seismic exploration is disclosed. The method includes receiving data based on a first emitted signal as a complete dataset. The first emitted signal is a range of frequencies between a starting frequency and a stopping frequency. The method further includes receiving data based on a second emitted signal as an incomplete data subset. The second emitted signal is a subset of the frequencies used by the first emitted signal between the starting frequency and the stopping frequency. The method further includes creating a reconstructed dataset by supplementing the incomplete data subset with the complete dataset and generating a seismic image based on the reconstructed dataset.

Computer-implemented method for determining optimal sampling grid during seismic data reconstruction includes: a) constructing an optimization model, via a computing processor, given by min.sub.uSu.sub.1s.t. Rub.sub.2 wherein S is a discrete transform matrix, b is seismic data on an observed grid, u is seismic data on a reconstruction grid, and matrix R is a sampling operator; b) defining mutual coherence as $\sqrt{\frac{C}{S}\frac{m}{{\left(\log n\right)}^6}},$
wherein C is a constant, S is a cardinality of Su, m is proportional to number of seismic traces on the observed grid, and n is proportional to number of seismic traces on the reconstruction grid; c) deriving a mutual coherence proxy, wherein the mutual coherence proxy is a proxy for mutual coherence when S is over-complete and wherein the mutual coherence proxy is exactly the mutual coherence when S is a Fourier transform; and d) determining a sample grid r.sub.*=arg min.sub.r (r).

A method for determining spatial distribution of proppant incudes using signals detected by seismic sensors disposed proximate a formation treated by pumping fracturing fluid containing the proppant. Origin time and spatial position of seismic events induced by pumping the fracturing fluid are determined. Volume and orientation of at least one fracture in the subsurface formation associated with each induced seismic event are determined. Spatial distribution of a volume of the pumped fracturing fluid is determined using the volume and orientation of each fracture. A length of ellipsoidal axes is selected using a surface defined by a selected fractional amount of the total volume of frac fluid pumped into the formation. Spatial distribution of the proppant is determined using proppant mass, specific gravity and expected proppant porosity in the fractures, and spatially distributing a volume of the fractures within an ellipsoid defined by the ellipsoidal axes.

Method for acquiring seismic data is described. The method includes obtaining undersampled seismic data acquired from a non-uniform sampling grid. Attenuating multiples from the undersampled seismic data.

Systems and methods are provided for performing multidimensional deconvolution. An exemplary method includes: receiving, using at least one processor, a first data associated with waves propagating in a seismic structure; selecting, using the at least one processor, a first transform to be applied to the first data; determining, using the least one processor, whether the first transform is a sparsity or rank revealing transform to optimize sparsity or rank minimization; if the first transform is the sparsity or rank transform, applying, using the at least one processor, the first transform to the first data to produce a second data; calculating, using the at least one processor and the second data, at least one Green's function associated with the first data; and predicting, using the at least one processor and the at least one Green's function, material properties throughout the seismic structure to facilitate exploratory and/or production operations.

A method for acoustic logging a wellbore includes making sonic logging measurements while rotating a logging while drilling tool in a wellbore, the sonic logging measurements including low frequency measurements and high frequency measurements; estimating a low frequency slowness of the subterranean formation from the low frequency measurements; estimating a high frequency slowness of the subterranean formation from the high frequency measurements; and classifying the subterranean formation as homogeneous when a difference between the low frequency slowness and the high frequency slowness is less than a threshold and heterogeneous when the difference is greater than the threshold.

A method may include ocean bottom sensor (OBS) acquisition designed for complex earth model building and imaging with full waveform inversion (FWI) technology. Various combinations of OBS source and receiver patterns, as well as source design may be validated with FWI sensitivity kernel analysis technique. Usually, OBS design is done using conventional methods based on wavelength, frequency requirements, ray tracing and rules of thumps. The method of the disclosed embodiments utilizes OBS design and acquisition combined with FWI sensitivity kernel analysis.