Abstract: A methodology for extending bandwidth of geophysical data is disclosed. Geophysical data, obtained via a towed streamer, may have significant noise in a certain band (such as less than 4 Hz), rendering the data in the certain band unreliable. To remedy this, geophysical data, from a band that is reliable, may be extended to the certain band, resulting in bandwidth extension. One manner of bandwidth extension comprises using machine learning to generate a machine learning model. Specifically, because bandwidth may be viewed as a sequence, machine learning configured to identify sequences, such as recurrent neural networks, may be used to generate the machine learning model. In particular, machine learning may use a training dataset acquired via ocean bottom nodes in order to generate the machine learning model. After which, the machine learning model may be used to extend the bandwidth of a test dataset acquired via a towed streamer.

Abstract: A multi-stage FWI workflow uses multiple-contaminated FWI models to predict surface-related multiples. A method embodying the present technological advancement, can include: using data with free surface multiples as input into FWI; generating a subsurface model by performing FWI with the free-surface boundary condition imposed on top of the subsurface model; using inverted model from FWI to predict multiples; removing predicted multiples from the measured data; using the multiple-free data as input into FWI with absorbing boundary conditions imposed on top of the subsurface model; and preparing a multiple free data set for use in conventional seismic data processing.

Abstract: An extended subspace method for inverting geophysical data to infer models for two or more subsurface physical properties, using gradients of an objective function as basis vectors for forming model updates. The extended set of basis vectors provides explicit mixing between gradient components corresponding to different medium parameters, for example P-wave velocity and an anisotropy parameter. In a preferred embodiment, off-diagonal elements of the mixing matrix may be scaled to adjust the degree of mixing between gradient components. Coefficients of the basis vector expansion are determined in a way that explicitly accounts for leakage or crosstalk between different physical parameters. The same extended subspace approach may be used to make further improvement to the model updates by incorporating well constraints, where well log data are available.

Abstract: Method for correcting seismic simulations, RTM, and FWI for temporal dispersion due to temporal finite difference methods in which time derivatives are approximated to a specified order of approximation. Computer-simulated seismic data (51) are transformed from time domain to frequency domain (52), and then resampled using a mapping relationship that maps, in the frequency domain, to a frequency at which the time derivative exhibits no temporal dispersion (53), or to a frequency at which the time derivative exhibits a specified different order of temporal dispersion. Alternatively, measured seismic data from a field survey (61) may have temporal dispersion of a given order introduced, by a similar technique, to match the order of approximation used to generate simulated data which are to be compared to the measured data.

Abstract: Method for using the full wavefield (primaries, internal multiples and free-surface multiples) in inversion of marine seismic data, including both pressure and vertical velocity data (21), to infer a subsurface model of acoustic velocity or other physical property. The marine seismic data are separated (22) into up-going (23) and down-going (24) wavefields, and both wavefields are inverted in a joint manner, in which the final model is impacted by both wavefields. This may be achieved by inverting both wavefields simultaneously (25), or one after the other, i.e. in a cascaded approach (35?37, or 45?47), for the subsurface properties (26, 38, 48).

Abstract: The invention includes a method for reducing noise in migration of seismic data, particularly advantageous for imaging by simultaneous encoded source reverse-time migration (SS-RTM). One example embodiment includes the steps of obtaining a plurality of initial subsurface images; decomposing each of the initial subsurface images into components; identifying a set of components comprising one of (i) components having at least one substantially similar characteristic across the plurality of initial subsurface images, and (ii) components having substantially dissimilar characteristics across the plurality of initial subsurface images; and generating an enhanced subsurface image using the identified set of components. For SS-RTM, each of the initial subsurface images is generated by migrating several sources simultaneously using a unique random set of encoding functions. Another embodiment of the invention uses SS-RTM for velocity model building.

Abstract: A multi-stage FWI workflow uses multiple-contaminated FWI models to predict surface-related multiples. A method embodying the present technological advancement, can include: using data with free surface multiples as input into FWI; generating a subsurface model by performing FWI with the free-surface boundary condition imposed on top of the subsurface model; using inverted model from FWI to predict multiples; removing predicted multiples from the measured data; using the multiple-free data as input into FWI with absorbing boundary conditions imposed on top of the subsurface model; and preparing a multiple free data set for use in conventional seismic data processing.

Abstract: Method for performing a full wavefield inversion (FWI) without simulating free-surface multiple reflections. The free-surface multiples are removed from the field gathers of seismic data, which are then used to generate a subsurface velocity model by FWI. In the FWI, the field monopole sources and receivers are replaced with dipole (actual and mirror image) sources and receivers (21) when model-simulating (23) synthetic survey data. Also, direct arrivals at the mirror receiver locations are preferably simulated (25) with the dipole sources for each shot location and added (26) to the synthetic survey data (24) for that shot location, resulting in corrected synthetic survey data (27), which is used in the FWI to generate residuals. A model update may be computed by back-propagating the residuals by injecting them at both mirror and actual receiver locations.

Abstract: Method for correcting seismic simulations, RTM, and FWI for temporal dispersion due to temporal finite difference methods in which time derivatives are approximated to a specified order of approximation. Computer-simulated seismic data (51) are transformed from time domain to frequency domain (52), and then resampled using a mapping relationship that maps, in the frequency domain, to a frequency at which the time derivative exhibits no temporal dispersion (53), or to a frequency at which the time derivative exhibits a specified different order of temporal dispersion. Alternatively, measured seismic data from a field survey (61) may have temporal dispersion of a given order introduced, by a similar technique, to match the order of approximation used to generate simulated data which are to be compared to the measured data.

Abstract: Method for estimating the Hessian of the objective function, times a vector, in order to compute an update in an iterative optimization solution to a partial differential equation such as the wave equation, used for example in full wave field inversion of seismic data. The Hessian times vector operation is approximated as one forward wave propagation (24) and one gradient computation (25) in a modified subsurface model (23). The modified subsurface model may be a linear combination of the current subsurface model (20) and the vector (21) to be multiplied by the Hessian matrix. The forward-modeled data from the modified model are treated as a field measurement in the data residual of the objective function for the gradient computation in the modified model. In model parameter estimation by iterative inversion of geophysical data, the vector in the first iteration may be the gradient of the objective function.

Abstract: Method for stabilizing the updated model (13) in iterative seismic data inversion so that the model-simulated data for the next iteration does not “blow up.” A Projection Onto Convex Sets (“POCS”) operator is defined that converts the matrix corresponding to the model to a positive semi-definite matrix. The stability projection operator may be looped with physical constraint projection operators until the model converges (15). The resulting stable and constrained model is then used to simulate seismic data in the next cycle of the outer iteration loop (16).

Abstract: Method for speeding up iterative inversion of seismic data (106) to obtain a subsurface model (102), using local cost function optimization. The frequency spectrum of the updated model at each iteration is controlled to match a known or estimated frequency spectrum for the subsurface region, preferably the average amplitude spectrum of the subsurface P-impedance. The controlling is done either by applying a spectral-shaping filter to the source wavelet (303) and to the data (302) or by applying the filter, which may vary with time, to the gradient of the cost function (403). The source wavelet's amplitude spectrum (before filtering) should satisfy D(f)=fIp(f)W(f), where f is frequency, D(f) is the average amplitude spectrum of the seismic data, and Ip(f) is the average amplitude spectrum for P-impedance in the subsurface region (306,402) or an approximation thereof.

Abstract: Method for speeding up iterative inversion of seismic data (106) to obtain a subsurface model (102), using local cost function optimization. The frequency spectrum of the updated model at each iteration is controlled to match a known or estimated frequency spectrum for the subsurface region, preferably the average amplitude spectrum of the subsurface P-impedance. The controlling is done either by applying a spectral-shaping filter to the source wavelet (303) and to the data (302) or by applying the filter, which may vary with time, to the gradient of the cost function (403). The source wavelet's amplitude spectrum (before filtering) should satisfy D(f)=fIp(f)W(f), where f is frequency, D(f) is the average amplitude spectrum of the seismic data, and Ip(f) is the average amplitude spectrum for P-impedance in the subsurface region (306,402) or an approximation thereof.

Abstract: Method for using the full wavefield (primaries, internal multiples and free-surface multiples) in inversion of marine seismic data, including both pressure and vertical velocity data (21), to infer a subsurface model of acoustic velocity or other physical property. The marine seismic data are separated (22) into up-going (23) and down-going (24) wavefields, and both wavefields are inverted in a joint manner, in which the final model is impacted by both wavefields. This may be achieved by inverting both wavefields simultaneously (25), or one after the other, i.e. in a cascaded approach (35?37, or 45?47), for the subsurface properties (26, 38, 48).

Abstract: Method for reconstructing subsurface profiles for seismic velocity or other geophysical properties from recorded seismic data. In one embodiment, a starting model of seismic velocity is assumed (10). The computational domain is divided into two (or more) subdomains by horizontal planes based on an analysis of velocity model (30), and the allowed maximum grid size for each subdomain is determined (50). Auxiliary perfectly matched layers (PML's) are attached to each planar interface between subdomains (80), e.g. two PML's on each side of the interface between the coarse and fine subdomains. Simulated seismic data are computed using the SG-DO technique (100-230). The simulated seismic data are compared to the recorded seismic data, then the residual is calculated (240) and used to update the model (320). The method may be iterated until the model is suitably converged (260).

Abstract: An extended subspace method for inverting geophysical data to infer models for two or more subsurface physical properties, using gradients of an objective function as basis vectors for forming model updates. The extended set of basis vectors provides explicit mixing between gradient components corresponding to different medium parameters, for example P-wave velocity and an anisotropy parameter. In a preferred embodiment, off-diagonal elements of the mixing matrix may be scaled to adjust the degree of mixing between gradient components. Coefficients of the basis vector expansion are determined in a way that explicitly accounts for leakage or crosstalk between different physical parameters. The same extended subspace approach may be used to make further improvement to the model updates by incorporating well constraints, where well log data are available.

Abstract: Method for speeding up iterative inversion of seismic data (106) to obtain a subsurface model (102), using local cost function optimization. The frequency spectrum of the updated model at each iteration is controlled to match a known or estimated frequency spectrum for the subsurface region, preferably the average amplitude spectrum of the subsurface P-impedance. The controlling is done either by applying a spectral-shaping filter to the source wavelet (303) and to the data (302) or by applying the filter, which may vary with time, to the gradient of the cost function (403). The source wavelet's amplitude spectrum (before filtering) should satisfy D(f)=fIp(f)W(f), where f is frequency, D(f) is the average amplitude spectrum of the seismic data, and Ip(f) is the average amplitude spectrum for P-impedance in the subsurface region (306,402) or an approximation thereof.

Abstract: Method for simultaneous full-wavefield inversion of gathers of source (or receiver) encoded (30) geophysical data (80) to determine a physical properties model (20) for a subsurface region, especially suitable for surveys where fixed-receiver geometry conditions were not satisfied in the data acquisition (40). The inversion involves optimization of a cross-correlation objective function (100).

Abstract: Method for improving convergence in gradient-based iterative inversion of seismic data (101), especially advantageous for full wavefield inversion. The method comprises decomposing the gradient into two (or more) components (103), typically the migration component and the tomographic component, then weighting the components to compensate for unequal frequency content in the data (104), then recombining the weighted components (105), and using the recombined gradient to update (106) the physical properties model (102).

Abstract: Method for converting seismic data to obtain a subsurface model of, for example, bulk modulus or density. The gradient of an objective function is computed (103) using the seismic data (101) and a background subsurface medium model (102). The source and receiver illuminations are computed in the background model (104). The seismic resolution volume is computed using the velocities of the background model (105). The gradient is converted into the difference subsurface model parameters (106) using the source and receiver illumination, seismic resolution volume, and the background subsurface model. These same factors may be used to compensate seismic data migrated by reverse time migration, which can then be related to a subsurface bulk modulus model. For iterative inversion, the difference subsurface model parameters (106) are used as preconditioned gradients (107).