Abstract: A method, including: determining, with a computer, point spread functions for a plurality of parameter locations by performing at least a portion of a first iteration of an iterative full wavefield inversion process; determining at least one property for each of the point spread functions; and evaluating a candidate survey design based on the at least one property for each of the point spread functions.

Abstract: A method and apparatus for imaging seismic data includes obtaining an initial model of a subsurface formation, wherein the model includes a plurality of nodes that form at least part of a grid; an initial dip value for the nodes; and a set of origin coordinates for each of the nodes; performing bottom-up ray tracing for each node in the model, resulting in a set of arrival coordinates for each node; identifying a plurality of gathers from the seismic data; for each gather: calculating a set of midpoint coordinates; defining a midpoint vicinity surrounding the set of midpoint coordinates; identifying the nodes having arrival coordinates within the midpoint vicinity; and estimating a unique aperture for each of the gathers based on the respective origin coordinates; storing the estimated apertures in a table; and generating a subsurface volume or image with subsurface reflectors determined with apertures of the respective gathers.

Abstract: Methods for updating a physical properties model of a subsurface region that combine advantages of FWI and tomography into a joint inversion scheme are provided. One method comprises obtaining measured seismic data; generating simulated seismic data using an initial model; computing at least one of an FWI gradient and a tomography gradient; minimizing a joint objective function E, wherein the objective function E is based on a combination of the FWI gradient and the tomography gradient or preconditioning of the FWI gradient or the tomography gradient; generating a final model based on the minimized joint objective function E; and using the final model to generate a subsurface image. The joint objective function E may be a function of one or both a FWI objective function CFWI and a tomography objective function CTomo. The joint objective function E may be defined as a weighted sum of CFWI and CTomo.

Abstract: Seismic data processing may include computing the travel time shift between two seismic signals or the depth shift between two seismic images. In Full Waveform Inversion (FWI), the travel time difference between an observed trace and a simulated trace may be computed such that the two traces match after the travel time shift is applied to the observed trace. The travel time shift may be computed based on a constrained optimization that maximizes the windowed cross-correlation between the two seismic traces by constraining the time derivative of the travel time shift to be less than a constant while maximizing the windowed cross-correlation. Further, the travel time shift may be computed during the model line search in FWI by computing a plurality of travel time shifts where a first travel time shift is dependent on the observed trace and a second travel time shift is independent of the observed trace.

Abstract: A computer-implemented method for generating missing frequencies within geophysical data, said method including: decomposing, with a computer, geophysical data into frequencies and slowness or wavenumber along time and one or more spatial dimensions; estimating, with a computer, a filter across known frequencies within the geophysical data for each time, spatial dimension, and slowness or wavenumber sample; extrapolating or interpolating, with a computer, the missing frequencies from the known frequencies by applying the filter; recomposing, with a computer, the known frequencies and the missing frequencies back into time and the one or more spatial dimensions; and prospecting for hydrocarbons with geophysical data that includes the missing frequencies.

Abstract: A computer-implemented method for updating subsurface models including: using an offset continuation approach to update the model, and at each stage defining a new objective function where a maximum offset for each stage is set, wherein the approach includes, performing a first stage iterative full wavefield inversion with near offset data, as the maximum offset, to obtain velocity and density or impedance models, performing subsequent stages of iterative full wavefield inversion, each generating updated models, relative to a previous stage, wherein the subsequent stages include incrementally expanding the maximum offset until ending at a full offset, wherein a last of the stages yields finally updated models, the subsequent stages use the updated models as starting models, and the full wavefield inversions include constraining scales of the velocity model updates at each stage of inversion as a function of velocity resolution; and using the finally updated models to prospect for hydrocarbons.

Abstract: A computer-implemented method for updating a physical properties model of a subsurface region in an iterative inversion of seismic data using a gradient of a cost function that compares the seismic data to model-simulated data, said method comprising: obtaining a contrast model of a subsurface physical parameter that is sensitive to data dynamics and a kinematic model of a subsurface physical parameter; determining a gradient of a cost function using the contrast model and the kinematic model, wherein the cost function compares seismic data to model-simulated data; updating the kinematic model using a search direction derived from the gradient; adapting the contrast model according to an update to the kinematic model performed in the updating step; iteratively repeating the determining, updating, and adapting steps until a predetermined stopping criteria is reached, and generating a subsurface image from a finally updated kinematic model; and using the subsurface image to prospect for hydrocarbons.

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: Methods for updating a physical properties model of a subsurface region that combine advantages of FWI and tomography into a joint inversion scheme are provided. One method comprises obtaining measured seismic data; generating simulated seismic data using an initial model; computing at least one of an FWI gradient and a tomography gradient; minimizing a joint objective function E, wherein the objective function E is based on a combination of the FWI gradient and the tomography gradient or preconditioning of the FWI gradient or the tomography gradient; generating a final model based on the minimized joint objective function E; and using the final model to generate a subsurface image. The joint objective function E may be a function of one or both a FWI objective function CFWI and a tomography objective function CTomo. The joint objective function E may be defined as a weighted sum of CFWI and CTomo.

Abstract: A method for iteratively inverting seismic data to jointly infer a model for at least P-wave velocity and attenuation parameters of the subsurface, the method including: jointly inverting the P-wave velocity and attenuation parameters with an iterative visco-acoustic full wavefield inversion process, wherein the iterative visco-acoustic full wavefield inversion process includes computing a gradient of an objective function, the objective function measuring a misfit between all or part of the seismic data and corresponding model-simulated seismic data; for each of the P-wave velocity and attenuation parameters, computing a search direction in model space from the gradient; determining line search step sizes ? and ? for the search directions for the P-wave velocity and attenuation parameters, respectively, wherein a ratio of the step sizes is a function of the P-wave velocity parameter; and using the step sizes ? and ? and the search directions for each of the P-wave velocity and attenuation parameters, computi

Abstract: A method and apparatus for imaging seismic data includes obtaining an initial model of a subsurface formation, wherein the model includes a plurality of nodes that form at least part of a grid; an initial dip value for the nodes; and a set of origin coordinates for each of the nodes; performing bottom-up ray tracing for each node in the model, resulting in a set of arrival coordinates for each node; identifying a plurality of gathers from the seismic data; for each gather: calculating a set of midpoint coordinates; defining a midpoint vicinity surrounding the set of midpoint coordinates; identifying the nodes having arrival coordinates within the midpoint vicinity; and estimating a unique aperture for each of the gathers based on the respective origin coordinates; storing the estimated apertures in a table; and generating a subsurface volume or image with subsurface reflectors determined with apertures of the respective gathers.

Abstract: A method, including performing, with a computer, up/down separation of geophysical data, which produces an approximate up-going wavefield and an approximate down-going wavefield; creating an areal source based at least in part on the down-going wavefield; and performing, with a computer, a full wavefield inversion process with the areal source, and an objective function measuring a misfit between modeled up-going wavefields and recorded up-going wavefields, wherein the full wavefield inversion process generates a final subsurface physical property model.

Abstract: A computer-implemented method for generating missing frequencies within geophysical data, said method including: decomposing, with a computer, geophysical data into frequencies and slowness or wavenumber along time and one or more spatial dimensions; estimating, with a computer, a filter across known frequencies within the geophysical data for each time, spatial dimension, and slowness or wavenumber sample; extrapolating or interpolating, with a computer, the missing frequencies from the known frequencies by applying the filter; recomposing, with a computer, the known frequencies and the missing frequencies back into time and the one or more spatial dimensions; and prospecting for hydrocarbons with geophysical data that includes the missing frequencies.

Abstract: A computer-implemented method for updating subsurface models including: using an offset continuation approach to update the model, and at each stage defining a new objective function where a maximum offset for each stage is set, wherein the approach includes, performing a first stage iterative full wavefield inversion with near offset data, as the maximum offset, to obtain velocity and density or impedance models, performing subsequent stages of iterative full wavefield inversion, each generating updated models, relative to a previous stage, wherein the subsequent stages include incrementally expanding the maximum offset until ending at a full offset, wherein a last of the stages yields finally updated models, the subsequent stages use the updated models as starting models, and the full wavefield inversions include constraining scales of the velocity model updates at each stage of inversion as a function of velocity resolution; and using the finally updated models to prospect for hydrocarbons.

Abstract: Method for reducing computational time in inversion of geophysical data to infer a physical property model (91), especially advantageous in full wavefield inversion of seismic data. An approximate Hessian is pre-calculated by computing the product of the exact Hessian and a sampling vector composed of isolated point diffractors (82), and the approximate Hessian is stored in computer hard disk or memory (83). The approximate Hessian is then retrieved when needed (99) for computing its product with the gradient (93) of an objective function or other vector. Since the approximate Hessian is very sparse (diagonally dominant), its product with a vector may therefore be approximated very efficiently with good accuracy. Once the approximate Hessian is computed and stored, computing its product with a vector requires no simulator calls (wavefield propagations) at all. The pre-calculated approximate Hessian can also be reused in the subsequent steps whenever necessary.

Abstract: Method for simultaneously inverting full-wavefield seismic data (51) for multiple classes of physical property parameters (e.g., velocity and anisotropy) by computing the gradient (53), i.e. search direction (54), of an objective function for each class of parameters, then applying (preferably exhaustive) first-pass independent line searches to each parameter class to obtain the corresponding step size (55) along the search direction for each parameter class; then without yet updating the model, using the step sizes to define a relative scaling between gradients of all parameter classes. Next, each scaled search direction is recombined to form a new search direction (56), and a new second-pass line search is performed along the new search direction (57), and all parameters are simultaneously updated with the resulting step size (58). Alternatively to the preceding alternating two-pass embodiment, the model may be updated after each first-pass line search, and no second-pass line search is performed.

Abstract: A computer-implemented method for updating a physical properties model of a subsurface region in an iterative inversion of seismic data using a gradient of a cost function that compares the seismic data to model-simulated data, said method comprising: obtaining a contrast model of a subsurface physical parameter that is sensitive to data dynamics and a kinematic model of a subsurface physical parameter; determining a gradient of a cost function using the contrast model and the kinematic model, wherein the cost function compares seismic data to model-simulated data; updating the kinematic model using a search direction derived from the gradient; adapting the contrast model according to an update to the kinematic model performed in the updating step; iteratively repeating the determining, updating, and adapting steps until a predetermined stopping criteria is reached, and generating a subsurface image from a finally updated kinematic model; and using the subsurface image to prospect for hydrocarbons.

Abstract: A method for iteratively inverting seismic data to jointly infer a model for at least P-wave velocity and attenuation parameters of the subsurface, the method including: jointly inverting the P-wave velocity and attenuation parameters with an iterative visco-acoustic full wavefield inversion process, wherein the iterative visco-acoustic full wavefield inversion process includes computing a gradient of an objective function, the objective function measuring a misfit between all or part of the seismic data and corresponding model-simulated seismic data; for each of the P-wave velocity and attenuation parameters, computing a search direction in model space from the gradient; determining line search step sizes ? and ? for the search directions for the P-wave velocity and attenuation parameters, respectively, wherein a ratio of the step sizes is a function of the P-wave velocity parameter; and using the step sizes ? and ? and the search directions for each of the P-wave velocity and attenuation parameters, computi

Abstract: A method, including performing, with a computer, up/down separation of geophysical data, which produces an approximate up-going wavefield and an approximate down-going wavefield; creating an areal source based at least in part on the down-going wavefield; and performing, with a computer, a full wavefield inversion process with the areal source, and an objective function measuring a misfit between modeled up-going wavefields and recorded up-going wavefields, wherein the full wavefield inversion process generates a final subsurface physical property model.

Abstract: A method, including: determining, with a computer, point spread functions for a plurality of parameter locations by performing at least a portion of a first iteration of an iterative full wavefield inversion process; determining at least one property for each of the point spread functions; and evaluating a candidate survey design based on the at least one property for each of the point spread functions.