Abstract: A method for approximating an inverse Hessian is provided. One methodology to generate the inverse Hessian is to precondition the gradient, such as by using point-spread function deconvolution, T-power, or source-illumination compensation, prior to using non-stationary matching filters (NMF) to generate the inverse Hessian. Various types of NMF are contemplated, including using filters for different windows in the subsurface or using filters assigned to specific locations in the subsurface. Further, the number of filters for NMF may vary from iteration to iteration. For example, the filters assigned to the specific locations in the subsurface may be generated in a multi-scale manner, in which an initial iteration uses longer scale/longer wavelength features for inversion and subsequent iterations use finer scale/smaller wavelength features for inversion.

Abstract: A method for partitioning a search direction when using least squares reverse time migration (LSRTM) is provided. LSRTM may be used iteratively in order to improve imaging accuracy. As part of LSRTM, multiple local line searches may be performed. In particular, image space may be partitioned, such as by using a set of masks. The search direction, such as the gradient, may be partitioned using the set of masks. Local line searches may be performed for each partition of the search direction, resulting in finding respective line search constants. The respective line search constants may then be used for iterating the model in order to improve imaging accuracy.

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: obtaining, with a computer, an initial geophysical model; modeling, with a computer, a forward wavefield based on the initial geophysical model with wave equations including a second order z-derivative in a rotated coordinate system that accounts for a tilted transverse isotropic (TTI) medium; modeling, with a computer, an adjoint wavefield with adjoint wave equations including a second order z-derivative in a rotated coordinate system that accounts for a tilted transverse isotropic (TTI) medium, wherein the wave equations and the adjoint wave equations include relaxation terms accounting for anelasticity of earth in an update of a primary variable and an evolution relationship for the relaxation terms; and obtaining, with a computer, a gradient of a cost function based on a combination of a model of the forward wavefield and a model of the adjoint wavefield.

Abstract: A method for partitioning a search direction when using least squares reverse time migration (LSRTM) is provided. LSRTM may be used iteratively in order to improve imaging accuracy. As part of LSRTM, multiple local line searches may be performed. In particular, image space may be partitioned, such as by using a set of masks. The search direction, such as the gradient, may be partitioned using the set of masks. Local line searches may be performed for each partition of the search direction, resulting in finding respective line search constants. The respective line search constants may then be used for iterating the model in order to improve imaging accuracy.

Abstract: A method for approximating an inverse Hessian is provided. One methodology to generate the inverse Hessian is to precondition the gradient, such as by using point-spread function deconvolution, T-power, or source-illumination compensation, prior to using non-stationary matching filters (NMF) to generate the inverse Hessian. Various types of NMF are contemplated, including using filters for different windows in the subsurface or using filters assigned to specific locations in the subsurface. Further, the number of filters for NMF may vary from iteration to iteration. For example, the filters assigned to the specific locations in the subsurface may be generated in a multi-scale manner, in which an initial iteration uses longer scale/longer wavelength features for inversion and subsequent iterations use finer scale/smaller wavelength features for inversion.

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 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: obtaining, with a computer, an initial geophysical model; modeling, with a computer, a forward wavefield based on the initial geophysical model with wave equations including a second order z-derivative in a rotated coordinate system that accounts for a tilted transverse isotropic (TTI) medium; modeling, with a computer, an adjoint wavefield with adjoint wave equations including a second order z-derivative in a rotated coordinate system that accounts for a tilted transverse isotropic (TTI) medium, wherein the wave equations and the adjoint wave equations include relaxation terms accounting for anelasticity of earth in an update of a primary variable and an evolution relationship for the relaxation terms; and obtaining, with a computer, a gradient of a cost function based on a combination of a model of the forward wavefield and a model of the adjoint wavefield.

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.