摘要:
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.
摘要:
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).
摘要:
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).
摘要:
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).
摘要:
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.
摘要:
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.
摘要:
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.
摘要:
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.
摘要:
An exemplary embodiment of the present invention provides a method for interpolating seismic data. The method includes collecting seismic data of two or more types over a field (401), determining an approximation to one of the types of the seismic data (402), and performing a wave-field transformation on the approximation to form a transformed approximation (405), wherein the transformed approximation corresponds to another of the collected types of seismic data. The method may also include setting the transformed approximation to match the measured seismic data of the corresponding types at matching locations (408), performing a wave-field transformation on the transformed approximation to form an output approximation (412), and using the output approximation to obtain a data representation of a geological layer (416).
摘要:
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.