Offshore broadband processing of varibable-depth streamer data based on deghosting by wavefield extrapolation and iterative inversion method

Summary There has been a continually expanding interest in wide azimuth (WAZ) data in all its variations. We are now challenged to take full advantage of the additional information available with minimal compromise. It has been shown that the wider azimuths alone do not supply a dataset sufficient for the full range of processing that must be applied for quality imaging. The narrow azimuth (NAZ) portion of the data is also necessary for shallow imaging as well as multiple prediction and attenuation. Final imaging and both 3D Surface Related Multiple Elimination (SRME) and Wave Field Extrapolation (WFE) methods of demultiple benefit from the presence of near offset / narrow azimuth data. In this paper we present the use of narrow azimuth data from a pre-existing survey to enhance the overall azimuth and offset distribution in a wide azimuth survey with primary emphasis on better prediction of multiples with WFE method.

The inverse scattering series (ISS) direct non-linear inversion and the iterative linear inversion for parameter estimation are examined and compared. The convergence and the rate of convergence of both the ISS inversion subseries and the iterative inversion method are tested for different velocity contrasts on a simple 1D one parameter acoustic model. The rate of convergence of the ISS inversion method is analytically and numerically studied. When the reflection coefficient R 0.618, the ISS inversion subseries still converges, but not monotonically. Numerical tests show that when the velocity contrast is small, both inversion methods converge and the ISS inversion method converges faster than the iterative inversion method. When the velocity contrast increases, the iterative inversion method will not converge when R > 0.5, while the ISS inversion method always converges.

The revisited total least squares problems with linear equality constraint

In areas of complex geology, migration-velocity analysis (MVA) should use methods that describe the complexity of wavefield propagation, such as focusing and defocusing, multipathing, and frequency-dependent velocity sensitivity. MVA by wavefield extrapolation has the ability to address these issues because it uses wavefields as carriers of information. However, its high cost and lack of flexibility with respect to model parametrization have prevented its routine industrial use. We overcome those limitations by using new wavefields: the image-space generalized wavefields. These wavefields are synthesized from a prestack image computed with wavefield-extrapolation methods, using the pre-stack exploding-reflector model. Cost of MVA by wavefield extrapolation is decreased because only a small number of image-space generalized wavefields are necessary to accurately describe the kinematics of velocity errors and because these wavefields can be easily used in a target-oriented way. Flexibility is naturally incorporated because modeling these wavefields have selected reflectors as the initial conditions, allowing the use of a horizon-based parametrization of the model space. In a 3D real data example, we show that using wavefields synthesized by the prestack exploding-reflector model greatly improves efficiency of migration-velocity analysis by wavefield-extrapolation, while yielding a final accurate migration-velocity model evidenced by good quality and reliable depth images.

Recursive wavefield extrapolation methods are more powerful than ray theory based methods because of their greater ability to handle strong lateral velocity variations. Wavefield extrapolation methods have two major problems: (1) the extrapolator instability and (2) the computational expense. The forward operator and conjugate inverse (FOCI) method is an appropriate method for designing accurate and efficient extrapolation operators that remain stable in a recursive algorithm. FOCI’s results are comparable with results obtained with other known methods such as Hale’s and the weighted least square (WLSQ) extrapolation methods. Further, the spatial resampling in the FOCI method offers computational advantages.

A modified algorithm for computing the eigenvalues and the eigenvectors using the bimodal optical computer

Two accurate finite-difference frequency-domain (FDFD)-based iterative inverse methods, referred to as FDFD-based iterative method (FIM) and distorted FDFD-based iterative method (DFIM), are proposed for electromagnetic inverse scattering. They can be considered as FDFD-based versions of BIM and DBIM and inherit the advantage of the traditional direct FDFD inversion method, i.e., there is no need for Green’s function of complex background, especially for the inhomogeneous medium. The difference is that full-wave consideration is implemented in the proposed methods to build an iterative framework. Then, the scattered field and object parameter profile are updated in each iteration. Using the high-order components in iteration formulation, both the methods are able to reconstruct high-contrast objects and provide accurate reconstruction results. Compared with other full-wave methods based on differential equation, the two methods also have a distinct characteristic that the inversion accuracy is not limited by extra constraints. The difference between the two proposed methods is whether the background coefficient matrix is updated. Generally, DFIM has faster convergence than FIM due to the updated background coefficient matrix in the iterations. To demonstrate the effectiveness of both the methods, several typical 2-D experiments are conducted. The results show that the proposed methods could achieve good accuracy and high imaging quality.

An explicit algorithm for the extrapolation of one-way wavefields is proposed which combines recent developments in information theory and theoretical signal processing with the physics of wave propagation. Because of excessive memory requirements, explicit formulations for wave propagation have proven to be a challenge in 3-D. By using ideas from “compressed sensing”, we are able to formulate the (inverse) wavefield extrapolation problem on small subsets of the data volume, thereby reducing the size of the operators. According to compressed sensing theory, signals can successfully be recovered from an imcomplete set of measurements when the measurement basis is incoherent with the representation in which the wavefield is sparse. In this new approach, the eigenfunctions of the Helmholtz operator are recognized as a basis that is incoherent with curvelets that are known to compress seismic wavefields. By casting the wavefield extrapolation problem in this framework, wavefields can successfully be extrapolated in the modal domain via a computationally cheaper operatoion. A proof of principle for the “compressed sensing” method is given for wavefield extrapolation in 2-D. The results show that our method is stable and produces identical results compared to the direct application of the full extrapolation operator.

An efficient solution method is presented to solve the eigenvalue problem arising in the dynamic analysis of nonproportionally damped structural systems. The proposed method is obtained by applying the modified Newton-Raphson technique and the orthonormal condition of the eigenvectors to the linear eigenproblem through matrix augmentation of the quadratic eigenvalue problem. In the iteration methods, such as the vector inverse iteration and subspace iteration methods, singularity may occur during the factorizing process when the shift value is close to an eigenvalue of the system. However, even though the shift value is an eigenvalue of the system, the proposed method provides nonsingularity, if the desired eigenvalue is not multiple, and this is analytically proved. Because the modified Newton-Raphson technique is adapted to the proposed method, initial values are needed. The initial values of the proposed method can be obtained by the intermediate results of iteration methods or results of approximate m...

We discuss iterative methods for computing criticality in nuclear reactors. In general this requires the solution of a generalized eigenvalue problem for an unsymmetric integro-differential operator in six independent variables, modeling transport, scattering, and fission, where the dependent variable is the neutron angular flux. In engineering practice this problem is often solved iteratively, using some variant of the inverse power method. Because of the high dimension, matrix representations for the operators are often not available and the inner solves needed for the eigenvalue iteration are implemented by matrix-free inner iterations. This leads to technically complicated inexact iterative methods, for which there appears to be no published rigorous convergence theory. For the monoenergetic homogeneous model case with isotropic scattering and vacuum boundary conditions, we show that, before discretization, the general nonsymmetric eigenproblem for the angular flux is equivalent to a certain related eigenproblem for the scalar flux, involving a symmetric positive definite weakly singular integral operator (in space only). This correspondence to a symmetric problem (in a space of reduced dimension) permits us to give a convergence theory for inexact inverse iteration and related methods. In particular this theory provides rather precise criteria on how accurate the inner solves need to be in order for the whole iterative method to converge. We also give examples of discretizations which have a corresponding symmetric finite-dimensional reduced form. The theory is illustrated with numerical examples for several test problems of physical relevance, using GMRES as the inner solver.

Determination of the natural frequencies and mode shapes for large structures by accelerated Newton-Raphson method

Study of the Thermal-Hydraulic Characteristics of a Printed Circuit Heat Exchanger Using a Novel Iterative Inversion Method Combined with Genetic Algorithm

The eigenvalue method with selective compression and modal masking (EVM-SCMM) allows to develop criteria to generate effectivemodes efficiently, to remove residual modes and to build the modal mask that accelerates the simulations. Based on the above, algorithms to generate effective modes and to configure modal masks are proposed. These algorithms are based on iterative methods (inverse iteration and related methods, rational Lanczos’ method and Rayleigh quotient minimization techniques) to solve a generalized symmetric eigenvalue problem (SGEVP), combined with physical indices that allow to evaluate the effectiveness of any mode and to stop the sequence of eigenpair generation. The detection of the effective modes is performed calculating their participation factors and comparing them with a modal participation limit. The stop of the effective modes generation process is evaluated calculating the percentage of mass conservation and comparing it with an imposed level of continuity.KeywordsEigenvalue methodModel reductionEigenproblem

Eigensolutions of boundary value problems using inverse iteration

Full Waveform Inversion (FWI) is an iterative inversion method whose purpose is to retrieve high-resolution models of subsurface physical parameters. Because FWI relies on the solution of a non-linear ill-posed inverse problem, uncertainty estimation is a crucial issue in practical applications, both in seismology and exploration seismic. While uncertainty assessment is a strongly desired feature for FWI, it remains a challenging problem. In this presentation, we investigate uncertainty estimation within the framework provided by ensemble data-assimilation strategies. We combine the Ensemble Transform Kalman Filter and FWI. We review the concepts underlying our ETKF-FWI method, discuss its limitations and appeals for uncertainty estimation, and illustrate it on a 2D multiparameter inversion of an exploration scale field dataset.