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SEP-142 (2010)


Book (pdf)

Wave-equation Velocity Analysis

Target-oriented wavefield tomography: A field data example 

Yaxun Tang and Biondo Biondi

We present a strategy for efficient migration velocity analysis in complex geological settings. The proposed strategy contains two main steps: simulating a new data set using an initial unfocused image and performing wavefield-based tomography using this data. We show that the new data set can be synthesized for a specific target region where velocities are inaccurate. We also show that the new data set can be much smaller than the original one due to the target-oriented modeling strategy, but it contains necessary velocity information for successful velocity analysis. These interesting features make this new data set suitable for target-oriented, fast and interactive velocity modeling building. We demonstrate the performance of our method on a selected 2-D line of a 3-D data set acquired from the Gulf of Mexico, where we update the subsalt velocity in a target-oriented fashion and obtain a subsalt image with improved continuities and signal to noise ratio.

Migration velocity analysis based on linearization of the two-way wave equation 

Ali Almomin and Yaxun Tang

Wave equation migration velocity analysis (WEMVA) is a family of techniques that aims to improve the subsurface velocity model by minimizing the residual in image space. This process is performed iteratively by linearizing the imaging operator in order to relate image perturbations to model updates. This linearization is conventionally based on the one-way wave equation, which has some pitfalls in terms of accuracy and ability to image certain wavepaths in complex geology. We present a formulation of WEMVA based on the two-way wave equation which can improve the accuracy of the model estimate. There are two approximations used to linearize this operator. First is the Born approximation and the second envolves dropping the second order slowness perturbation term. In this paper, we show preliminary results of using the two-way based WEMVA, as well as the resolution matrix of the operator.

Wave-equation migration velocity analysis by residual moveout fitting 

Biondo Biondi

Flatness in migrated angle-domain common image gathers is an effective criterion for measuring migration-velocity accuracy. An objective function that measures the power of the stack as a function of residual-moveout parameters directly, and indirectly as a function of migration velocity, can be robustly maximized by using a gradient-based method. This paper presents a method to compute the gradient of this objective function by wave-equation operators. The proposed algorithm has the additional advantage of not requiring the picking of the residual-moveout parameters.

Simultaneous Source

Seismic reservoir monitoring with encoded permanent seismic arrays 

Gboyega Ayeni

Hydrocarbon reservoirs can be efficiently monitored with encoded data recorded by permanent seismic arrays. Permanent seismic sources and receivers can yield a vast amount of data that may enable near-real-time monitoring. I propose an encoding approach that may overcome some of the operational, storage and processing challenges posed by these vast data volumes. Although data encoding introduces cross-talk artifacts, permanent arrays allow for good repeatability of such artifacts, thereby aiding time-lapse seismic cross-equalization. Because the proposed method utilize low-energy intermittent seismic sweeps, data must be recorded for longer durations compared to conventional data recording. Direct migration of these long-duration data is efficient and gives good-quality time-lapse images. Using a 2D numerical model, I show that this method can produce reliable time-lapse images of comparable quality to those from conventional seismic sources.

On the separation of simultaneous-source data by inversion 

Gboyega Ayeni, Ali Almomin, and Dave Nichols

Simultaneous-source data can be adequately separated using an inversion formulation. To recover component shot records, we formulate the data-separation problem as a simultaneous Radon inversion problem. By minimizing the resulting objective function with a robust hybrid solver, we obtain high-quality estimates of the component shot records. Furthermore, regularization with directional Laplacians improves the data quality. In our approach, we estimate a single model that predicts all recorded data, and we treat all components of the recorded data as signal. Within limits of operational possibilities, our method can be applied to any number of sources within a single survey and can be easily extended to multiple (time-lapse) surveys. Using 2D sections extracted from the 3D SEAM geophysical model, we show that our method can give results of comparable quality to the original independent shot records.


A preconditioning scheme for full waveform inversion

Antoine Guitton and Gboyega Ayeni

The waveform inversion problem is inherently ill-posed. Traditionally, regularization terms are used to address this issue. For waveform inversion where the model is expected to have many details reflecting the physical properties of the Earth, regularization and data fitting can work in opposite directions: the former smoothing and the later adding details to the model. In this paper, we constrain the velocity model with a model-space preconditioning scheme based on directional Laplacian filters. This preconditioning strategy preserves the details of the velocity model while smoothing the solution along known geological dips. The Laplacian filters have the property to smooth or kill local planar events according to a local dip field. By construction, these filters can be inverted and used in a preconditioned waveform-inversion scheme to yield geologically meaningful models. We illustrate on a 2-D synthetic example how preconditioning with non-stationary directional Laplacian filters outperforms traditional waveform inversion when sparse data are inverted for. We think that preconditioning could benefit waveform inversion of real data where (for instance) irregular geometry, coherent noise and lack of low frequencies are present.

Hybrid-norm and Fortran 2003: Separating the physics from the solver

Robert G. Clapp

Object-oriented approaches allow a separation between solvers and operators. An abstract vector class is created with a limited set of methods. Solvers are written in terms of this abstract vector class and operators act on vectors inherited from the abstract class. Ideally, this separation allows the geophysicist to leverage the work of the mathematician without needing to understand the implementation details of the optimization method. The minimal set of object-oriented features of Fortran95 and its predecessors limited the potential separation between the physics and the solver. New inversion approaches, such as the hybrid norm, further hampered this separation when using conventional vector class descriptions. By using the object-oriented features of Fortran 2003, a more complete separation between solvers and operators can be achieved. By expanding the vector class definition, approaches such as the hybrid norm can be implemented.


A new bidirectional deconvolution method that overcomes the minimum phase assumption 

Yang Zhang and Jon Claerbout

Traditionally blind deconvolution makes the assumption that the reflectivity spike series is white. Earlier we dropped that assumption and adopted the assumption that the output spike series is sparse under a hyperbolic penalty function. This approach now here allows us to take a step further and drop the assumption of minimum phase. In this new method (what we called Bidirectional Sparse Deconvolution), We solve explicitly for the maximum phase part of the source. Results on both synthetic data and field data show clear improvements.

Short note: Three dimensional deconvolution of helioseismic data 

Chris Leader, Jon Claerbout, and Antoine Guitton

This is a short note on helioseismic deconvolution. Herein results are presented by deconvolving helioseismic data with a calculated impulse response in 3D to help determine source information in the shallow solar interior. Tentatively it can be concluded that there the solar acoustic energy is close to uniformaly distributed throughout the convective envelope.


Implementing implicit finite-difference in the time-space domain using spectral factorization and helical deconvolution 

Ohad Barak

The method of modeling wavefield propagation with an implicit finite-difference approximation to the two-way acoustic isotropic wave equation, using spectral factorization and helical deconvolution, exhibits instability of the propagating wavefield as the time step is increased. In this study, I test several potential sources of the instability problem: the implicit finite-difference scheme itself, the precision of the floating point representation of the filter coefficients, the number of filter coefficients, and the spectral factorization method. None of these issues is the cause for the apparent instability.

Short note: GPU accelerated 3D wave propagation and continuous coil shooting

Chris Leader, Robert Clapp, and Biondo Biondi

This short note discusses how continuous coil shooting for a synthetic VSP survey could lead towards more azimuth rich data whilst keeping the survey time below that of a conventional towed streamer survey.

A. Almomin
G. Ayeni
O. Barak
B. Biondi
J. Claerbout
R. Clapp
A. Guitton
C. Leader
D. Nichols
Y. Tang
Yang Zhang
Publication Date
October 30, 2010