# SEP-145 (2011)

## Download

Book (pdf)

## Wave-equation migration velocity analysis

Two-parameters residual-moveout analysis for wave-equation migration velocity analysis [pdf 468K] [source]

**Biondo Biondi**

The use of two-parameter RMO functions has the potential of improving the flatness of RMO-corrected gathers. The two RMO functions I propose add a second term to the conventional angle-domain RMO function. The proposed RMO functions achieve improved flatness when applied to two test CIGs that are representative of situations when either strong lateral velocity variations or anisotropy occur. The use of two-parameter RMO functions could also improve the velocity gradients when applied within automatic MVA methods. My numerical experiments indicate that the RMO function that I defined by adding a term proportional to the fourth power of the tangent of the aperture angle should yield more accurate gradients than the one-parameter RMO function. This choice is also more robust with respect to the setting of processing parameters than the other two-parameter RMO function I introduce in the paper, which adds a term proportional to the absolute value of the sine of of the aperture angle

Velocity model evaluation through Born modeling and migration: a feasibility study [pdf 1.6M] [source]

**Adam Halpert and Yaxun Tang**

A way to quickly test many possible migration velocity models would be a valuable interpretation tool. Here, a modified Born modeling scheme is used to simulate a new, smaller dataset from an initial image, allowing for target-oriented migrations in a fraction of the time needed for a full migration of the original dataset. Furthermore, the simulated dataset is migrated with a generalized source function derived from the original prestack image, preserving important velocity information that would be lost if a standard wavelet were used as the source function. While the method is currently limited to analysis of a single reflector, initial tests on a simple 2D synthetic model indicate that this method can accurately and efficiently produce images comparable to full standard migrations.

## Simultaneous sources

Fast automatic wave-equation migration velocity analysis using encoded simultaneous sources [pdf 1.4M][source]

**Yaxun Tang**

I present a method based on source encoding for fast wave-equation migration velocity analysis (WEMVA). Instead of migrating each impulsive-source gather separately, I assemble all gathers together and migrate only one super shot gather. This procedure results in the computational cost of WEMVA to be independent from the number of impulsive-source gathers, which is typically huge for large surveys. The proposed encoding method can be applied to data acquired from any acquisition geometry, such as land or marine acquisition geometries. The velocity inversion is done automatically by solving a nonlinear optimization problem that maximizes the image stack power, which is shown to be equivalent to the data-domain inversion using only primary reflections. Preliminary results show that WEMVA with encoded sources can produce inversion results similar to those produced by conventional separate-source WEMVA, but with drastically reduced computational cost.

Preconditioned least-squares reverse-time migration using random phase encoding [pdf 1.8M] [source]

**Ali Almomin**

Least-squares reverse-time migration (LSRTM) provides very accurate images of the subsurface. However, the computational cost of this technique is extremely high. One way to reduce that cost is to encode the sources using a random phase function and create a "super source". This encoding method introduces crosstalk artifacts that require averaging several realizations of the random encodings to suppress. I compare the convergence rates of the conventional and phase-encoded LSRTM for a fixed-spread geometry and show that the performance gain for the phase-encoded LSRTM far exceeds the loss due to the additional realizations. I also reduce the inversion cost by using the diagonal of the Hessian matrix as a preconditioner to the gradient. I also compare the convergence rates of different encoding methods used to estimate the true Hessian matrix. Then, I introduce a new source-based Hessian approximation and compare it to the other methods of approximating the Hessian matrix. Finally, I show the effect of each preconditioner on the LSRTM inversion. Results from the Marmousi synthetic model show that, for the same cost, preconditioning with the source-based Hessian gives the most accurate results.

## Linearized wave-equation modeling/inversion

Least-squares wave-equation inversion of time-lapse seismic data sets - A Valhall case study [pdf 9.7M] [source]

**Gboyega Ayeni and Biondo Biondi**

We demonstrate an application of least-squares wave-equation inversion using time-lapse data sets from the Valhall field. We pose time-lapse imaging as a joint least-squares problem that utilizes target-oriented approximations to the Hessian of the objective function. Because this method accounts for illumination mismatches-caused by differences in acquisition geometries-and for band-limited wave-propagation effects, it provides better estimates of production-related changes in reservoir acoustic properties than conventional time-lapse processing methods. We show that our method improves image resolution (compared to migration) and that it attenuates obstruction artifacts in time-lapse images.

Elastic Born modeling in an ocean-bottom node acquisition scenario [pdf 984K][source]

**Ohad Barak**

PZ summation is a common method for separating the upgoing wavefield from the downgoing wavefield in data acquired by four-component ocean-bottom node surveys. It assumes that the vertical geophone component records mostly pressure waves. If this assumption is not satisfied, non-pressure wave energy (such as shear waves) will be introduced as pressure waves into the receiver wavefield, which may generate artifacts in the migration image. I formulate an elastic Born modeling and migration method for ocean-bottom node acquired data. I then use a synthetic example to demonstrate the effect of the introduction of non-pressure wave energy into the receiver data on the resulting image.

## Object-oriented inversion

Krylov space solver in Fortran 2009: Beta version [pdf 168K] [source]

**Robert G. Clapp**

Solving linear systems using Krylov subspace methods is an ideal candidate for object-orient programming. Iterative solver approaches use only a few different operations on vectors and operators. These operations form the basis of abstract vector and operator classes. Sophisticated solvers can then be written on top of these abstract classes separating the geophysics (operators) from the mathematics (solvers). The minimal set of object-oriented features of Fortran95 and its predecessors limited the potential separation. 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 2008, a separation between solvers and operators can be achieved.

## Bidirectional deconvolution

Data examples of logarithm Fourier-domain bidirectional deconvolution [pdf 2.7M] [source]

**Qiang Fu, Yi Shen, and Jon Claerbout**

Time-domain bidirectional deconvolution methods show great promise for overcoming the minimum-phase assumption in blind deconvolution of signals containing a mixed-phase wavelet, such as seismic data. However, time-domain bidirectional methods usually suffer from slow convergence (Slalom method) or the starting model (Symmetric method). Claerbout proposed a logarithm Fourier-domain method to perform bidirectional deconvolution. In this paper, we test the new logarithm Fourier-domain method on both synthetic data and field data. The results demonstrate that the new method is more stable than previous methods and that it produces better results.

Preconditioning a non-linear problem and its application to bidirectional deconvolution [pdf 1.5M] [source]

**Yi Shen, Qiang Fu, and Jon Claerbout**

Non-linear optimization problems suffer from local minima. When we use gradient-based iterative solvers on these problems, we often find the final solution to be highly dependent on the initial guess. Here we introduce preconditioning and show how it helps resolve these issues in our current problem-bidirectional deconvolution. Using three data examples, we show that results with preconditioning are more spiky than results without preconditioning. Additionally, field data results with preconditioning have fewer precursors, cleaner salt bodies, more symmetric wavelets, and faster convergence than those without preconditioning. In addition to the field data, we illustrate the theory and application of two methods of preconditioning: prediction-error filter (PEF) preconditioning and gapped anti-causal leaky integration followed by PEF (GALI-PEF) preconditioning. Unlike PEF preconditioning, GALI-PEF preconditioning helps constrain the spike to the central wavelet, or allows us to shift it to another position in the wavelet by manipulating the length of the gap.