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Monday October 26, Houston, Schlumberger, 10001 Richmond Avenue

2015 SINBAD Fall Consortium meeting

Tuesday October 27, Houston, Schlumberger, 10001 Richmond Avenue

2015 SINBAD Fall Consortium meeting

Randomized Seismic Survey Design & Recovery

During this session, we will present new work deriving computationally feasible sampling criteria for matrix-based recovery. These criteria are based on the spectral gap (difference between the first and second largest singular value) of the sampling mask and there are indications that this measure can be extended to quantitatively predict the performance of our source separation and recovery from continuous recording techniques. During this session, we will present examples of matrix-based source separation and compare them to transform-based (curvelet) techniques. We will also discuss the impact of source/receiver positioning on the recovery of time-lapse surveys with our joint-recovery model. Finally, we present preliminary results on the removal of coherent noise that lives in the range of the wave equation with an iterative sparsity-promoting scheme that derives directly from the wave equation.

Universal Matrix Completion: Applications to Seismic Data Acquisition

Oscar Lopez

Abstract: This talk discusses the potential applications of universal matrix completion for infill management and acquisition design. We consider recent developments in the theory of matrix completion that produce practical tools to quantify how successful a given sub sampling mask will be for seismic trace interpolation via nuclear norm minimization. This approach provides an on the fly infill management system as well as instruments to design acquisition schemes that favor interpolation via rank penalization techniques.

Source separation for simultaneous towed-streamer acquisition via compressed sensing

Haneet Wason

Abstract. We show a comparison between two compressed-sensing based source-separation algorithms, i.e., sparsity promotion and rank minimization, for simultaneous data.

Randomization of time-lapse marine surveys

Haneet Wason

Abstract. We present an extension of our time-jittered (simultaneous) marine acquisition for time-lapse surveys, where we work on more realistic field acquisition scenarios by incorporating irregular spatial grids without insisting on repeatability between the surveys. Since we are always subsampled in both the baseline and monitor surveys, we recover the densely sampled baseline and monitor and then the (complete) 4-D difference from subsampled baseline and monitor data.

Source collocation using the method of Linearized Bregman

Shashin Sharan presented by Rongrong Wang

Abstract: In this work, we present a method to collocate sources from seismic reflections recorded at receiver locations. We use the method of linearized Bregman. This algorithm focuses unknown sources by promoting sparsity in the “Helmholtz domain”—i.e., the wavefield under the action of the the Helmholtz system—under the constraint of a data misfit within a particular tolerance. We extend this method to noisy measurements. We are in particular interested in situations where the noise is coherent because it is in the range of the Helmholtz equation.

Wave-equation based Inversion — leveraging (multiple) reflections

Specular (multiple) reflections contain key information in seismic records. In this session, we review a wide range of topics involving reflections ranging from imaging with multiples to time-lapse migration with multiples, (reflection) data-constrained FWI, and anisotropic RTM on field data.

Fast imaging with surface-related multiples and source estimation based on linearized Bregman

Mengmeng Yang

Abstract: In this talk, we will show surface-related multiples imaging with source estimation. Here the algorithms are based on linearized bregman, and we give the source estimation formulation in this case. With the featured blocked structure of linearized bregman, we can do efficient imaging in straightforward way by randomly choosing sources and frequencies. Another benefit is the simplicity to delivery the algorithm.

Time-lapse imaging with multiples and distributed Compressive Sensing

Felix Oghenekohwo

Abstract. In this talk, we leverage our joint-recovery model, which uses the fact that time-lapse images generally have a lot in common, to improve imaging problems with large gaps. We demonstrate that the adverse effects of large acquisition gaps can be mitigated by using this joint-recovery model especially in combination with imaging with surface-related multiples.

Affordable omnidirectional image volumes: extension to 3D

Rajiv Kumar presented by Felix J. Herrmann

Abstract. Image gathers are an important tool for velocity analysis, AVA analysis and targeted imaging, however, the computational cost involving in forming the image volumes makes them prohibitively expensive in case of large scale 3D seismic data acquisition. In this work, we propose the extension of our probing techniques from 2D to 3D to form the extended image volumes efficiently. We show the efficacy of proposed formulation on synthetic data set.

Anisotropic RTM applied to field data

Philipp Witte

Abstract. In this talk we present our latest reverse time-migration results of the BP Machar data set, a 2D seismic line from the North sea featuring a large chalk dome. In contrast to our prior imaging attempts, we now account for anisotropic effects in the data using our new TTI pure quasi-P wave modeling code in the time domain.

Wave-equation based Inversion — recent developments in FWI

In this session, we review new and preliminary results on new directions in FWI including 3-D Wavefield-Reconstruction Inversion (WRI), implicit extension of the search space of FWI via time shifts, FWI from spectrally extrapolated (to the low frequencies) data, and FWI in TTI media.

3-D WRI — preliminary results

Bas Peters

Abstract. The Wavefield Reconstruction Inversion (WRI) approach to seismic inversion is a topic of active research in the SLIM group. Several variants have been proposed, all of which rely on the solution of a linear least-squares problem with a Helmholtz discretization. While algorithms based on LU or QR factorization are very efficient for 2D problems, 3D problems required the development of a factorization-free iterative method. This talk introduces the current version of the algorithm, which requires significantly less memory and computation and uses existing Helmholtz solvers as an important building block. We plan to discuss early results of 3-D WRI on a small 3-D synthetic example.

Extending the search space of time-domain adjoint-state FWI w/ randomized implicit time shifts

Mathias Louboutin

Abstract. We introduce a modified adjoint-state method for time domain FWI that allows us to extend the research space. As a result, we arrive at a formulation where the sensitivity to cycle skipping is reduced. Our method obtains results with the same computational costs as FWI (The PDE solved is the same) but with significantly reduced memory costs. We use new results in non-convex optimization to justify the method as well as new regularization techniques and stochastic optimization to improve the behavior of the algorithm.

Improving Full Waveform Inversion with Spectral Extrapolation

Rongrong Wang

Abstract: We develop a sparsity based frequency extrapolation method to obtain low frequency data from the high frequency ones. As other frequency extrapolation methods, the extrapolation introduces noise due to dispersion and possibly densely distributed reflectors. To mitigate such noise, we incorporate Curvlet coefficient regularization in the extrapolation algorithm. Numerical results demonstrate the effectiveness of the extrapolation in frequency domain FWI in models of moderate complexity.

Time-domain FWI in TTI media

Philipp Witte

Abstract We develop an inversion workflow for tilted transverse isotropic (TTI) media using a purely acoustic formulation of the wave equation. The anisotropic modeling kernel is used for the forward modeling operator, as well as for the adjoint Jacobian to back propagate the data residual, thus providing the true gradient of the FWI objective function. We apply this workflow on a synthetic FWI example and perform RTM on a field data set. Furthermore, we discuss alternatives for the pseudo-spectral Laplacian operator of the current implementation.

Wave-equation based Inversion — novel formulations & convex constraints

Aside from extending the search space, imposing convex constraints helps to mitigate the adverse effects of the ill-posedness of FWI & WRI. After presenting our latest results on the Chevron blind data set, we present two expository presentations on how to include computational feasible constraints into nonlinear wave-equation based inversions. We follow these talks by presenting a novel full-space method for WRI, where the data-augmented equation is no longer eliminated, and a time-lapse method based on our joint-recovery model. The former approach removes the requirement of solving WRI’s data-augmented equation accurately while exploring common information in time-lapse FWI leads to significant improvements for the latter. We conclude this session by presenting a new mixed \(\ell_1/\ell_2-\)norm minimization approach to blind deconvolution with feedback. We show that this optimization in combination with surface-related multiples removes the scaling ambiguity in blind deconvolution.

Wavefield reconstruction inversion with source estimation and its application to 2014 Chevron synthetic blind test dataset

Zhilong Fang

Abstract. We present a robust wavefield reconstruction inversion with source estimation. The source wavelet is estimated with the reconstruction of wavefield simultaneously by solving an extended data-augmented problem. We apply this method to the 2014 Chevron synthetic blind test dataset and show the robustness of our method.

Regularizing waveform inversion by projections onto intersections of convex sets

Bas Peters

Abstract. Common strategies to regularize waveform inversion (and other geophysical inverse problems) are adding quadratic penalty terms to the objective function or filtering the gradients used to update the model estimate. An example are penalties or filters to prevent/filter spurious high spatial frequency oscillations in the model while working with low frequency data.

We present an alternative way of regularization, which works by projecting the model onto an intersection of convex sets, where each sets encodes certain desired model properties. This approach has certain theoretical and practical advantages over quadratic penalties or gradient filters. Some examples of useful convex sets in various challenging waveform inversion settings are shown on both real and synthetic data.

Automatic salt delineation — Wavefield Reconstruction Inversion with convex constraints

Ernie Esser (posthumously presented by Felix J. Herrmann)

Abstract. We extend full-waveform inversion by Wavefield Reconstruction Inversion by including convex constraints on the model. Contrary to the conventional adjoint-state formulations, Wavefield Reconstruction Inversion has the advantage that the Gauss-Newton Hessian is well approximated by a diagonal scaling, which allows us to add convex constraints, such as the box- and the edge-preserving total-variation constraint, on the square slowness without incurring significant increases in computational costs. As the examples demonstrate, including these constraints yields far superior results in complex geological areas that contain high-velocity high-contrast bodies (e.g. salt or basalt). Without these convex constraints, adjoint-state and Wavefield Reconstruction Inversion get trapped in local minima for poor starting models.

This is joint work with Sub Salt Solutions ltd.

A quadratic-penalty full-space method for waveform inversion

Bas Peters

Abstract. In PDE-constrained optimization problems other than geophysical full-waveform inversion, full-space optimization methods are commonly used. This type of optimization method updates both the medium parameters and the wavefields, instead of solving wave equations explicitly. In the FWI context, this means the objective function value and gradient can be obtained at very little computational cost. A major obstacle is, however, the requirement to have all wavefields in memory.

We present a novel full-space method which has the main advantages of existing full-space methods, but has a significantly lower memory requirement. This is achieved by combining quadratic-penalty methods which ideas from randomized numerical linear algebra.

Comparative study of time-lapse FWI approaches

Felix Oghenekohwo

Abstract. This talk will be divided into two parts:

Comparative study of time-lapse FWI approaches

Felix Oghenekohwo

Abstract. I will illustrate the performance of our joint recovery model for time-lapse FWI. Specifically, I will compare our method to other conventional methods, namely, parallel difference and sequential difference FWI. I will illustrate the robustness of our method compared to others especially in the presence of missing data caused by large acquisition gaps. In addition, I will assess the performance of these methods in the detectability of the time-lapse change in synthetic data. Analysis of these methods under different starting FWI model will also be highlighted.

Resolving Scaling Ambiguities with the L1/L2 Norm in a Blind Deconvolution Problem with Feedback

Ernie Esser (posthumously presented by Rongrong Wang)

Abstract. Compared to more mundane blind deconvolution problems, blind deconvolution in seismic applications involves a feedback mechanism related to the free surface. The presence of this feedback mechanism gives us an unique opportunity to remove ambiguities that have plagued blind deconvolution for a long time. While beneficial, this feedback by itself is insufficient to remove the ambiguities even with L1 constraints. However, when paired with an L1/L2 constraint the feedback allows us to resolve the scaling ambiguity under relatively mild assumptions. Inspired by lifting approaches, we propose to split the sparse signal into positive and negative components and apply an \ell_1/\ell_2 constraint to the difference, thereby obtaining a constraint that is easy to implement. Numerical experiments demonstrate robustness to the initialization as well as to noise in the data.

Wave-equation based Inversion — UQ & computational aspects

As we move towards 3-D field data, computational aspects and uncertainty become increasingly important. During this session, we present two expository talks on Uncertainty Quantification, where we exploit the unique structure of WRI’s Gauss-Newton Hessian, and our parallel software framework for 3-D wave-equation based inversion. We conclude by a providing a rational for the choices we have made in the design of this parallel software framework including early results on how our algorithms scale to 3-D.

An approximate Hessian for Wavefield Reconstruction Inversion and its application to Uncertainty Quantification

Zhilong Fang

Abstract We analyze the Hessian of wavefield reconstruction inversion (WRI) and propose a new approximated Hessian. Instead of requiring PDE solves, the matrix-vector multiplication action of the approximate Hessian can be achieved with several matrix-vector multiplications. The diagonal part of the approximated Hessian can be also calculated without additional PDE solves. We apply this approximated Hessian to uncertainty quantification and obtain statistical parameters such as standard deviation and confidence interval. Numerical example illustrate the accuracy of the estimated Hessian and the feasibility of the method to quantify uncertainties.

A modern software-development framework for 3D FWI

Curt Da Silva

Abstract. In this work, I have implemented a scalable and extendable framework for 3D Full Waveform Inversion in Matlab. This approach uses modern software design principles to create a codebase that is easy to understand, maintain, and extend and that also allows for rapid prototyping of new algorithmic ideas that can be easily transferred to large scale problems. The code itself is modularized in a proper way, which allows straightforward testing of each component (e.g., Taylor error test, adjoint tests, etc.). Improvements to the computational kernel (i.e., Helmholtz solves with more efficient matrix-vector products, new preconditioners, etc.) propagate to the entire framework.

Our student-driven HPC environment

Tim Tai-Yi Lin presented by Felix J. Herrmann

Abstract. A major role of academic environments is to provide learning experiences for students to critically analyze and develop methods, both at a high-level of mathematical rigour, and at a low-enough level of implementation in order to yield experimental results on real datasets. Often these two goals are in conflict with each other, in terms of both learning time and attention. At SLIM, we strive to strike a balance between the two by abstracting away many of the low-level aspects of distributed HPC under a framework that matches syntactically with the mathematics of our field, while exposing enough control parameters for tuning performance characteristics. This talk will touch on the history of our efforts at SLIM, and culminate in an overview of our current method of interacting with the in-house compute cluster.

Scaling SINBAD software to 3-D on Yemoja

Curt Da Silva and Haneet Wason

Abstract. We present early results on the scalability of SINBAD’s wavefield reconstruction and wave-equation based inversion technologies on Yemoja, a 17k core cluster made available to us by BG Group at SENAI CIMATEC Supercomputing Centre in Brazil.

Discussion

This time slot is designated to informal discussion, feedback & possible demos. It is important for us to get input on the application and possible use of our work and we therefore greatly value your input. We hope that this for will continue to be conducive to lively discussions.