Program 2014 SINBAD Fall Consortium meeting

Sunday December 7th (Spirit Room)

07:00—08:00 PM Icebreaker

Monday December 8th (Empress Ballroom)

Tuesday December 9th (Empress Ballroom)

Wednesday December 10th (Empress Ballroom)

Abstracts

Latest developments in randomized (4D) acquisition

Felix J. Herrmann—slides

Abstract We will present the latest developments in randomized (4D) seismic data acquisition.

Source separation via SVD-free rank-minimization in the hierarchical semi-separable representation

Haneet Wason—slides

Abstract. During this talk, we will show a source separation algorithm for blended marine acquisition, where two sources are deployed at different depths (over/under acquisition). The separation method incorporates the Hierarchical Semi-Separable (HSS) structure inside rank-regularized least-squares formulations. We also compare this deblending scheme with the sparsity-promoting one-norm minimization scheme.

Randomized subsampling in time-lapse surveys and recovery techniques

Felix Oghenekohwo—slides

Abstract. This talk centres on new insights on how we think of acquisition of time-lapse data using ideas from compressed sensing. Specifically, we will show how simultaneous processing of time-lapse data from randomized subsampling gives more reliable estimates of the vintages and time-lapse signal, compared to parallel processing.

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.

Randomization and repeatability in time-lapse marine acquisition

Haneet Wason—slides

Abstract. During this talk, we will show how randomization techniques from (distributed) compressed sensing affect the way we think about time-lapse surveys.

Off-the-grid matrix completion

Oscar Lopez—slides

Abstract. This talk discusses a modified rank minimization workflow designed to handle unstructured matrix completion problems. We extend current rank minimization based trace interpolation techniques to optimally handle undersampled irregular data, in such a way that allows us to recover regularized densely sampled data. This is achieved by introducing a regularization operator, that accurately allows us to simulate the effect of an unstructured grid. We provide reconstruction error bounds to demonstrate the potential of our procedure.

Time-jittered marine acquisition: low-rank v/s sparsity

Rajiv Kumar—slides

Abstract. _ In this work we will show how simultaneous or blended acquisition can be setup as a – rank-minimization (deblending) problem. The simultaneous acquisition scenario is a pragmatic time-jittered marine acquisition scheme, where a source vessel (with two airgun arrays) sails across an ocean-bottom array firing at jittered source locations and instances in time, resulting in better spatial sampling and acquisition speedup. We make comparisons with sparsity-promoting based techniques and demonstrate that rank-minimization based debelending techniques are computationally faster and memory efficient. This is joint work with Haneet Wason._

Large-scale seismic data interpolation in a parallel computing environment

Curt Da Silva—slides

Abstract. This talk will outline the details for a parallel implementation of the SPG-LR algorithm for matrix completion and its applications to large-scale seismic data interpolation. Previous work done in our group on LR-based matrix factorization has been shown to be extremely efficient for seismic data interpolation that fits in memory. We extend the SPGL1 framework that this method is built on to instances where the full seismic data volume cannot entirely fit in the memory of one computational node and must be run in a distributed environment. We will also look at off-the-grid regularization for tensor completion using a non-uniform FFT operator and examine its effects on interpolating an irregularly sampled, 3D seismic frequency slice.

Rank Minimization via Alternating Optimization

Oscar Lopez—slides

Abstract. This talk discusses the benefits of an alternating optimization approach for seismic trace interpolation via rank minimization. We consider recent factorization approaches to rank minimization problems where we write our low rank matrix in bi-linear form, and modify this workflow by alternating our optimization to handle a single matrix factor at a time. This allows for a more tractable procedure that can better handle highly sub sampled data sets without increasing the time complexity. We demonstrate the potential of this approach with several seismic trace interpolation experiments.

Sparse inversion simplified

Ning Tu Navid Ghadermarzy—slides

Abstract. Implementation of the SPGl1 solver in low-level computer languages such as C or Fortran may sound daunting to many. This talk is tailored for you if you would like to reap benefits from using sparse constraints to regularize your inversion problem, and at the same time want some easy-to-implement algorithm to solve it. We discuss in this talk the linearized Bregman projection method that embraces both ingredients, and show promising applications in fast least-squares imaging and seismic data interpolation problems.

Analog-to-digital conversion in compressive sampling

Ozgur Yilmaz—slides

Abstract Compressive sampling theory is now established as an effective method for dimension reduction when the underlying signals (e.g., seismic data) are sparse with respect to some suitable basis or frame (e.g., curvelets in the case of seismic). One important problem directly related to the acquisition of analog signals is how to perform analog-to-digital conversion. This is directly related to two important issues: (i) how accurately one can acquire a signal using compressive sampling (in terms of bit depth), and (ii) how “compressed” is compressive sampling (in terms of the total number of bits one ends up using after acquiring the signal). We will present recent results that provide answers to these questions. Specifically, we provide an analog-to-digital conversion method that achieves nearly optimal compression using cheap analog devices with a large margin for imperfections.

Wavefield reconstruction from randomized sampling: How far can we go?

Navid Ghadermarzy—slides

Abstract. Regular sampling along the time axis is a common approach for seismic imaging. However, seismic data are often spatially undersampled due to economical reasons as well as ground surface limitations. Operational conditions might result in noisy traces or even gaps in coverage and irregular sampling which often leads to image artifacts. Seismic trace interpolation aims to interpolate missing traces in an otherwise regularly sampled seismic data to a complete regular grid. In this talk, we explain some techniques, with low computational complexity, that can be used to improve the results. In particular, we talk about weighting, switching to midpoint-offset domain from frequency-space domain, and uniform versus jittered undersampling. We illustrate the advantages of these modifications using a real seismic line from the Gulf of Suez.

Wavefield Reconstruction Inversion (WRI) — a new take on wave-equation based inversion

Felix J. Herrmann—slides

Abstract We discuss a recently proposed novel method for waveform inversion: Wavefield Reconstruction Inversion (WRI). As opposed to conventional FWI – which attempts to minimize the error between observed and predicted data obtained by solving a wave equation – WRI reconstructs a wave-field from the data and extracts a model-update from this wavefield by minimizing the wave-equation residual. The method does not require explicit computation of an adjoint wavefield as all the necessary information is contained in the reconstructed wavefield. We show how the corresponding model updates can be interpreted physically analogously to the conventional imaging-condition-based approach.

Single- and multi-parameter WRI — synthetic examples

Bas Peters—slides

Abstract. We demonstrate the performance of WRI on a number of single- and multi-parameter synthetic examples. The examples shot that WRI is less reliant on accurate starting models while this formulation is also conducive to multi-parameter inversion.

Total Variation Constrained Full Waveform Inversion with Continuation

Ernie Esser—slides

Abstract Adding a total variation constraint to the Wavefield Reconstruction Inversion model proposed by van Leeuwen and Herrmann can improve robustness and remove artifacts by encouraging piecewise smooth solutions. However, if the parameter controlling the strength of the TV regularization is not well chosen, important details can be lost. We investigate continuation strategies that gradually reduce the strength of the TV constraint so that these important details are eventually allowed back into the solution. Preliminary numerical experiments suggest that this can improve the solution path and lead to better velocity models than if TV regularization were not used during the intermediate steps.

Quadratic-penalty based full-space methods for waveform inversion

Bas Peters—slides

Abstract. Waveform inversion problems are commonly solved by eliminating the field variables. Full-space methods store and update the fields, rather than solving for them. This leads to a problem with nice properties, such as free function value evaluation and exact gradients and Hessians at no cost. The existing literature is almost exclusively based on the Lagrangian formulation. We propose to work with a quadratic penalty formulation, which allows us to reduce the storage requirements and gives the Newton system a favourable structure which we exploit to obtain a intrinsically parallel updating scheme for the fields and medium parameters. We will show a comparison with reduced-space methods.

Why the modified Gauss-Newton method?

Xiang Li—slides

Abstract. In our earlier work, we develop the modified Gauss-Newton method for FWI, which requires each update of FWI to be sparse in the curvelet domain. Our empirical observation of the MGN method is that it can find us a solution for FWI problem with sparse perturbation of the initial guess without changing the underlying objective. In this talk, we will analyze the MGN method to find out the reason why it can generate a sparse perturbation of the initial model, because sum of spares updates could easily generate non-sparse perturbations. Moreover, we will illustrate when do we expect the modified Gauss-Newton method to yield a solution with sparse perturbation and in what circumstances should we use it in place of other algorithms like standard Gauss-Newton.

Denoising the wavefield inversion problem through source blending and penalty method

Rongrong Wang—slides

Abstract. Previous FWI denoising techniques, such as source blending and stacking, are designed applied to the seismic traces. Hence no physical information is used to improve the fidelity of the reconstruction, even when a good initial model is available. Moreover, traditional source blending requires the existence of common source gathers, which might be missing from the data. In this talk, we incorporate the source blending idea into the penalty method, and extract the synthetic sources corresponding to the principle directions of the gradient update. By blending the sources, we can not only achieve an acceleration and storage efficiency of the penalty method, but also make the reconstruction more robust to the random noise. This method is applicable to any source receiver position but is more efficient if common source gathers are available.

Use what’s in common: time-lapse FWI with distributed Compressive Sensing

Felix Oghenekohwo—slides

Abstract. In this talk, we will extend our joint recovery formulation to FWI in time-lapse seismic, using the modified Gauss-Newton approach. Leveraging ideas from distributed compressive sensing, we exploit shared information in the sparse model perturbations of the baseline and monitor data.

Dealing with acquisition gaps in Robust EPSI without interpolation using wavefield auto-convolution

Tim T. Y. Lin—slides

Abstract. Straightforward modifications to the Estimation of Primaries by Sparse Inversion (EPSI) problem allows us to mitigate acquisition holes without any reconstruction of the missing traces, neither prior to nor during the inversion process. This is achieved by simulating the missing multiple contributions with terms involving auto-convolutions of the primary wavefield. In this formulation we no longer need to treat the missing data as another unknown in the inversion process, which is important in eliminating a significant source of possible local minima from attempting to invent data using incorrect primary and multiple models. In this talk we investigate the necessary modifications to the Robust EPSI problem, as well as algorithms that account for the resulting non-linear modelling operator. We will also investigate the reconstruction limits of this approach in relation to acquisition geometry and subsurface characteristics.

A lifted \(\ell_1/\ell_2\) constraint for sparse blind deconvolution

Ernie Esser—slides

Abstract. We propose a modification to a sparsity constraint based on the ratio of l1 and l2 norms for solving blind seismic deconvolution problems in which the data consist of linear convolutions of different sparse reflectivities with the same source wavelet. No assumptions are made about the location of the support of either the wavelet or the sparse signals. Minimizing the ratio of l1 and l2 norms has been previously shown to promote sparsity in a variety of applications including blind deconvolution. Most existing implementations are heuristic or require smoothing the l1/l2 penalty. Lifted versions of l1/l2 constraints have also been proposed but are still challenging to implement. Inspired by the lifting approach, we propose to split the sparse signals into positive and negative components and apply an l1/l2 constraint to the difference, thereby obtaining a constraint that is easy to implement without smoothing the l1 or l2 norms. We show that a method of multipliers implementation of the resulting model can recover source wavelets that are not necessarily minimum phase and approximately reconstruct the sparse reflectivities. It appears to be robust to the initialization and to small amounts of noise in the data. We also discuss extensions to the Estimation of Primaries by Sparse Inversion (EPSI) convolution model.

Fast imaging with surface-related multiples by sparse inversion

Ning Tu—slides

Abstract. When used correctly, surface-related multiples can provide extra illumination coverage compared with primaries. In this talk, I will discuss how to jointly image primaries and surface-related multiples in a computationally efficient fashion. We bring down the computational cost by two means. First we use wave-equation solvers to implicitly carry out the expensive dense matrix-matrix multiplications in the prediction of surface-related multiples. Second we bring down the simulation cost by subsampling the frequencies and monochromatic source experiments together with curvelet-domain sparsity-promoting and rerandomization. As a result, we obtain true-amplitude least-squares migrated seismic images with computational costs that are comparable to a single RTM with all the data. We demonstrate the efficacy of the proposed method using realistic synthetic examples.

Extended imaging with surface-related multiples

Rajiv Kumar—slides

Abstract. Common image gathers are used in building velocity models, invert anisotropy parameters and to analyze reservoir attributes. Often primary reflections are used to form the image gathers and multiples are typically attenuated in processing. However, researchers have shown that, if correctly used, they can provide useful information about the subsurface during reverse-time migration. In this work, i will show how we can use multiples along with primaries to form the image-gathers.

Imaging with source estimation

Ning Tu—slides

Abstract. In seismic imaging, an inaccurate estimate of the source wavelet may result in degraded seismic images. While conventional reverse-time migration requires the knowledge of the source wavelet as prior information, we propose to include source estimation in the fast compressive imaging procedure. Using the proposed method, we can obtain seismic images that are comparable to those imaged with the true source wavelet, with computational costs that are comparable to conventional RTM images with all the data. We also extend the proposed method to image data with surface-related multiples, where these multiples help to mitigate the amplitude ambiguity in source estimation. We verify the proposed method using realistic synthetic examples.

Minimal-residual iterative methods for time-harmonic wave-equation

Rafael Lago—slides

Abstract In this work we aim at comparing the performance of some iterative methods for solving the time-harmonic acoustic wave-equation, one of the most challenging problems in the numerical linear algebra community. Widely used in frequency domain full waveform inversion, the discrete wave-equation yields very large, complex, sparse, ill-conditioned linear systems. In this extended abstract we aim at further comparing our recently proposed method, CRMN, against CGMN and another method renown for being very memory efficient, the two-level preconditioner with shifted Laplacian operator. We propose several improvements for the two-level preconditioner by combining this method with CRMN in several senses.

Iterative solution strategy for least-squares problem with a PDE-block

Bas Peters—slides

Abstract. Waveform inversion using the Wavefield Reconstruction Inversion (WRI) is a quadratic-penalty based method developed in our group and has shown to have advantages over the reduced Lagrangian based conventional FWI methods. WRI involves no explicit PDE solves, but a least-squares problem with a PDE block. This type of least-squares problem is very challenging to solve using iterative methods. In this talk we show algorithms we developed specifically for this application and which involve a combination of preconditioning, low-rank decomposition and deflation.

2D/3D time-stepping for imaging and inversion

Xiang Li—slides

Abstract. In this talk, we present a SLIM version of 2D/3D time-stepping modeling kernel for inversion and imaging. One key aspect of this framework is that the implementation follows some mathematic principles, such as linear operator test. Aside from obeying mathematic principles, we also developed a strategy that allows us to compute the gradient of conventional FWI objective or RTM imaging without storing extra wavefield. We also show some applications of this framework on the Chevron 2014 benchmark elastic synthetic data set.

Ultra-fast time stepping for acoustic modelling and inversion

Mathias Louboutin—slides not available for this presentation

Abstract.Two ways to improve the efficiency and the memory cost of the acoustic time stepping method is presented here. First we take advantage of new developments in hardware technology, namely reconfigurable hardware accelerators (FPGA’s) and the new finite differences library developed for propagation on this hardware (MaxGenFD). These accelerators can compute certain types of operations, such as the convolution within a Laplacian, very fast and therefore lead to a considerable speed-up in the global time domain FWI workflow. Such a speed-up will allow an increase of the number of iterations in the inversion process leading to more accurate model and permit work on realistic 3D dataset with a reduced computational cost. We will show here the speed-up obtained and the precision we can expect from this solver. In the second part a new approximate gradient for acoustic inversion will be presented. By exploiting new devellopments in randomization and compressed sensing we can efficiently reduce the memory cost and the computational cost of time domain inversion and imaging via the adjoint state method. Early results and a brief description of the method will be presented here.

Uncertainty quantification for Wavefield Reconstruction Inversion

Zhilong Fang—slides

Abstract. This talk discusses the uncertainty quantification for the wavefield reconstruction inversion. The Hessian and gradient of the WRI can be easily obtained once the wave field is generated. As a result, we use a Newton type McMC method to sample the posterior distribution. Statistical property such as mean, standard deviation, confidence interval are calculated based on the sampled distribution.

Low-rank extensions of Wavefield Reconstruction Inversion

Rajiv Kumar—slides not available for this presentation

Abstract. We propose a computationally tractable velocity model extension to the quadratic penalty formulation for full waveform inversion, where our model is extended from an unknown vector to an unknown low-rank matrix. We show that the additional degrees of freedom by making unknown earth model low-rank has several potential advantages ,i.e the full-waveform inversion problem becomes i) more robust to the initial guess, ii) robust to outlier in the data iii) avoid bad local minima. Preliminary results on realistic-synthetic BG model show the robustness of low-rank extension of wavefield reconstruction inversion to the initial guess of velocity model.

Challenges and developments arising from 2D FWI of a land VSP dataset in the Permian Basin

Brendan Smithyman, Bas Peters—slides

Abstract. Full-waveform inversion was carried out to map 3D velocity structures for a site in the Permian Basin of Texas, USA. The data come from co-located surface and 3D VSP seismic surveys that share common source vibration points. This challenging on-land setting has been used as a testbed to evaluate our FWI algorithms and their effectiveness when applied to real-data problems. We discuss the challenges posed by this case study, and several new techniques and methodological refinements that have been developed and tested as a result. These include: regularization and incorporation of multiple datasets in an on-land FWI workflow; restrictions on the types of models allowed (viz., smoothness regularization) by quadratic penalty and by Projected Quasi-Newton (PQN) inversion; corrections to enable 2D FWI and recovery of 3D models; the state of ongoing work in WRI (“Penalty Method” inversion) and the handling of anisotropy.

Imaging with multiples of the Nelson dataset

Ning Tu—slides

Abstract We will present out latest finding on migration with multiples on the Nelson dataset.