Program 2014 SINBAD Spring Consortium meeting

Friday June 20, Rosarium, Amstelpark, Amsterdam, the Netherlands

Abstracts:

SVD-free matrix completion for seismic data reconstruction

Rajiv Kumar (third year PhD)

Abstract. Seismic data interpolation via rank-minimization techniques has been recently introduced in the seismic community. All the existing rank-minimization techniques assumes the underlying grid to be regular. Irregularity is one of the common impediments in acquisition. In this work, we studied the effect of irregularity on structured and show that how we can modify the existing techniques to handle it. Other then irregularity, we often have missing data. We also show that we can tackle both regularization and interpolation issue simultaneously. The objective of this work is to extend our existing method of interpolation on structured grid to unstructured grid. We illustrate the advantages of the modification in existing methodology using a seismic line from Gulf of Suez to obtain high quality results for regularization and interpolation, a key application in exploration geophysics.

Low-rank promoting transformations and tensor interpolation - applications to seismic data denoising

Curt Da Silva (second year PhD)

Abstract. In this presentation, we extend our previous work in Hierarchical Tucker (HT) tensor completion, which uses an extremely efficient representation for representing high-dimensional tensors exhibiting low-rank structure, to handle subsampled tensors with noisy entries. We consider a ’low-noise’ case, so that the energies of the noise and the signal are nearly indistinguishable, and a ’high-noise’ case, in which the noise energy is now scaled to the amplitude of the entire data volume. For the low-noise case in particular, standard trace-by-trace energy comparisons cannot distinguish noise from signal.

We examine the behaviour of noise in terms of the singular values along different matricizations of the data, i.e. reshaping of the tensor along different dimensions. By interpreting this effect in the context of tensor completion, we demonstrate the inefficacy of denoising by this method in the source-receiver domain. In light of this observation, we transform the decimated, noisy data in to the midpoint-offset domain, which promotes low-rank behaviour in the signal and high-rank behaviour in the noise. This distinction between signal and noise allows low-rank interpolation to effectively denoise the signal, without knowledge of the noise location, with only a marginal increase in computational cost. We demonstrate the effectiveness of this approach on a 4D frequency slice.

Implicit interpolation of trace gaps in REPSI using auto-convolution terms

Tim T. Y. Lin (fourth year PhD)

Abstract. It is possible to solve the Estimation of Primaries by Sparse Inversion problem from a sesimic record with large holes without any explicit data reconstruction, by instead simulating the missing multiple contributions with terms involving auto-convolutions of the primary wavefield. Exclusion of the unknown data as an inversion variable from the REPSI process is desireable, since it eliminates a significant source of local minima that arises from attempting to invert for the unobserved traces using primary and multiple models that may be far-away from the true solution. In this talk we investigate the necessary modifications to the REPSI algorithm to account for the resulting non-linear modeling operator, and demonstrate that just a few auto-convolution terms are enough to satisfactorily mitigate the effects of data gaps during the inversion process.

Multilevel acceleration strategy for REPSI

Tim T. Y. Lin (fourth year PhD)

Abstract. This talk discusses a multilevel inversion strategy that aims to substantially reduce the computational costs of the Robust Estimation of Primaries by Sparse Inversion algorithm. The proposed method solves early iterations of REPSI at very coarse spatial sampling grids while gradually ramping-up the spatial sampling when more accuracy is desired. No changes to the the core implementation of the original algorithm are necessary while in addition only requiring trace decimation, low-pass filtering, and rudimentary interpolation techniques.

Latest developments in randomized marine (4D) acquisition

Felix J. Herrmann

Abstract. During this talk, we will show the advantages of randomly dithered marine acquisition with ocean bottom nodes and how randomization techniques from compressive sensing affect the way we think about time-lapse surveys. This is joint work with Felix and Haneet.

Randomized sampling without repetition in time-lapse seismic surveys

Felix Oghenekohwo (second year PhD)

Abstract. In this talk, we will show a method for acquiring time-lapse data, where we do not have to repeat the survey geometry. Our method works provided our acquisition is randomized, where sources and receivers are at random locations on a computational grid, and provided we know the spatial locations of the shots and receivers. In addition, we show the implications of either (sub)sampling more for the baseline and less for the monitor or vice-versa, and how this sampling scheme affects the 4-D signal.

DNOISE III

Felix J. Herrmann

Abstract. During this presentation I will discuss our plans for the NSERC Collaborative Research and Development Grant DNOISE III. With this grant, we aim to match the industry contributions of SINBAD dollar-for-dollar.

A stochastic quasi-Newton McMC method for uncertainty quantification of full-waveform inversion

Zhilong Fang (second year PhD)

Abstract. In this work, we present a fast McMC method using the stochastic l-BFGS Hessian to quantify the uncertainty of full-waveform inversion. Using the stochastic l-BFGS Hessian, we do not need the assumption that the Hessian of data misfit is low rank and we also reduce the computational cost of estimating the Hessian. Numerical result shows the capability of this fast McMC method.

Collaborators: Felix J. Herrmann and Chia Ying Lee

Relax the physics & expand the search space – FWI via Wavefield Reconstruction Inversion

Felix J. Herrmann

Abstract. During this talk, we will present a new formulation of full-waveform inversion that combines the best of full-space constrained methods and reduced-space unconstrained methods. Instead of eliminating the constraint, which leads to the reduced adjoint-state method that underpins most formulations of full-waveform inversion, our method relaxes the PDE constraint by replacing it by an additive (least-squares) penalty term. By using the method of variable projection, we arrive at a formulation that alternates between solving for the wavefield, given the velocity model & data, and solving for velocity-model updates, given the wavefields. We named this method Wavefield Reconstruction Inversion (WRI) because it inverts for the model updates by reconstructing the wavefield everywhere given data observed at the receivers and the physics of the wave equation. During the talk, we present this new method and discuss how the increased search space, now consisting of the wavefields and model, mitigates the effects of local minima. We will also discuss recent extensions including multi-parameter inversion and regularization.

This is joint work with Tristan van Leeuwen, Bas Peters, and Ernie Esser.

Adaptive Waveform Inversion - FWI Without Cycle Skipping - Theory

Mike Warner (Imperial College London)

Conventional FWI minimises the direct differences between observed and predicted seismic datasets. Because seismic data are oscillatory, this approach will suffer from the detrimental effects of cycle skipping if the starting model is inaccurate. We reformulate FWI so that it instead adapts the predicted data to the observed data using Wiener filters, and then iterates to improve the model by forcing the Wiener filters towards zero-lag delta functions. This adaptive FWI scheme is demonstrated on synthetic data where it is shown to be immune to cycle skipping, and is able to invert successfully data for which conventional FWI fails entirely. The new method does not require low frequencies or a highly accurate starting model to be successful. Adaptive FWI has some features in common with wave-equation migration velocity analysis, but it works for all types of arrivals including multiples and refractions, and it does not have the high computational costs of WEMVA in 3D.

A scaled gradient projection method for total variation regularized full waveform inversion

Ernie Esser (first year PDF)

Abstract. _We propose a modification to the quadratic penalty formulation for seismic full waveform inversion proposed by van Leeuwen and Herrmann that includes convex constraints on the model. In particular, we show how to simultaneously constrain the total variation of the slowness squared while enforcing bound constraints to keep it within a physically realistic range. Synthetic experiments show that including total variation regularization can improve the recovery of a high velocity perturbation to a smooth background model.

Collaborators: Tristan van Leeuwen, Aleksandr Y. Aravkin and Felix J. Herrmann

Multi-parameter waveform inversion; exploiting the structure of penalty-methods

Bas Peters (second year PhD)

Abstract. In this talk I consider the problem of inverting waveforms for multiple medium parameters. The governing PDE is chosen to be the Helmholtz equation with compressibility and buoyancy as the unknowns. Both unknowns occur in the same equation and practice has shown it is very hard to estimate both equally accurate; the buoyancy estimate (or density if a slightly different parametrization is used) is typically much smoother than the compressibility (or velocity). Here I introduce a new waveform inversion algorithm: a full Newton-type method based on a penalty method which adds the PDE constraint as a quadratic penalty term. This method updates both the ‘wavefields’ and medium parameters, without explicitly solving PDE’s. One of the main advantages is the availability of a sparse Hessian and exact gradient which are not the result of any PDE solves. We asses if the availability of the Hessian, which includes information about the coupling between the two medium parameters, can help reconstruct both compressibility and buoyancy.

Accelerating an iterative Helmholtz Solver using reconfigurable hardware

Art Petrenko (MSc - now graduated)

Abstract. An implementation of seismic wave simulation on a platform consisting of a conventional host processor and a reconfigurable hardware accelerator is presented. This research is important in the field of exploration for oil and gas resources, where a 3D model of the subsurface is frequently required. By comparing seismic data collected in a real-world survey with synthetic data generated by simulated waves, it is possible to deduce such a model. However this requires many time-consuming simulations with different Earth models to find the one that best fits the measured data. Speeding up the wave simulations would allow more models to be tried, yielding a more accurate estimate of the subsurface.

The reconfigurable hardware accelerator employed in this work is a field programmable gate array (FPGA). FPGAs are computer chips that consist of electronic building blocks that the user can configure and reconfigure to represent their algorithm in hardware. Whereas a traditional processor can be viewed as a pipeline for processing instructions, an FPGA is a pipeline for processing data. The chief advantage of the FPGA is that all the instructions in the algorithm are already hardwired onto the chip. This means that execution time depends only on the amount of data to be processed, and not on the complexity of the algorithm.

The main contribution is an implementation of the well-known Kaczmarz row projection algorithm on the FPGA, using techniques of dataflow programming. This kernel is used as the preconditioning step of CGMN, a modified version of the conjugate gradients method that is used to solve the time-harmonic acoustic isotropic constant density wave equation. Using one FPGA accelerator, the current implementation allows seismic wave simulations to be performed over twice as fast, compared to running on one Intel Xeon E5-2670 core. I also discuss the effect of modifications of the algorithm necessitated by the hardware on the convergence properties of CGMN.

Finally, a specific plan for future work is set-out in order to fully exploit the accelerator platform, and my work is set in its larger context._

Heuristics in full-waveform inversion

Rafael Lago (First year PDF)

Abstract. For many full-waveform inversion techniques, the most computationally intensive step is the computation of a numerical solution for the wave equation on every iteration. In the frequency domain approach, this requires the solution of very large, complex, sparse, ill-conditioned linear systems. In this abstract we bring out attention specifically to CGMN method for solving PDEs, known for being flexible (i.e. it is able to treat equally acoustic data as well as visco-elastic or more complex scenarios) efficient with respect both to memory and computation time, and controllable accuracy of the final approximation. We propose an improvement for the known CGMN method by imposing a minimal residual condition, which incurs in one extra model vector storage. The resulting algorithm called CRMN enjoys several interesting properties as monotonically nonincreasing behaviour of the norm of the residual and minimal residual, guaranteeing optimal convergence for the relative residual criterion. We discuss numerical experiments both in an isolated PDE solve and also within the inversion procedure, showing that in a realistic scenario we can expect a speedup around 25% when using CRMN rather than CGMN.

Joint work with Art Petrenko, Zhilong Fang, Felix J. Herrmann.

Exploring applications of depth stepping in seismic inverse problems

Polina Zheglova (first year PDF)

Abstract. We are exploring applications of stable depth extrapolation with the full wave equation to imaging and inversion. Depth stepping with full wave equation can be advantageous to the time and frequency domain modelling if special care is taken to stabilize the depth exptrapolator efficiently, since it reduces the higher dimensional modelling problem to a number of lower dimensional subproblems. We are interested in exploring applications in inversion, modelling and imaging. For example, just as the reverse time migration can be shown to be the gradient of the reduced formulation of the full waveform inversion problem, it is interesting to explore whether a formulation of the inversion problem can be achieved whose gradient can be computed using depth stepping techniques. We are also interested in such applications as preconditioning of iterative methods for Helmholtz equation and imaging.