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**File Type**

Jennings, Joseph (Stanford University) | Biondi, Biondo (Stanford University) | Clapp, Robert (Stanford University) | Ronen, Shuki (Stanford University)

We present a new algorithm for directly imaging blended data via waveform inversion. The algorithm relies on performing a data-space deblending step at each iteration of the waveform inversion. Following a pattern-based approach, this data-space deblending step is done through independent modeling of the source wavefields on which filters can be estimated and used to deblend the blended data. As the velocity model is updated, the filters will be estimated on increasingly more accurate data and therefore will provide improved deblending results fromiteration to iteration. We show that with the introduction ofthese filters, the waveform inversion results contain significantly fewer artifacts than those obtained with conventional waveform inversion of blended data.

Presentation Date: Wednesday, October 17, 2018

Start Time: 9:20:00 AM

Location: Poster Station 21

Presentation Type: Poster

SPE Disciplines: Reservoir Description and Dynamics > Reservoir Characterization > Seismic processing and interpretation (1.00)

Biondi, Ettore (Stanford University) | Biondi, Biondo (Stanford University) | Barnier, Guillaume (Stanford University)

The high computational cost of elastic full-waveform inversion (FWI) limits its applicability to real exploration datasets; hence more simplistic and computationally cheaper methods are usually employed. However, these methods are affected by strong assumptions (e.g., planar reflectors or ray approximation), which reduce their use in complex geological scenarios. We propose a target-oriented approach that alleviates the computational burden associated with elastic FWI by limiting the inversion process to only a portion of the subsurface where an accurate and high resolution elastic model is needed (e.g., reservoir level). The proposed method is based on the reconstruction of the data generated within the target area at a depth level directly above it. This data reconstruction is performed by an extended least-square migration of the surface data followed by a demigration to the desired depth level. We demonstrate the efficacy of this approach on a layered model in which a complex reflector is considered to be our inversion target.

Presentation Date: Wednesday, October 17, 2018

Start Time: 1:50:00 PM

Location: 207C (Anaheim Convention Center)

Presentation Type: Oral

acquisition, acquisition geometry, algorithm, Artificial Intelligence, computational, data difference, elastic full-waveform inversion, elastic fwi, full-waveform inversion, geophysics, inversion, least-square migration, migration, migration process, operator, perturbation, Reservoir Characterization, subsurface, sunk-acquisition data, target area, Upstream Oil & Gas

SPE Disciplines: Reservoir Description and Dynamics > Reservoir Characterization > Seismic processing and interpretation (1.00)

Barnier, Guillaume (Stanford University) | Biondi, Ettore (Stanford University) | Biondi, Biondo (Stanford University)

The main issue inherent to full waveform inversion (FWI) is its inability to correctly recover the Earth’s subsurface seismic parameters from inaccurate starting models. This behavior is due to the presence of local minima in the FWI objective function. To overcome this problem, we propose a new objective function in which we modify the nonlinear modeling operator of the FWI problem by adding a correcting term that ensures phase matching between predicted and observed data. This additional term is computed by demigrating an extended model variable, and its contribution is gradually removed during the optimization process while ensuring convergence to the true solution. Since the proposed objective function is quadratic with respect to the extended model variable, we make use of the variable projection method. We refer to this technique as full waveform inversion by model extension (FWIME). We illustrate its potential on two synthetic examples for which FWI fails to retrieve the correct solution. First, by inverting data generated in a borehole setup. Then, by inverting diving waves recorded with a standard surface acquisition geometry.

Presentation Date: Wednesday, October 17, 2018

Start Time: 8:30:00 AM

Location: 207C (Anaheim Convention Center)

Presentation Type: Oral

Artificial Intelligence, conventional fwi, full waveform inversion, FWI, fwi objective function, fwime, gradient, inversion, iteration, model extension, objective, objective function, operator, optimization problem, perturbation, Reservoir Characterization, Upstream Oil & Gas, variable projection, Waveform Inversion

SPE Disciplines: Reservoir Description and Dynamics > Reservoir Characterization > Seismic processing and interpretation (1.00)

Technology: Information Technology > Artificial Intelligence > Representation & Reasoning > Optimization (0.95)

Biondi, Ettore (Stanford University) | Barnier, Guillaume (Stanford University) | Biondi, Biondo (Stanford University)

We present a simple method of preconditioning the gradient of elastic multi-component full-waveform inversion (FWI) using an approximated Gauss-Newton Hessian. By sampling this matrix we are able estimate the Hessian elements. We use this approximated matrix to compute a preconditioner to apply during the inversion. We show on a synthetic 2D sediment model that a main-diagonal approximation already improves the convergence rate of the FWI optimization and properly scales the gradients for different parameter classes. Therefore, it also decreases the differential sensitivities to the data of the simultaneously inverted parameters.

Presentation Date: Wednesday, September 27, 2017

Start Time: 10:10 AM

Location: Exhibit Hall C/D

Presentation Type: POSTER

approximated hessian, Artificial Intelligence, convergence, convergence rate, frequency, full-waveform inversion, FWI, gauss-newton hessian, gradient, Hessian, Hessian matrix, inversion, matrix, objective function, operator, optimization problem, parameter class, Reservoir Characterization, subsurface, Upstream Oil & Gas, wave velocity

Technology: Information Technology > Artificial Intelligence > Representation & Reasoning > Optimization (0.31)

Almomin, Ali (Saudi Aramco) | Biondi, Biondo (Stanford University)

We calculate a shot profile from the modeled data with a slow background velocity using an extended image. We then calculate a shot profile from the model with a slow background velocity using DSO operator regularization and shifting operator regularization, respectively, on the extended image. Figure 2 compares a trace at 2 km offset (bottom) with the DSO regularization residual (middle) and shifting operator regularization (top). Again, we can see there is no significant change in the phase when we compare the DSO regularization residual to the modeled data and only a small amplitude change. On the other hand, the shifting operator shows a clear phase rotation (and in the opposite direction to the previous example).

amplitude, background velocity, convergence, data-fitting term, DSO, full waveform inversion, inversion, modification, operator, operator regularization, reflector, regularization, regularization residual, regularization term, Reservoir Characterization, TFWI, tomographic full-waveform inversion, tomographic update, Upstream Oil & Gas, Waveform Inversion

Manea, A. M. (Stanford University) | Tchelepi, H. A. (Stanford University)

In this work, we have designed and implemented a massively parallel version of the Semicoarsening Multigrid Solver (

The design of the algorithm uses a combination of plane relaxation and semicoarsening to efficiently handle anisotropies in 3D, (

The two versions of the solver were tested using various highly heterogeneous multi-million-cell problems derived from SPE10 Second Dataset Benchmark. For problems with sizes large enough, the GPU implementation, running on KEPLER-Based K40c cards, is found to be always faster than the multi-core implementation running on 12 Intel® Xeon® E5-2620 v2 2.10 GHz cores. In addition, the inherent serial nature of multiplicative multigrid, along with the approach taken to minimize the communication through PCI-e, were found to limit the scalability beyond 3-4 cores/GPU's.

Technology:

- Information Technology > Hardware (1.00)
- Information Technology > Graphics (1.00)

Manea, A. M. (Stanford University) | Hajibeygi, H. (TU Delft) | Vassilevski, P. (Lawrence Livermore National Lab) | Tchelepi, H. A. (Stanford University)

A Parallel Enriched Algebraic Multiscale Solver (PEAMS) for simulation of flow in heterogeneous formations with high contrasts is introduced. Built on the recently developed enrichment strategy for single processing algorithms, i.e., EAMS of Manea et al. (2016), the PEAMS describes an efficient parallel implementation procedure as to how to enrich a given multiscale formulation with additional local basis functions. These additional basis functions, constructed in parallel computational platform, aim to resolve large error components for a generic fine-scale system with no right-hand-side term. The design and computational overhead of the enrichment kernels in shared-memory parallel environments are discussed in detail. The robustness and scalability of PEAMS are then illustrated for highly heterogeneous and anisotropic 3D multi-milion-cell reservoir models. The presented results show that, by adding only a few locally-supported complementary basis functions, the convergence of the original multiscale method is significantly enhanced. This is achieved with incurring a marginal overhead in the complexity to the coarse-scale operator. Moreover, in shared-memory parallel environments, it is shown that both of the enrichment procedure and the resulting enriched solver are scalable. Therefore, PEAMS casts a promising framework for robust iterative multiscale formulations for real-field applications, where parallel processing architectures are essential.

algebraic multiscale solver, basis function, computational, convergence, enriched algebraic multiscale solver, enrichment, enrichment stage, manea, Multiscale, operator, parallel enriched algebraic multiscale solver, PEAM, procedure, prolongation, reservoir simulation, scalability, scaling method, solver, Upstream Oil & Gas

Manea, Abdulrahman M. (Stanford University) | Sewall, Jason (Intel Corporation) | Tchelepi, Hamdi A. (Stanford University)

To realize the potential of the latest high-performance computing (HPC) architectures for reservoir simulation, scalable linear solvers are necessary. We describe a parallel algebraic multiscale solver (AMS) for the pressure equation of heterogeneous reservoir models. AMS is a two-level algorithm that uses domain decomposition with a localization assumption. In AMS, basis functions, which are local (subdomain) solutions computed during the setup phase, are used to construct the coarse-scale system and grid-transfer operators between the fine and coarse levels. The solution phase is composed of two stages: global and local. The global stage involves solving the coarse-scale system and interpolating the solution to the fine grid. The local stage involves application of a smoother on the fine-scale approximation.

The design and implementation of a scalable AMS on multicore and many-core architectures, including the decomposition, memory allocation, data flow, and compute kernels, are described in detail. These adaptations are necessary to obtain good scalability on state-of-the-art HPC systems. The specific methods and parameters, such as the coarsening ratio (*C _{r}*), basis-function solver, and relaxation scheme, have significant effects on the asymptotic convergence rate and parallel computational efficiency.

The balance between convergence rate and parallel efficiency as a function of *C _{r}* and the local stage parameters is analyzed in detail. The performance of AMS is demonstrated using heterogeneous 3D reservoir models, including geostatistically generated fields and models derived from SPE10 (Christie and Blunt 2001). The problems range in size from several million to 128 million cells. AMS shows excellent behavior for handling fixed-size problems as a function of the number of cores (so-called strong scaling). Specifically, for a 128-million-cell problem, a ninefold speedup is obtained on a single-node 12-core shared-memory architecture (dual-socket multicore Intel Xeon E5-2620-v2), and more than 12-fold on a single-node 20-core shared-memory architecture (dual-socket multicore Intel Xeon E5-2690-v2). These are encouraging results given the limited memory bandwidth that cores can share within a single node, which tends to be the major bottleneck for truly scalable solvers. We also compare the robustness and performance of our method with the parallel system algebraic mutligrid (SAMG) solver (Stüben 2012) from Fraunhofer SCAI.

algorithm, AMG, architecture, Artificial Intelligence, basis function, coarse-scale system, computational, gridblock, kernel, local-stage preconditioner, Multiscale, operator, preconditioner, reservoir simulation, scalability, scaling method, scientific computing, setup, solution phase, solver, Upstream Oil & Gas, wirebasket definition

Technology:

Almomin, Ali (Stanford University) | Biondi, Biondo (Stanford University)

**Summary**

Tomographic Full Waveform Inversion (TFWI) provides a robust but expensive method to invert the seismic data. Scale separation of the model greatly reduces the cost but adds complexity to theory and the implementation of the inversion. In addition, maintaining simultaneous inversion of scales is hindered when the modeling operator cannot accurately match the amplitudes of the data. In this paper, I provide two improvements that reduce the complexity of TFWI and increase robustness against amplitude inaccuracies in the modeling operator. First, I rederive TFWI with one model in an abstract formulation that is applicable to any form of the wave-equation. Then, I modify the objective function using a running-window normalization. Finally, we test the proposed algorithm on the SEG 2014 blind test data. The results of the modified TFWI show a major improvement in the accuracy and convergence rate of the inversion.

**Introduction**

Previously, we reduced the cost of TFWI by separating the extended model into two components: a non-extended smooth background and an extended rough perturbation (Almomin and Biondi, 2013; Biondi and Almomin, 2013). This might have caused some confusion on the resulting relationship and balance between these two parameters and their relationship to the original model. Furthermore, the interpretation of these two parameters limited the way we could separate them and increased the difficulty of moving to different wave-equations, such as the elastic.

Another limitation to TFWI is when the amplitude of the data cannot be accurately matched by the modeling operator. TFWI, similar to other data-space inversion method, produces highly accurate results due to matching both the phase and amplitude of the data. One solution is to only match the phase using a single frequency per iteration (Pratt, 1999; Shin and Ha, 2008). Using phase only will prevent simultaneous inversion of scales. Another approach is to normalize each trace by its norm, as presented in Shen (2014). The issue with trace normalization is that it does not take into account the large difference in amplitude behavior between the transmission and reflection data, which makes it only usable when inverting a few events to match.

To overcome these limitations, I first derive the “original” TFWI using the two-parameter approach. Next, I rederive TFWI while keeping one abstract model that makes it applicable to different forms of the wave-equation. Then, I generalize the amplitude normalization inversion to use any nonlinear weighting function that is based on the data. Finally, I propose using a running window normalization that uses a Gaussian function to extract the local amplitude of the data.

almomin, amplitude, Amplitude Normalization, approximation, Artificial Intelligence, derivative, evolutionary algorithm, gradient, inversion, machine learning, modeling operator, normalization, objective function, operator, Reservoir Characterization, rough component, separation, TFWI, tomographic full waveform inversion, Upstream Oil & Gas, velocity model, Waveform Inversion

Technology:

Manea, A. M. (Stanford University) | Sewall, J. (Intel Corporation) | Tchelepi, H. A. (Stanford University)

To realize the potential of the latest High-Performance-Computing (HPC) architectures for reservoir simulation, scalable linear solvers are necessary. We describe a parallel Algebraic Multiscale Solver (AMS) for the pressure equation of heterogeneous reservoir models. AMS is a two-level algorithm that employs domain decomposition with a localization assumption. In AMS, basis functions, which are local (subdomain) solutions computed during the setup phase, are used to construct the coarse-scale system and grid transfer operators between the fine and coarse levels. The solution phase is composed of two stages: global and local. The global stage involves solving the coarse-scale system and interpolating the solution to the fine grid. The local stage involves application of a smoother on the fine-scale approximation.

The design and implementation of a scalable AMS on multi- and many-core architectures, including the decomposition, memory allocation, data flow, and compute kernels, are described in detail. These adaptations are necessary to obtain good scalability on state-of-the-art HPC systems. The specific methods and parameters, such as the coarsening ratio (_{r}

The balance between convergence rate and parallel efficiency as a function of the coarsening ratio (_{r}

algorithm, architecture, Artificial Intelligence, basis function, coarse-scale system, computational, convergence, kernel, local stage preconditioner, Modeling & Simulation, operator, permeability, preconditioner, reservoir simulation, scalability, scaling method, scientific computing, setup, solution phase, solver, Upstream Oil & Gas

Technology:

Thank you!