Josep de la Puente

Finite-difference staggered grids in GPUs for anisotropic elastic wave propagation simulation

The 3D elastic wave equations can be used to simulate the physics of waves traveling through the Earth more precisely than acoustic approximations. However, this improvement in quality has a counterpart in the cost of the numerical scheme. A possible strategy to mitigate that expense is using specialized, high-performing architectures such as GPUs. Nevertheless, porting and optimizing a code for such a platform require a deep understanding of both the underlying hardware architecture and the algorithm at hand. Furthermore, for very large problems, multiple GPUs must work concurrently, which adds yet another layer of complexity to the codes. In this work, we have tackled the problem of porting and optimizing a 3D elastic wave propagation engine which supports both standard- and fully-staggered grids to multi-GPU clusters. At the single GPU level, we have proposed and evaluated many optimization strategies and adopted the best performing ones for our final code. At the distributed memory level, a domain decomposition approach has been used which allows for good scalability thanks to using asynchronous communications and I/O. HighlightsWe use staggered grids to simulate an elastic wave propagation across the earth.As the performance is critical, we make use of GPUs to accelerate the simulation.We show how the work is distributed among the nodes in a domain decomposition case.Regarding the complexity of the simulation, we obtain speed-ups from 10i? to 14i?.

Rotational motions in homogeneous anisotropic elastic media

Rotational motions in homogeneous anisotropic elastic media are studied under the assumption of plane wave propagation. The main goal is to investigate the influences of anisotropy in the behavior of the rotational wavefield. The focus is on P-waves that theoretically do not generate rotational motion in isotropic media. By using the Kelvin–Christoffel equation, expressions are obtained of the rotational motions of body waves as a function of the propagation direction and the coefficients of the elastic modulus matrix. As a result, the amplitudes of the rotation rates and their radiation patterns are quantified and it is concluded that (1) for strong local earthquakes and typical reservoir situations quasi P-rotation rates induced by anisotropy are significant, recordable, and can be used for inverse problems; and (2) for teleseismic wavefields, anisotropic effects are unlikely to be responsible for the observed rotational energy in the P coda.

Edge-based electric field formulation in 3D CSEM simulations: A parallel approach

This paper presents a parallel computing scheme for the data computation that arise when applying one of the most popular electromagnetic methods in exploration geophysics, namely, controlled-source electromagnetic (CSEM). The computational approach is based on linear edge finite element method in 3D isotropic domains. The total electromagnetic field is decomposed into primary and secondary electromagnetic field. The primary field is calculated analytically using an horizontal layered-earth model and the secondary field is discretized by linear edge finite element method. We pre-calculated the primary field through of an embarrassingly-parallel framework in order to exploit the parallelism and the advantages of geometric flexibility. The numerical-computational formulation presented here is able to work with three different orientations for the dipole or excitation source. Our code is implemented on unstructured tetrahedral meshes because are able to represent complex geological structures and they allow local refinement in order to improve the solutions accuracy. The codes performance is studied through a test of scalability.

Parallel and numerical issues of the edge finite element method for 3D controlled-source electromagnetic surveys

This paper deals with the most relevant parallel and numerical issues that arise when applying the Edge Element Method in the solution of electromagnetic problems in exploration geophysics. In this sense, in recent years the application of land and marine controlled-source electromagnetic (CSEM) surveys has gained tremendous interest among the offshore exploration community. This method is especially significant in detecting hydrocarbon in shallow/deep waters. On the other hand, in Finite Element Methods for solving electromagnetic field problems, the use of Edge Elements has become very popular. In fact, Edge Elements are often said to be a cure to many difficulties that are encountered (particularly eliminating spurious solutions) and are claimed to yield accurate results. CSEM, linear vectorial edge basis functions and its implementation on unstructured tetrahedral meshes are discussed. The use of its kind of discretisation enables the representation of complex geological structures and allows local refinement in order to improve the solutions accuracy. A parallel shared memory approach is proposed to meet the high computational cost of EM modeling. Performance results and an convergence study are presented in order to validate our numerical method.

Probabilistic Assessment of Seismic Risk of Dwelling Buildings of Barcelona. Implication for the City Resilience

The knowledge of seismic risk of buildings can contribute to increase the resilience of cities. In the present work a new assessment of the seismic risk of dwelling buildings of Barcelona was done. This assessment was performed according to a probabilistic methodology, which is summarized in the following steps: (1) performing a probabilistic seismic hazard assessment (PSHA) to obtain exceedance rates of macroseismic intensities; (2) performing a probabilistic seismic vulnerability assessment (PSVA) of each building in order to determine probability density functions that describe the variation of a vulnerability index; and (3) performing a probabilistic seismic risk assessment (PSRA) to generate seismic risk curves in terms of frequencies of exceedance of damage states. In the present work 69,982 dwelling buildings of Barcelona were assessed. According to the results the percentage of dwelling buildings of Barcelona that have a probability equal or greater than 1% of suffer partial collapse in the next 50 years is a value between 0% and 34.29%. A value of 0% corresponds to the results of seismic risk obtained for the case where regional vulnerability modifiers were not considered during the procedure to assess the seismic vulnerability of buildings and 34.29% correspond to the case where regional vulnerability modifiers were considered. For the same two options, the losses due to the physical damage of the dwelling buildings of Barcelona assessed for an exposure time of 50 years, could vary from 807.3 to 1739.4 millions of euros, respectively. Finally, possible uses of the seismic risk results computed in the present work are mentioned.

PETGEM: A parallel code for 3D CSEM forward modeling using edge finite elements

Abstract We present the capabilities and results of the Parallel Edge-based Tool for Geophysical Electromagnetic modeling (PETGEM), as well as the physical and numerical foundations upon which it has been developed. PETGEM is an open-source and distributed parallel Python code for fast and highly accurate modeling of 3D marine controlled-source electromagnetic (3D CSEM) problems. We employ the Nedelec Edge Finite Element Method (EFEM) which offers a good trade-off between accuracy and number of degrees of freedom, while naturally supporting unstructured tetrahedral meshes. We have particularised this new modeling tool to the 3D CSEM problem for infinitesimal point dipoles asumming arbitrarily isotropic media for low-frequencies approximations. In order to avoid source-singularities, PETGEM solves the frequency-domain Maxwells equations of the secondary electric field, and the primary electric field is calculated analytically for homogeneous background media. We assess the PETGEM accuracy using classical tests with known analytical solutions as well as recent published data of real life geological scenarios. This assessment proves that this new modeling tool reproduces expected accurate solutions in the former tests, and its flexibility on realistic 3D electromagnetic problems. Furthermore, an automatic mesh adaptation strategy for a given frequency and specific source position is presented. We also include a scalability study based on fundamental metrics for high-performance computing (HPC) architectures.

Acceleration strategies for elastic full waveform inversion workflows in 2D and 3D

Full waveform inversion (FWI) is one of the most challenging procedures to obtain quantitative information of the subsurface. For elastic inversions, when both compressional and shear velocities have to be inverted, the algorithmic issue becomes also a computational challenge due to the high cost related to modelling elastic rather than acoustic waves. This shortcoming has been moderately mitigated by using high-performance computing to accelerate 3D elastic FWI kernels. Nevertheless, there is room in the FWI workflows for obtaining large speedups at the cost of proper grid pre-processing and data decimation techniques. In the present work, we show how by making full use of frequency-adapted grids, composite shot lists and a novel dynamic offset control strategy, we can reduce by several orders of magnitude the compute time while improving the convergence of the method in the studied cases, regardless of the forward and adjoint compute kernels used.

Improving edge finite element assembly for geophysical electromagnetic modelling on shared-memory architectures

This work presents a set of node-level optimizations to perform the assembly of edge finite element matrices that arise in 3D geophysical electromagnetic modelling on shared-memory architectures. Firstly, we describe the traditional and sequential assembly approach. Secondly, we depict our vectorized and shared-memory strategy which does not require any low level instructions because it is based on an interpreted programming language, namely, Python. As a result, we obtained a simple parallel-vectorized algorithm whose runtime performance is considerably better than sequential version. The set of optimizations have been included to the work-flow of the Parallel Edge-based Tool for Geophysical Electromagnetic Modelling (PETGEM) which is developed as open-source at the Barcelona Supercomputing Center. Finally, we present numerical results for a set of tests in order to illustrate the performance of our strategy.

Three-Dimensional CSEM Modelling on Unstructured Tetrahedral Meshes Using Edge Finite Elements

The last decade has been a period of rapid growth for electromagnetic methods (EM) in geophysics, mostly because of their industrial adoption. In particular, the marine controlled-source electromagnetic method (CSEM) has become an important technique for reducing ambiguities in data interpretation in hydrocarbon exploration. In order to be able to predict the EM signature of a given geological structure, modelling tools provide us with synthetic results which we can then compare to real data. On the other hand and among the modelling methods for EM based upon 3D unstructured meshes, the Nedelec Edge Finite Element Method (EFEM) offers a good trade-off between accuracy and number of degrees of freedom, i.e. size of the problem. Furthermore, its divergence-free basis is very well suited for solving Maxwell’s equation. On top of that, we present the numerical formulation and results of 3D CSEM modelling using the Parallel Edge-based Tool for Geophysical Electromagnetic Modelling (PETGEM) on unstructured tetrahedral meshes. We validated our experiments against quasi-analytical results in canonical models.

Elastic Full Waveform Inversion (FWI) of reflection data with a phase misfit function

Full Waveform Inversion of elastic dataset is challenging due to the complexity introduced by free-surface effects or P-S wave conversions among others. In this context, large offsets are preferred for inversion because they favor transmission modes which are more linearly related to P-wave velocity. In this paper, we present an original approach which allows to dynamically select the near offset at each frequency. We illustrate this approach with the inversion of a dataset without density. In order to deal with a more realistic scenario, we next present the inversion with density effects included into the modeling. As inverting density is known to be a hard task, we choose to not invert it. This approach leads to the use of a phase misfit function, which is more connected to the kinematics of the problem than the classic \(L^2\) norm.