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Geophysical Exploration using Advanced GAlerkin Methods

Periodic Reporting for period 2 - GEAGAM (Geophysical Exploration using Advanced GAlerkin Methods)

Période du rapport: 2017-01-01 au 2017-12-31

The main objective of this Marie Curie RISE action is to improve and exchange interdisciplinary knowledge on applied mathematics, high performance computing, and geophysics to be able to better simulate and understand the materials composing the Earth's subsurface. This is essential for a variety of applications such as CO2 storage, hydrocarbon extraction, mining, and geothermal energy production, among others. All these problems have in common the need to obtain an accurate characterization of the Earth's subsurface, and to achieve this goal, several complementary aspects need to be studied, including the mathematical foundations of various high-order Galerkin multiphysics simulation methods, the efficient computer implementation of these methods in large parallel machines and GPUs, and some crucial geophysical aspects such as the design of measurement acquisition systems in different scenarios. Specific objectives of this Project include:

I) Working with both borehole and on surface measurements, including: (a) complex borehole environments such as those encountered in deviated (and possibly cased) wells when the logging instrument is borehole ex-centered, (b) marine controlled-source electromagnetic (CSEM) measurements in shallow waters, and (c) magnetotelluric (MT) measurements.

II) Developing (a) a mathematical modeling of multi-wave problems, (b) advanced numerical methods for Helmholtz problems, (c) a mathematical analysis of Helmholtz problems, and (d) construction of stabilized high-order hybrid Galerkin schemes.

III) Developing a large parallel simulation software of geophysical measurements.

IV) Building a multiphysics inversion method based on an adaptive multi-dimensional model for the rapid inversion of borehole geophysical resistivity, elastoacoustic, and possibly nuclear measurements that can be interpreted in terms of a 1D model plus a salient 2D or 3D feature.

V) Apply the simulation and inversion software to complex geological environments. For example, those containing subsalt and pre-salt layers, and/or hydrocarbon-bearing shales exhibiting low porosity and permeability values.

VI) To study the application of the developed numerical methods for geophysical exploration to other industries, including mining.
We have made a relevant contribution to the development of state-of-the-art numerical methods for better estimating material properties composing the Earth´s subsurface. Specifically, we have:

(a) Made exceptional unexpected advances in the area of Isogeometric Analysis (IGA).

(b) Developed a parallel high-order Discontinuous Galerkin library for the efficient simulation of three-dimensional (3D) on surface and borehole elasto-acoustic measurements.

(c) Improved currently existing one-dimensional (1D) based model reduction methods for geophysical electromagnetic and elasto-acoustic problems.

(d) Developed an adaptive multi-dimensional inversion algorithm for geophysical measurements based on both semi-analytical 1D methods and high-order Galerkin methods for the secondary field.

(e) Developed a high-order goal-oriented adaptive method for wave propagation problems using unconventional dual problems for geophysical applications.

(f) Studied efficient grid generation techniques to model the Earth's subsurface, including the use of non-fitting grids.

(g) Performed multiscale modeling of wave propagation and elliptic problems with highly-heterogeneous coefficients.

(h) Ported and optimized a geophysical exploration software to target High Performance Computing (HPC) platforms.

(i) Solved inverse borehole resistivity problems for geosteering operations.

(k) Developed a Source Time Reversal (STR) method to find sources of micro-seismic events in mines.
GEAGAM Network has developed a variety of numerical methods that have been widely disseminated through publications, workshops, post-graduate courses to train new researchers, a dedicated webpage, and visits to companies working in the area. As a result of it:

(a) Some partners of the Consortium have signed new contracts with oil companies for the further development of certain numerical methods.

(b) We have developed a novel Refined Isogeometric Analysis (rIGA) method that is approximately 50 times faster than other existing methods providing the same level of numerical error.

(c) We are providing an excellent training network for Graduate Students, Postdoctoral Researchers, and Professors.

(d) We have implemented a program of co-supervised dissertations between different institutions. So far, we have 7 co-supervised Ph.D. students.

(e) We have delivered several presentations to 25+ companies.

(f) We have published over 100 articles in peer-reviewed journals with high impact factor in different areas of knowledge (mathematics, numerical analysis, computer sciences, geophysics, and engineering) and delivered high-quality presentations on the topic at International Congresses.

(g) We have delivered intensive courses on geophysical exploration methods, advanced Galerkin methods for geophysics, and HPC for geophysical applications.

(h) We have organized lectures to high-school students in the area to disseminate the research results to the society at large.
Project Leaflet for diffusion