Multiscale Inversion of Porous Rock Physics using High-Performance Simulators: Bridging the Gap between Mathematics and Geophysics

Project Information

MATHROCKS

Grant agreement ID: 777778

DOI

10.3030/777778

Project closed

EC signature date 25 September 2017

Start date 1 April 2018

End date 31 March 2023

Funded under

• EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions

Total cost

€ 765 000,00

EU contribution

€ 765 000,00

Coordinated by

UNIVERSIDAD DEL PAIS VASCO/ EUSKAL HERRIKO UNIBERTSITATEA
Spain

Periodic Reporting for period 2 - MATHROCKS (Multiscale Inversion of Porous Rock Physics using High-Performance Simulators: Bridging the Gap between Mathematics and Geophysics)

Reporting period: 2020-04-01 to 2023-03-31

Summary of the context and overall objectives of the project

MATHROCKS aims at designing and providing efficient and trustable mathematical tools and computational algorithms to be used in subsurface geology.
This project is important for society because an accurate description of the Earth’s constitutive materials is essential for a variety of applications such as CO2 underground storage, hydrocarbon extraction, mining, and geothermal energy production.
Essentially, mapping a region of the Earth’s subsurface requires geophysical techniques that consist in generating artificial waves that travel through the Earth’s layers, and then inferring the geology from the analysis of the returning waves. The main drawback of these procedures, occurring even with the most recent technological advances, is the highly-elevated computational cost, which results in the impossibility of performing the interpretation (inversion) of the recorded measurements in real time.
Within this project, the following scientific aspects are addressed: mathematical modelling of porous rocks’ physical properties, simulation of geophysical wave propagation problems, and, the ultimate goal, inversion of the measurements.
MATHROCKS breakthroughs and techniques are intended to reach and serve the geophysical industry, including leading companies in oil exploration and mining, but also smaller companies and corporations that require interpretation of geophysical measurements for their daily activities.

Conclusions of the Action:
The MATHROCKS project has been a great success in developing efficient and trustworthy mathematical tools and computational algorithms for subsurface geology. The project has brought together world-class scientists with complementary expertise in applied mathematics, geophysical exploration, and high-performance computing to address the highly-elevated computational cost of mapping the Earth's subsurface.
Through the project, deep learning algorithms for geophysics have been developed. These techniques have the potential to significantly advance our understanding of the Earth's subsurface and improve the accuracy of applications such as CO2 underground storage, hydrocarbon extraction, mining, and geothermal energy production.
The success of the project is evidenced by the transfer of knowledge to the academic community through articles in leading journals, mini-symposia, and courses for a broad or specialized audience. The project has also disseminated its results to society at large through press releases, posters, participation in educational events, and social media campaigns.
Moreover, the project has been able to serve the geophysical industry, including leading companies in oil exploration and mining, as well as smaller companies and corporations that require interpretation of geophysical measurements for their daily activities. Overall, the MATHROCKS project has been successful in achieving its objectives, and its results will continue to benefit society and advance our understanding of the Earth's subsurface for years to come.

Work performed from the beginning of the project to the end of the period covered by the report and main results achieved so far

The project achieved meaningful advances in this period, many of which are already described in the first period. Specifically, an acoustic characterization of porous rocks was completed through a process that required identifying and overcoming important mathematical and computational issues, such as the reduction of the infinite domain to a bounded one through the use of absorbing boundary conditions. The wave propagation difficulties were undertaken through the theoretical and numerical development of efficient and stable high-order approximation schemes that allow the computation of an accurate solution, even in high-frequency regime, which is known to be problematic due to the highly oscillating nature of the solution. As for the interpretation (inversion) of the recorded measurements in real time, which is the ultimate problem to properly describe the geology of the analyzed region, an important step has been taken through the use of the integration of deep learning (DL) algorithms in the existing numerical methods. Multiple DL techniques for the inversion of elasto-acoustic and electromagnetic properties were designed, implemented, and tested on synthetic examples. Preliminary results show the potential of this technology to solve inverse problems in real time. In addition, several parametrization models have been proposed and validated through experiments. They constitute the alpha version of the model, which will eventually be enriched and updated, according to the real Earth´s subsurface profile.

Some of the results are already of interest to the geophysical industry: the idea of integrating deep learning algorithms in the numerical methods for wave propagations caught the interest of several international oil companies. The intermediate outcomes presented in the annual meeting on Formation Evaluation at the University of Texas, Austin were shown to representatives of over 25 different oil-related companies.
Finally, the message of the project reached the society through dissemination of its work at local, national, and European levels, such as encounters between researchers and high-school students, open‐day scientific events to introduce children to science, and also the collaboration established with the initiative “Mujeres con Ciencia” to promote awareness of the fundamental role of women in sciences.

MATHROCKS has published over 160 publications in journals with high-impact factor in applied mathematics, HPC, artificial intelligence, and geophysics, with strong scientific collaboration between project members. The project has also organized several courses and workshops related to deep learning and numerical methods in geophysics. MATHROCKS has contributed to sustainable development by developing less expensive geophysical exploration processes and has made important advancements in petrophysical exploration in collaboration with several universities. The project has also provided training opportunities for undergraduate and graduate students through courses, secondments, and co-supervised theses, allowing them to gain new competences and establish contacts with researchers from different institutions.

Progress beyond the state of the art and expected potential impact (including the socio-economic impact and the wider societal implications of the project so far)

Through the work performed, MATHROCKS started to bridge the gap between mathematics and geophysics by identifying and characterizing mathematically key parameters in geophysics, and by launching the design and implementation of innovative numerical algorithms for geophysical problems. Rigorous mathematical analysis of the models has accompanied the development of these algorithms. Through extensive research, we have optimized the mathematical and computational methods for solving both direct and inverse problems. Advanced deep learning techniques have been successfully integrated into the resulting algorithms. These efforts have resulted in a comprehensive, rapid, and reliable set of algorithms for producing subsurface maps.
By doing so, this action has contributed to the advances in science and geophysical industry, and also to socio-economic progress. For instance, with more adequate procedures for mapping the Earth’s subsurface, CO2 storage techniques would be less costly, safer and more efficient, allowing a better care of the environment. Also, by addressing some of the mathematical gaps in the understanding of artificial intelligence techniques, the project has contributed to their use and exploitation in the benefits of our society.

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