Fractional Viscoacoustic Wave Equations: Mathematical Analysis, Efficient Simulations, and Applications to Full-Waveform Inversion of Seismic Data

Missouri University Of Science And Technology, Rolla MO

Investigators

Abstract

Seismic waveform inversion is a widely used technique in the oil and gas industry as well as in geophysical research. This technique is among the most powerful subsurface imaging techniques; its success relies on both an accurate model of seismic wave propagation and efficient numerical computation for the practical implementation. This project addresses fundamental mathematical and computational issues in these two aspects and thus is of central importance for various applications, including imaging of the Earth's interior, subsurface exploration in the oil and gas industry, monitoring in carbon sequestration and geothermal facilities, and earthquake engineering. Students will be trained through involvement in the interdisciplinary research activities. The main objectives of this research are to build mathematical and computational treatments for fractional viscoacoustic wave equations, to provide efficient and accurate modeling algorithms, and to further construct the viscoacoustic full-waveform inversion algorithm of seismic data. The fractional viscoacoustic wave equation, accounting for both seismic attenuation and dispersion in wave propagation, opens a promising direction to study seismic waves with attenuation. However, its nonlocality introduces considerable challenges. This project will involve systematic research in mathematical analysis, numerical simulations, and geophysical applications of data inversion, validation, and applications. On the theoretical side, the nonlocal properties of the fractional viscoacoustic wave equation will be investigated. On the numerical side, numerical analysis and efficient algorithms will be developed for its effective simulation. Building on these results, implementation issues for the viscoacoustic full-waveform inversion associated with fractional viscoacoustic wave equations will be addressed. The validation of the full-waveform inversion will be carried out with both synthetic data and field data from the Frio Formation carbon dioxide sequestration site in Texas. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.