幸运飞艇计划

Project description
Seismic full-waveform inversion (FWI) is a crucial technique in geophysics for creating high-resolution subsurface images. It utilizes complete seismic waveform data to provide detailed information about the Earth's interior, aiding in applications like hydrocarbon exploration, geothermal energy development, and earthquake hazard assessment.

This project aims to develop a methodology for frequency domain seismic FWI in acoustic media with variable velocity and density. The focus will be on addressing multi-parameter cross-talk and incorporating approximate Hessian information. An efficient scattering approach based on volume integral equation representation will be developed. The project represents a continuation of several previous master and PhD projects (e.g., Jakobsen et al., 2023).

Frequency domain analysis allows for isolating specific frequency components, improving resolution and stability. It also reduces computational burden through discrete Fourier transforms, enabling efficient parallel processing and faster convergence rates (Pratt, 1999).

Multi-parameter cross-talk, the interference between physical parameters during inversion, can lead to inaccuracies. Strategies to decouple parameters and enhance robustness will be explored. Incorporating approximate Hessian information is crucial for improving convergence and stability by providing insights into the solution space's curvature.

The student will develop a scattering approach using volume integral equation representation. This method transforms the acoustic wave equation into a volume integral equation for the pressure field (Jakobsen et al., 2023). The student should compare different numerical methods for solving this integral equation that differs in the way they compute the gradient of the pressure field.

To solve the inverse scattering problem, the student should use the L-BFGS method from numerical optimization and the adjoint state method for computing the Fr茅chet derivatives (Jakobsen et al., 2024). A multiplicative regularization method for obtaining stable solutions to an ill-posed inverse problem should be implemented and compared with the standard additive regularization method (Jakobsen et al., 2024).

The inversion algorithm will be tested on synthetic waveform data obtained using an independent finite difference time domain (FDTD) method to avoid inverse crime. Numerical noise will be added to simulate real-world conditions. The effects of model error and noise will be investigated by inverting data with and without variable density assumptions.

This project will advance seismic imaging techniques by addressing multi-parameter cross-talk and incorporating approximate Hessian information. The development of an efficient scattering approach and rigorous testing on synthetic data will enhance the methodology's accuracy and applicability in real-world scenarios.

REFERENCES
Pratt, R. G. (1999). Seismic waveform inversion in the frequency domain; Part 1, Theory and verification in a physical scale model. Geophysics, 64(3), 888-901.

Jakobsen, M., Xiang, K., & van Dongen, K. W. A. (2023). Seismic and medical ultrasound imaging of velocity and density variations by nonlinear vectorial inverse scattering. The Journal of the Acoustical Society of America, 153(5), 3151- 3164.

Jakobsen, M., Saputera, D., Psencik, I., Shekhar, U. and Xiang, K., 2024. Frequency domain full-waveform inversion for A-parameters using an adjoint integral equation method. Extended abstract, 3rd EAGE Workshop on Seismic Inversion, Napoli.

Proposed course plan during the master's degree (60 ECTS)
MAT212 Functions of several variables
GEOV218 Rock Physics
GEOV274 Reservoir geophysics
GEOV276 Introduction to theoretical seismology
GEOV277 Signal analysis and inversion in the earth sciences
GEOV375 Advanced applied seismic analysis

Prerequisites
This project is suitable for a student with an interest in applied mathematics and programming in addition to quantitative seismology.