Estimation of subsurface structures using pseudo-analytical full waveform inversion

Project description
Motivation:
Seismic data has been crucial for the exploration and production of hydrocarbons. Moreover, this type of data is also key in other applications, such as monitoring of underground CO2 storage and possible detection of leakage of CO2 as well as in delineating complicated shallow (i.e. less than 10-20 km depth) subsurface structures such as mid-ocean ridges and subduction zones. The processing of this data consists of four key steps (pre-processing, multiple attenuation/removal, velocity analysis and imaging/full waveform inversion (FWI)). The processing ultimately results in an image and/or velocity model of the subsurface which then is interpreted. The last of these four processing steps, imaging/FWI, is computationally very demanding. The main goal of this project is to get a better understanding of this crucial processing step and thereby reducing computation time without compromising on the quality of the inversion.

Hypothesis:
There are several ways to perform full waveform inversion. The first one, (pre-stack depth) imaging, is relatively cheap but still quite expensive. This method approximates the Hessian by its diagonal. This makes inversion of the Hessian straightforward, however the inversion results are not of the highest quality, in particular intermediate wavelength structures tend not to be well resolved. The second method numerically inverts the Hessian, is computationally demanding but gives very good inversion results. Because of the size of the Hessian, the inversion in this case has to be done using a low memory method, such as l-BFGS. A third inversion method, the Generalized Radon Transform (GRT), approximates the Hessian around the diagonal by first order Taylor expansion of the phase (which is computed using ray theory). This method is much less in use than the first two methods. However, in the few cases that it has been applied GRT inversion gives good results. In this project various theoretical and numerical aspects of GRT as well as a possible extension will be studied. Moreover, the GRT results will be compared with inversion using imaging as well as FWI.

Test/work:
After a review of the GRT and how it has been used in exploration and earthquake seismology the theoretical framework of GRT will be analyzed and where needed updated. Various possible extensions, involving the phase, as well as off-diagonal elements of the Hessian will be studied. This work involves both a theoretical and numerical component and the focus will be on speeding up the inversion. The numerical application will be both a simple test model as well as a more realistic model, such as the SEG-EAGE overthrust model and the focus will be mainly on acoustic media. If there is time the method can be extended to include viscoacoustic or elastic media. Finally, the performance of the GRT implementation in terms of accuracy and speed will be compared against imaging and FWI, with special emphasis on reconstruction of the intermediate wavenumbers of the velocity model. 

Proposed course plan during the master's degree (60 ECTS):

GEOV300, GEOV355, GEOV276, GEOV274, UiO GEO-DEEP, AG335, GEOV252