High Frequency Localised Elastic Full Waveform Inversion

We present a methodology to perform two and three dimensional (2D/3D) elastic full waveform inversion in a localised area, possibly containing reservoir, at depths far away from seismic sources and/or receivers. Even though full waveform inversion has shown its potential in resolving structures much superior to other seismic imaging techniques over the passed several decades, its computational costs have prevented the application of 3D elastic inversion in a practical sense. Furthermore, there are many cases in imaging problems where we are specially interested in some small subregions that are far too deep from source and receiver arrays, making a full-model inversion scheme very inefficient. Hence, we propose a localised waveform inversion using wavefield injection and extrapolation methods, in order to focus the seismic inversion within the region of interest. In this thesis, we focus on time-lapse active seismic configurations, which require semi-real-time inversion on a daily, weekly, monthly or yearly basis. Normally a time-lapse variation is restricted to a small sub-region, such as oil/gas reservoir or CO2 injection wells, requiring repeated wavefield simulations on the entire model in conventional full waveform inversion scheme. Here, we introduce the wavefield injection method and representation theorems in order to derive expressions for local virtual sources and receivers in the vicinity of sub-regions. Waveform inversions can then be conducted solely inside target areas. We perform various 2D time-lapse synthetic tests, in the presence of noise in data and/or model domain in order to examine the limitations, quantitatively evaluate errors in inverted models, in comparison to those of conventional full-model inversions. The results show that our method is not only efficient and robust but also accurate even under the presence of errors in both initial models and observed data. As high-frequency full-model waveform inversion is computationally too demanding, we introduce a two-step high-frequency elastic waveform inversion for 3D time-lapse surveys: i) a low-frequency and long-offset (<10 Hz) elastic waveform inversion that aims at recovering the background model; and ii) a high-frequency (up to 40 Hz) localised elastic waveform inversion seeking to quantitatively invert small-scale perturbations (<10 m), e.g., reservoir characterisation. The first low-frequency full-model inversion for the background model requires sparse grids, resulting in reduction of computational time and the second localised inversion can further mitigate the computational cost. We interpolate the inverted background model so that high-frequency contents can be better utilised in localised waveform inversion. It is shown that the inverted background model is sufficiently accurate for the high-frequency localised waveform inversion in the second step. The significantly reduced cost in terms of memory and computing time in 3D elastic localised full waveform inversion show its potential in the application to time-lapse seismic and high-resolution reservoir monitoring.