Elastic Full Waveform Inversion of Near-Surface Seismic Data Incorporating Topography

Abstract

Elastic full waveform inversion (FWI) is an imaging tool that can yield subsurface models of seismic velocities and density at sub-wavelength resolution. For near-surface applications (tens to hundreds of metres depth penetration), FWI is particularly valuable, because it requires no separation of different seismic phases, such as direct waves, reflections and surface waves, which is a difficult task at this scale. In contrast to conventional methods of seismic data analysis, FWI utilises and interprets the full wavefield. However, real data applications are still scarce. This is due to (i) the non-linearity of the inversion problem, (ii) the high computational costs and (iii) systematic errors that are not taken care of by the FWI algorithm. Although considerable progress has been made during the past few years, there are still a number of issues that remain to be resolved. In my thesis I have tackled three of these problems. Surface waves often dominate shallow seismic data. With their high amplitudes they dominate the misfit functional and control the model update. Due to their limited depth penetration they are mainly sensitive to shallow parts, such that model updates at greater depth are often very small. In order to balance sensitivities and to increase model updates at depth, I have introduced a novel scaling technique and I have demonstrated its efficiency on synthetic models of varying complexity. The scaling technique involves normalising the squared column sums of the Jacobian matrix prior to adding regularisation and updating the model. This leads to significantly improved velocity images at depth. Although the technique is introduced on near-surface FWI, it is rather general and can be applied to all kind of geophysical inversion problems such as the inversion of geoelectric or electromagnetic data. Investigating unstable slopes threatened by landslides is a typical near-surface application among many others, where significant topographic undulations are present. It is inevitable to account for such topography in FWI. Through the adaption of SPECFEM2D, a well-established forward solver incorporating irregular grids, I have made it possible to run FWI on profiles featuring arbitrary surface topography. I have demonstrated the capability to handle considerable topography in the presence of a complex subsurface model including stochastic fluctuations and several block anomalies. Furthermore, I have investigated the effects of neglecting such topography during inversion. It has turned out that topographic undulations with wavelengths or amplitudes similar to the minimum seismic wavelengths have a detrimental effect on model reconstruction. Seismic survey setups are typically governed by the needs of reflection seismology processing, that is, high fold and dense spatial sampling are required. Using tools of experimental design I have optimised the survey setup for the needs of FWI. I have established a clear recipe consisting of the following points: (i) use horizontally directed sources; (ii) multi-component geophones clearly outperform single-component receiv- ers; (iii) a receiver spacing in the order of the minimum seismic wavelength is sufficient; (iv) the sources employed can be reduced to a few well-selected positions. In this way the costs of a survey can be drastically reduced while the quality of the obtained subsurface images is only slightly affected. The topics addressed in my thesis shall be a step forward towards successful and efficient FWI of real data. It is anticipated that in a foreseeable future FWI will become a standard tool for the analysis of near-surface seismic data. --> Elastic full waveform inversion (FWI) is an imaging tool that can yield subsurface models of seismic velocities and density at sub-wavelength resolution. For near-surface applications (tens to hundreds of metres depth penetration), FWI is particularly valuable, because it requires no separation of different seismic phases, such as direct waves, reflections and surface waves, which is a difficult task at this scale. In contrast to conventional methods of seismic data analysis, FWI utilises and interprets the full wavefield. However, real data applications are still scarce. This is due to (i) the non-linearity of the inversion problem, (ii) the high computational costs and (iii) systematic errors that are not taken care of by the FWI algorithm. Although considerable progress has been made during the past few years, there are still a number of issues that remain to be resolved. In my thesis I have tackled three of these problems. Surface waves often dominate shallow seismic data. With their high amplitudes they dominate the misfit functional and control the model update. Due to their limited depth penetration they are mainly sensitive to shallow parts, such that model updates at greater depth are often very small. In order to balance sensitivities and to increase model updates at depth, I have introduced a novel scaling technique and I have demonstrated its efficiency on synthetic models of varying complexity. The scaling technique involves normalising the squared column sums of the Jacobian matrix prior to adding regularisation and updating the model. This leads to significantly improved velocity images at depth. Although the technique is introduced on near-surface FWI, it is rather general and can be applied to all kind of geophysical inversion problems such as the inversion of geoelectric or electromagnetic data. Investigating unstable slopes threatened by landslides is a typical near-surface application among many others, where significant topographic undulations are present. It is inevitable to account for such topography in FWI. Through the adaption of SPECFEM2D, a well-established forward solver incorporating irregular grids, I have made it possible to run FWI on profiles featuring arbitrary surface topography. I have demonstrated the capability to handle considerable topography in the presence of a complex subsurface model including stochastic fluctuations and several block anomalies. Furthermore, I have investigated the effects of neglecting such topography during inversion. It has turned out that topographic undulations with wavelengths or amplitudes similar to the minimum seismic wavelengths have a detrimental effect on model reconstruction. Seismic survey setups are typically governed by the needs of reflection seismology processing, that is, high fold and dense spatial sampling are required. Using tools of experimental design I have optimised the survey setup for the needs of FWI. I have established a clear recipe consisting of the following points: (i) use horizontally directed sources; (ii) multi-component geophones clearly outperform single-component receivers; (iii) a receiver spacing in the order of the minimum seismic wavelength is sufficient; (iv) the sources employed can be reduced to a few well-selected positions. In this way the costs of a survey can be drastically reduced while the quality of the obtained subsurface images is only slightly affected. The topics addressed in my thesis shall be a step forward towards successful and efficient FWI of real data. It is anticipated that in a foreseeable future FWI will become a standard tool for the analysis of near-surface seismic data.