Seismic Waveform Inversion: Bump functional, parameterization analysis and imaging ahead of a tunnel-boring machine

During a seismic experiment, mechanical waves are usually generated by various manmade sources. These waves propagate in the subsurface and are recorded at receivers. Modern seismic exploration methods analyze them to infer the mechanical properties of the subsurface; this is commonly referred as quantitative imaging. These properties assist in the determination of the subsurface rock type and structure. Exploration methods are not only useful while looking for the deposits such as crude oil, natural gas and minerals but also for near-surface geotechnical investigation. A motive of this thesis is to adopt these methods to image the subsurface ahead of a tunnel-boring machine for hazard assessment during excavation. Full-waveform inversion (FWI) is a gradient-based optimization problem that is employed in seismic exploration for quantitative imaging of the recorded waves. During FWI, seismic waves are simulated in a computer by using certain physical laws that govern the wave propagation. After inversion, output subsurface properties simulate waves that fit the recorded waves in a least-squares sense. In other words, the gradient-based optimization aims to find the minimum of the least-squares misfit between the simulated and the recorded waves. Finding such a minimum is not straight forward due to the existence of multiple local minima when using the least-squares objective. As a result, it might often happen that the optimizer converges to local minima, where the simulated waves only partially explain the recorded waves. The presence of local minima is associated to the strong non-linear dependence of the recorded waves on the subsurface properties. In this thesis, we attempt to overcome this difficulty. We propose a new measure of misfit between the recorded and the simulated waves. This measure compares the waveforms in a simplified form after taking the absolute value and blurring. We show that the new misfit measure suffers less from the local-minima problem. For robust inversion, we use a multi-objective inversion scheme, where the new measure is used as an auxiliary objective to pull the trapped solution out of the least-squares local minimum whenever necessary. In multi-parameter FWI, more than one kind of subsurface properties are simultaneously estimated. When only the first-order derivatives of the misfit are used during minimization, different choices of subsurface parameterization are not equivalent; they can be interpreted as different preconditioners. Therefore, the choice of parametrization will affect the rate of convergence in multi-parameter FWI and the best choice of parameterization is the one with the highest rate. In this thesis, we also analyse various choices of subsurface parameterization in search of the best one. It is well known that the local-minima problem in FWI can easily be resolved by reliably generating and recording low-frequency waves in the subsurface. Recently, a seismic source capable of generating such low frequencies is developed based on linear synchronous motors technology. Finally, we demonstrated a shear-wave seismic ground prediction system using these sources to enable imaging ahead of a tunnel boring machine (TBM).Applied Geophysics and Petrophysic

Full waveform inversion with an auxiliary bump functional

Least-squares inversion of seismic arrivals can provide remarkably detailed models of the Earth's subsurface. However, cycle skipping associated with these oscillatory arrivals is the main cause for local minima in the least-squares objective function. Therefore, it is often difficult for descent methods to converge to the solution without an accurate initial large-scale velocity estimate. The low frequencies in the arrivals, needed to update the large-scale components in the velocity model, are usually unreliable or absent. To overcome this difficulty, we propose a multi-objective inversion scheme that uses the conventional least-squares functional along with an auxiliary data-domain objective. As the auxiliary objective effectively replaces the seismic arrivals by bumps, we call it the bump functional. The bump functional minimization can be made far less sensitive to cycle skipping and can deal with multiple arrivals in the data. However, it can only be used as an auxiliary objective since it usually does not provide a unique model after minimization even when the regularized-least-squares functional has a unique global minimum and hence a unique solution. The role of the bump functional during the multi-objective inversion is to guide the optimization towards the global minimum by pulling the trapped solution out of the local minima associated with the least-squares functional whenever necessary. The computational complexity of the bump functional is equivalent to that of the least-squares functional. In this paper, we describe various characteristics of the bump functional using simple and illustrative numerical examples. We also demonstrate the effectiveness of the proposed multi-objective inversion scheme by considering more realistic examples. These include synthetic and field data from a cross-well experiment, surface-seismic synthetic data with reflections and synthetic data with refracted arrivals at long offsets.Applied Geophysics and Petrophysic

A Shear-Wave Seismic System to Look Ahead of a Tunnel Boring Machine

The Earth’s properties, composition and structure ahead of a tunnel boring machine (TBM) should be mapped for hazard assessment during excavation. We study the use of seismic-exploration techniques for this purpose. We focus on a seismic system for soft soils, where shear waves are better and easier to interpret than compressional waves, as has been shown over the last decade. The system is intended to be deployed on the machine’s cutter head, with a few seismic sources and sufficiently many seismic sensors to tackle spatial variability and noise characteristics. An important property of the newly developed system is its ability to process data with very little human interaction. Images need to be available in near real time, without human interactions slowing down the imaging process. This can be achieved by employing Full Waveform Inversion, which minimizes the difference between modeled and observed data. Because this method may suffer from local minima in the cost function if the data lack low-frequency information, we employ a dedicated seismic source that can generate sufficiently low frequencies for the relevant length scales. With data acquired in a number of field settings that mimic realistic TBM configurations, we show that the designed seismic system can successfully look ahead of the TBM and offers a valuable capability to support decision-making during tunnel excavation.Applied Geophysics and Petrophysic

A shear-wave seismic system using full waveform inversion to look ahead of a tunnel-boring machine

In the near surface with unconsolidated soils, shear-wave properties can often be characterised better and with a higher resolution than compressional-wave properties. To enable imaging ahead of a tunnel-boring machine, we developed a seismic prediction system with a few shear-wave vibrators and horizontal receivers. The boring process is interrupted at regular intervals to carry out active surveys. The vibrators are then pushed against the rock or soil in front of the cutting wheel of the machine. The design of the vibrators is based on linear synchronous motor technology that can generate very low frequencies, starting at 5 Hz. These vibrators generate a force in a direction perpendicular to the tunnel axis. Horizontal receivers measure the particle velocity, mainly due to the horizontally polarised shear waves. Because imaging with conventional migration methods suffers from artefacts, caused by the incomplete aperture and inaccuracies in the assumed velocity model, we use two-dimensional horizontally polarised shear full-waveform inversion to resolve the subsurface shear properties. The classic cycle-skipping problem, which can make the application of fullwaveform inversion cumbersome, is avoided by the capacity of the vibrators to generate low frequencies. In this paper, we demonstrate the capabilities of the proposed seismic system through a number of synthetic and field experiments.Applied Geophysics and Petrophysic