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.

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.