Surface wave inversion is a powerful tool for subsurface imaging at various scales, spanning from near-surface characterization to crustal imaging. This study focuses on the transdimensional Markov chain Monte Carlo (McMC) algorithm and its effectiveness for surface wave inversion. We explore its application at different dimensions (1D, 2D, 3D) and scales, encompassing both near-surface and crustal subsurface characterization.

We first demonstrate the fundamentals of surface wave inversion using a least-squares algorithm, a conventional McMC method, and the transdimensional McMC algorithm applied to the (non-linear) 1D inversion problem. We compare these algorithms by applying them to both synthetic and field data. In contrast to the least-squares method, the transdimensional algorithm successfully recovers rapid variations in velocity, particularly at a depth of around 3 km. This observation emphasizes the automatic and localized smoothing applied in the transdimensional McMC algorithm. Furthermore, the transdimensional McMC algorithm yields, inherently, the posterior probability density of the shear wave velocity as a function of depth, offering valuable insights.


In Chapter 3, we extend the study to two dimensions using surface waves retrieved by means of Distributed Acoustic Sensing (DAS), validating the transdimensional algorithm's potential for near-surface applications. We first determine the dispersive behavior of the Rayleigh wave considering lateral variation in the subsurface. This leads to a local dispersion curve at the location of each receiver. To recover a 2D shear wave velocity section of the subsurface, we develop a 2D transdimensional approach to invert all the dispersion curves simultaneously. This approach retains lateral correlations of the recovered shear wave velocities. This two-dimensional application demonstrates the ability of the transdimensional McMC algorithm to reconstruct the two-dimensional shear wave velocity structure of the near-surface.

Finally, we extend the study to three dimensions by recovering the crustal shear wave velocity structure of the Reykjanes Peninsula. As input, we use travel times extracted from Rayleigh waves that were retrieved through the application of seismic interferometry to recordings of ambient seismic noise. We then modify and use the one-step 3D transdimensional surface wave tomography algorithm. This implies that we depart from conventional two-step approaches. Synthetic tests showcase adaptability to ray density, yielding higher resolution in densely sampled areas. Reduced computational costs by modifying the algorithm enhance the applicability for 3D crustal imaging. Our application of the one-step 3D transdimensional algorithm to ambient-noise data provides the first comprehensive shear wave velocity model of the Reykjanes Peninsula. The detailed shear wave velocity model offers valuable geological and geothermal insights into the subsurface structure, confirming the algorithm's potential as a routine tool for surface wave tomography.

Collectively, these findings advocate the use of one-step transdimensional inversion algorithms for seismic tomography. Their adaptability, efficiency gains, and interpretability contribute to advancing our understanding of subsurface velocity structures. As seismic data volumes grow, embracing innovative inversion approaches becomes imperative, and the transdimensional algorithms showcased in this thesis emerge as a promising tool for pushing the boundaries of seismic tomography.
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Ambient noise seismic tomography has proven to be an effective tool for subsurface imaging, particularly in volcanic regions such as the Reykjanes Peninsula (RP), SW Iceland, where ambient seismic noise is ideal with isotropic illumination. The primary purpose of this study is to obtain a reliable shear wave velocity model of the RP, to get a better understanding of the subsurface structure of the RP and how it relates to other geoscientific results. This is the first tomographic model of the RP which is based on both on- and off-shore seismic stations. We use the ambient seismic noise data and apply a novel algorithm called one-step 3-D transdimensional tomography. The main geological structures in the study area (i.e. covered by seismic stations) are the four NE-SW trending volcanic systems, orientated highly oblique to the plate spreading on the RP. These are from west to east; Reykjanes, Eldvörp-Svartsengi, Fagradalsfjall and Krýsuvík, of which all except Fagradalsfjall host a known high-temperature geothermal field. Using surface waves retrieved from ambient noise recordings, we recovered a 3-D model of shear wave velocity. We observe low-velocity anomalies below these known high-temperature fields. The observed low-velocity anomalies below Reykjanes and Eldvörp-Svartsengi are significant but relatively small. The low-velocity anomaly observed below Krýsuvík is both larger and stronger, oriented near-perpendicular to the volcanic system, and coinciding well with a previously found low-resistivity anomaly. A low-velocity anomaly in the depth range of 5-8 km extends horizontally along the whole RP, but below the high-temperature fields, the onset of the velocity decrease is shallower, at around 3 km depth. This is in good agreement with the brittle-ductile transition zone on the RP. In considerably greater detail, our results confirm previous tomographic models obtained in the area. This study demonstrates the potential of the entirely data-driven, one-step 3-D transdimensional ambient noise tomography as a routine tomography tool and a complementary seismological tool for geothermal exploration, providing an enhanced understanding of the upper crustal structure of the RP.

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A geomechanics program for wellbore stability analysis has been developed consisting of two modules: an analytical-based solution and a numerical-based solution. In the first part, input data are imported, including petrophysical well logs, pressure data, formation well tops, and a well path. Lithology intervals are set with proper prediction equations to calculate rock mechanical properties based on laboratory tests. In-situ stress and pore pressure are determined using different methods, including the poroelastic plane strain model and stress polygon. From the theory of plane strain, new equations are solved to determine horizontal tectonic strains (ϵ h, ϵ H) from drilling events such as total mud loss and breakout during drilling. Safe mud weight bounds are calculated through depth and in different azimuths and inclinations applying the Mohr-Coulomb and the Mogi-Coulomb failure criteria. The latter underestimated the minimum mud weight to prevent wellbore breakout. The transversely vertical isotropy of shale formation is programmed with multiple stress transformations via the weak-plane method. In the second module, a 3D model around the wellbore is discretized with hexahedral eight-point elements and programmed using the finite-element (FE) method. Rock mechanical property and displacement boundary conditions are applied to solve FE equations. Stress from the numerical model matched to the Kirsch model and results show that maximum stress concentration around the wellbore corresponds to the wellbore breakout, which has analytically been established. A new well plan across the 3D model was examined to obtain the safe mud weight bounds and results were in agreement with the analytical calculations.

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We report on a Bayesian (i.e., probabilistic) inversion for the shear-wave velocity structure of the Reykjanes peninsula, SW Iceland. Travel times of Rayleigh waves traversing the peninsula served as input to the probabilistic algorithm. These Rayleigh waves were retrieved through the application of seismic interferometry to yearlong recordings of ambient seismic noise. The Reykjanes peninsula is well placed for this technique because it is surrounded by ocean, which implies a relatively uniform seismic noise illumination; the latter being a condition for accurate interferometric surface wave retrieval. The Bayesian algorithm uses a variable model parametrization by employing Voronoi cells in conjunction with a reversible jump Markov chain Monte Carlo sampler. The algorithm is entirely data-driven, meaning that, contrary to conventional deterministic tomographic inversions, the user does not need to define any regularization or parameterization parameters to solve the inverse problem. The geology in the area of interest is characterized by four NE-SW trending volcanic systems, orientated oblique to the divergent plate boundary cutting across the Reykjanes Peninsula. These are from west to east; Reykjanes, Svartsengi, Fagradalsfjall and Krýsuvík, of which all except Fagradalsfjall host a known high-temperature geothermal field. We observe relatively high shear wave velocity patches close to the Earth’s surface (top two kilometers) at the location of these known high-temperature fields. These high velocity anomalies invert to relatively low shear wave velocities (in comparison to shear wave velocities in the same horizontal plane) at depths greater than 3 km. The latter low-velocity anomalies are relatively small below Reykjanes and Svartsengi. At depths of 5 to 8 km, a low-velocity anomaly extends horizontally below Reykjanes and Svartsengi, correlating relatively well with the inferred brittle-ductile transition below the high-temperature fields at 4-5 km depth. The low-velocity anomaly below Krýsuvík is much larger and coincides with a deep-seated low electrical resistivity anomaly. Horizontally, it coincides with the center of an inflation source at 4–5 km depth. For example, in 2010 this resulted in an uplift exceeding 50 mm/year, but several periods of alternating uplift and subsidence associated with increased seismicity have been observed in Krýsuvík since 2009. Our results both confirm and add details to previous models obtained in the area. Our study demonstrates the potential of Bayesian surface wave inversion as a complementary geophysical tool for geothermal exploration. @en

Seismic travel time tomography using surface waves is an effective tool for three-dimensional crustal imaging. Historically, these surface waves are the result of active seismic sources or earthquakes. More recently, however, surface waves retrieved through the application of seismic interferometry have also been exploited. Conventionally, two-step inversion algorithms are employed to solve the tomographic inverse problem. That is, a first inversion results in frequency-dependent, two-dimensional maps of phase velocity, which then serve as input for a series of independent, one-dimensional frequency-to-depth inversions. As such, a set of localized depth-dependent velocity profiles are obtained at the surface points. Stitching these separate profiles together subsequently yields a three-dimensional velocity model. Relatively recently, a one-step three-dimensional non-linear tomographic algorithm has been proposed. The algorithm is rooted in a Bayesian framework using Markov chains with reversible jumps, and is referred to as transdimensional tomography. Specifically, the three-dimensional velocity field is parameterized by means of a polyhedral Voronoi tessellation. In this study, we investigate the potential of this algorithm for the purpose of recovering the three-dimensional surface-wave-velocity structure from ambient noise recorded on and around the Reykjanes Peninsula, southwest Iceland. To that end, we design a number of synthetic tests that take into account the station configuration of the Reykjanes seismic network. We find that the algorithm is able to recover the 3D velocity structure at various scales in areas where station density is high. In addition, we find that the standard deviation of the recovered velocities is low in those regions. At the same time, the velocity structure is less well recovered in parts of the peninsula sampled by fewer stations. This implies that the algorithm successfully adapts model resolution to the density of rays. It also adapts model resolution to the amount of noise in the travel times. Because the algorithm is computationally demanding, we modify the algorithm such that computational costs are reduced while sufficiently preserving non-linearity. We conclude that the algorithm can now be applied adequately to travel times extracted from station–station cross correlations by the Reykjanes seismic network.@en