Transdimensional surface wave inversion

Abstract

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.