Bayesian inversion of refraction seismic traveltime data

Abstract

S U M M A R YWe apply a Bayesian Markov chain Monte Carlo (McMC) formalism to the inversion of refraction seismic, traveltime data sets to derive 2-D velocity models below linear arrays (i.e. profiles) of sources and seismic receivers. Typical refraction data sets, especially when using the far-offset observations, are known as having experimental geometries which are very poor, highly ill-posed and far from being ideal. As a consequence, the structural resolution quickly degrades with depth. Conventional inversion techniques, based on regularization, potentially suffer from the choice of appropriate inversion parameters (i.e. number and distribution of cells, starting velocity models, damping and smoothing constraints, data noise level, etc.) and only local model space exploration. McMC techniques are used for exhaustive sampling of the model space without the need of prior knowledge (or assumptions) of inversion parameters, resulting in a large number of models fitting the observations. Statistical analysis of these models allows to derive an average (reference) solution and its standard deviation, thus providing uncertainty estimates of the inversion result. The highly non-linear character of the inversion problem, mainly caused by the experiment geometry, does not allow to derive a reference solution and error map by a simply averaging procedure. We present a modified averaging technique, which excludes parts of the prior distribution in the posterior values due to poor ray coverage, thus providing reliable estimates of inversion model properties even in those parts of the models. The model is discretized by a set of Voronoi polygons (with constant slowness cells) or a triangulated mesh (with interpolation within the triangles). Forward traveltime calculations are performed by a fast, finite-difference-based eikonal solver. The method is applied to a data set from a refraction seismic survey from Northern Namibia and compared to conventional tomography. An inversion test for a synthetic data set from a known model is also presented.

Relocation of earthquakes in the Southern and Eastern Alps (Austria, Italy) recorded by the dense, temporary SWATH–D network using a Markov chain Monte Carlo inversion

“…Considering that hypocenter locations and velocity model are inherently linked to each other (coupled hypocenter-velocity problem, e.g., Kissling, 1988;Thurber, 1992;Kissling et al, 1994) especially in the local earthquake case, it is indicated to simultaneously invert for hypocenters and velocity structure (and/or station corrections). In this study, we use a Bayesian approach (Bayes, 1763), which has been applied in a number of geophysical studies (Tarantola et al, 1982;Duijndam, 1988a,b;Mosegaard and Tarantola, 1995;Gallagher et al, 2009;Bodin et al, 2012a,b;Ryberg and Haberland, 2018). This approach 8 https://doi.org/10.5194/se-2020-192 Preprint.…”

Bayesian simultaneous inversion for local earthquake hypocentres and 1-D velocity structure using minimum prior knowledge

“…This leads to characteristic shifts when calculating conventional average values to determine a reference (mean) model. However, to be able to derive a reference model, Ryberg & Haberland (2018) suggested a modified averaging procedure (in the following we use the term modified averages). Essentially, only velocity value samples with a probability exceeding the prior distribution are taken into account to calculate averages and standard deviations.…”

“…Essentially, only velocity value samples with a probability exceeding the prior distribution are taken into account to calculate averages and standard deviations. Details can be found in Ryberg & Haberland (2018).…”

“…McMC have recently gained a lot of attention in a broad range of geophysical disciplines such as waveform fitting (Mosegaard 1998), ambient noise tomography (Bodin et al 2012a) or electrical resistivity inversion (Schott et al 1999). In a recent paper, we used a McMC method to derive 2-D velocity models from refraction seismic data sets (Ryberg & Haberland 2018). Gesret et al (2015) applied a two-step approach of first using a Monte Carlo method to invert controlled source data to derive a velocity model, and then locate-again using a probabilistic framework-earthquakes using the previously derived velocity model.…”

Towards large‐scale stochastic refraction tomography: a comparison of three evolutionary algorithms

“…Rumpf and Tronicke () used a particle swarm optimizer to solve the tomographic problem and quantify uncertainties using a one‐dimensional layer‐based model parameterization. More recently, Ryberg and Haberland () directly applied a Bayesian MCMC formalism to invert refraction data and parameterized the velocity model using Voronoi tesselation and triangulated meshes. To our knowledge, no study has been published on the application of EA to the seismic tomography problem for a large number of model parameters.…”