Multimodal Layered Transdimensional Inversion of Seismic Dispersion Curves With Depth Constraints

Abstract

MuLTI (Multimodal Layered Transdimensional Inversion) is a Markov chain Monte Carlo implementation of Bayesian inversion for the probability distribution of shear wave velocity (Vs) as a function of depth. Based on Multichannel Analysis of Surface Wave methods, it requires as data (i) a Rayleigh‐wave dispersion curve and (ii) additional layer depth constraints, the latter we show significantly improve resolution compared to conventional unconstrained inversions. Such depth constraints may be drawn from any source (e.g., boreholes, complementary geophysical data) provided they also represent a seismic interface. We apply MuLTI to a Norwegian glacier, Midtdalsbreen, in which ground‐penetrating radar was used to constrain internal layers of snow, ice, and subglacial sediments, with transitions at 2 and 25.5 m, and whose Vs is assumed to be in the range 500–1,700, 1,700–1,950, and 200–2,800 m/s, respectively. Synthetic modeling demonstrates that MuLTI recovers the true model of Vs variation with depth. Significantly, compared to inversions without depth constraints, in this synthetic case MuLTI not only reduces by about a factor of 10 the error between the true and the best fitting model, but also reduces by a factor of 2 the vertically averaged spread of the distribution of Vs based on the 95% credible intervals. We further show that using frequencies above about 100 Hz lead to unconverged solutions due to mode ambiguities associated with fine spatial structures. For our acquired data on Midtdalsbreen, we use 14‐100 Hz data for which MuLTI produces a large‐scale converged inversion.

Characterisation of subglacial water using a constrained transdimensional Bayesian Time Domain Electromagnetic Inversion

“…This paper has presented the inversion algorithm 'MuLTI-TEM', used to overcome such problems. Our method uses a transdimensional Bayesian inversion approach adapted from the MuLTI algorithm (Killingbeck et al, 2018), which incorporates independent depth constraints to limit the solution space reducing ambiguity. Synthetic testing of multiple different scenarios representing a small glacier underlain by sediment showed the addition of depth constraints greatly improves numerical convergence and a reduction in misfit.…”

“…It is adapted from the MuLTI algorithm ('Multimodal Layered Transdimensional Inversion), developed for seismic surface wave inversions (see detailed in Killingbeck et al (2018)). The data input, d, to MuLTI-TEM are the measured voltages ( ) at each timegate ( ), together with an estimate of their uncertainty ( ) derived from the variance of each data point calculated from the stack recordings:…”

“…We describe the 1D variation of resistivity with depth as a piecewise constant function using Voronoi nuclei (see Killingbeck et al, 2018). Any available depth constraints separate the resistivity into different depth layers.…”

“…Table A1. Inversion parameters used in MuLTI-TEM for the synthetic feasibility study and 1D and 2D real data inversions, explained further in Killingbeck et al (2018). Burn in number is the number of iterations discounted at the start of the chain to remove any dependencies of the initial conditions.…”

“…This method is adapted from a transdimensional Bayesian framework, termed 'MuLTI' and described in Killingbeck et al (2018), originally applied to characterise subglacial sediment distribution from seismic surface wave data (Killingbeck et al, 2019). Here, we explore a similar concept for the TEM method.…”