A trans-dimensional polynomial-spline parameterization for gradient-based geoacoustic inversion

Abstract

This paper presents a polynomial spline-based parameterization for trans-dimensional geoacoustic inversion. The parameterization is demonstrated for both simulated and measured data and shown to be an effective method of representing sediment geoacoustic profiles dominated by gradients, as typically occur, for example, in muddy seabeds. Specifically, the spline parameterization is compared using the deviance information criterion (DIC) to the standard stack-of-homogeneous layers parameterization for the inversion of bottom-loss data measured at a muddy seabed experiment site on the Malta Plateau. The DIC is an information criterion that is well suited to trans-D Bayesian inversion and is introduced to geoacoustics in this paper. Inversion results for both parameterizations are in good agreement with measurements on a sediment core extracted at the site. However, the spline parameterization more accurately resolves the power-law like structure of the core density profile and provides smaller overall uncertainties in geoacoustic parameters. In addition, the spline parameterization is found to be more parsimonious, and hence preferred, according to the DIC. The trans-dimensional polynomial spline approach is general, and applicable to any inverse problem for gradient-based profiles. [Work supported by ONR.].

Taming uncertainty in geophysical inversion

“…These include seismic travel time and waveform tomography (Bodin and Sambridge, (2009), Bodin et al, 2012a, Hawkins & Sambridge (2015; geophysical imaging of the crust with seismic, ground based and airborne EM, Piana-Agostinetti and Malinverno (2010), Brodie, and Sambridge, (2012), Bodin et al, (2012b); Local earthquake tomography, Piana-Agostinetti et al (2015); Geoacoustic acoustic imaging of sea-bed and near surface properties, Dettmer and Dosso (2010), Dettmer et al (2012a&b), Steininger et al (2014) and more recently seismic and Tsunami source studies, Dettmer et al (2014). Trans-D approaches have also begun to make a mark in exploration geophysics.…”

Meso-scale seabed quantification with geoacoustic inversion

“…The conditional priors are uniform over a defined area and are used to constrain parameters that often correlate in nature—porosity β and compressional grain-grain modulus γ p as P ( β ∣ γ p ) (Supplementary Table 2 ) and compressional sound speed c p and density ρ as P ( c p ∣ ρ ) (Supplementary Table 3 ). The conditional prior distribution of c p and ρ is based on laboratory and in situ measurements 38 , 50 and has been used in previous studies with slight modifications 51 , 52 . It consists of the area between empirical lower and upper bound curves for c p as a function of ρ , with each curve of the form where g 1 to g 5 are fit parameters.…”

Bayesian geoacoustic inversion using mixture density network

“…The model parameter estimates and uncertainties can be characterized by the moments of the multidimensional PPD, such as the optimal model estimates (e.g., the posterior mean model, the maximum a posteriori (MAP) model), marginal probability density function (PDF) of the model parameter and the interparameter relationships (covariance matrix). Bayesian inversion has been applied to solve geoacoustic inverse problem since the 1990s (Gerstoft 1994b;Mosegaard & Tarantola 1995) and widely used during the past two decades (e.g., Dosso 2002;Dosso & Wilmut 2006;Bodin & Sambridge 2009;Dong & Dosso 2011;Dosso & Dettmer 2011;Steininger et al 2014;Galetti et al 2017;Zhang et al 2018).…”