Inversion of airborne EM data with an explicit choice of prior model

Abstract

Inversion of airborne electromagnetic (AEM) data is an under-determined inverse problem, in that infinitely many resistivity models exist that will be able to explain the observed data, within measurement errors. Therefore, additional information or constraints must be taken into account to solve the inverse problem. In deterministic approaches, the goal is to locate one optimal model that can be obtained by using some form of smoothness constraints implied through a number of regularization choices. This model, however, will not necessarily represent realistic geological features. Probabilistic methods offer an alternative in which the solution is not one model, but a collection of models, whose variability represents the uncertainty. The probabilistic approach can also rely on implicit model assumptions, representing prior information (a type of regularization information) that may or may not be consistent with the actual available information. Here, we present an approach for AEM inversion in which the prior model is explicitly chosen by a user, preferably selected based on actual prior information available and then integrated with AEM data using a general Monte Carlo based sampling approach. This approach leads to a new workflow to AEM inversion in which geological prior information is independently and explicitly chosen before inversion is carried out. The main benefit of this approach is that each model obtained will, by construction, be consistent with prior (geological) information as well as geophysical data. Through examples based on synthetic and real AEM data, we will demonstrate the methodology, not least that the choice of prior information cannot be avoided: Either it is done explicitly, or it will be chosen implicitly by the choice of method used to invert the AEM data.

Use of machine learning to estimate statistics of the posterior distribution in probabilistic inverse problems - an application to airborne EM data.

“…These data have been analyzed previously using probabilistic inversion using a 1D transdimensional prior favoring fewer isotropic layers (Minsley, 2011;Minsley et al, 2021) and a 1D prior based on a geostatistical spatially correlated prior model (T. M. Hansen & Minsley, 2019). In these cases, inversion of a sounding took 5-10 minutes of a single CPU.…”

“…In these cases, inversion of a sounding took 5-10 minutes of a single CPU. (T. M. Hansen, 2021) used a localized rejection sampler to sample the posterior, using around 1 second per sounding, using the same information as in T. M. Hansen and Minsley (2019). This work relied on the construction of a lookup table that is similar to the prior realizations corresponding to noise-free data [M * , D * ].…”

“…For this case, the same parameterization, noise model, and (initially) prior model is used as defined in T. M. Hansen and Minsley (2019). A 1D subsurface model, m, is parameterized through N m = 125 model parameters, representing the subsurface resistivity in 1m thick layers, from the surface down to 125 m depth.…”

“…A 1D subsurface model, m, is parameterized through N m = 125 model parameters, representing the subsurface resistivity in 1m thick layers, from the surface down to 125 m depth. Initially, a Gaussian type prior with a trimodal 1-D marginal distribution is used, specifically ρ 3 (m as defined in T. M. Hansen and Minsley (2019). The noise of the AEM data is assumed to be independent uncorrelated zero-mean Gaussian noise, with a standard deviation of 5 ppm (parts per million) plus 5 percent of the data value.…”

“…Once trained, the prediction of the posterior mean and standard deviation for the 451 soundings takes around 4 ms. Around 100000 1D soundings can be analyzed per second. A similar analysis will take around 451 seconds using the extended rejection sampler (T. M. Hansen, 2021), and around 6 hours using the extended Metropolis algorithm (T. M. Hansen & Minsley, 2019).…”