Use of Machine Learning to Estimate Statistics of the Posterior Distribution in Probabilistic Inverse Problems—An Application to Airborne EM Data. Issue 11 (31st October 2022)

• Record Type: Journal Article
• Authors: Hansen, T. M.; Finlay, C. C.
• Is Part Of: Journal of geophysical research. Volume 127:Issue 11(2022)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2022-10-31
• Subjects: inversion -- probabilistic -- machine learning -- neural network; Geomagnetism -- Periodicals; Geochemistry -- Periodicals; Geophysics -- Periodicals; Earth sciences -- Periodicals; 551.1
• DOI: 10.1029/2022JB024703
• Languages: English
• ISSNs: 2169-9313

Abstract

Abstract: The solution to a probabilistic inverse problem is the posterior probability distribution for which a full analytic expression is rarely possible. Sampling methods are therefore often used to generate a sample from the posterior. Decision‐makers may be interested in the probability of features related to model parameters (e.g., existence of pollution or the cumulative clay thickness) rather than the individual realizations themselves. Such features and their associated uncertainty, are simple to compute once a sample from the posterior distribution has been generated. However, sampling methods are often associated with high computational costs, especially when the prior and posterior distribution is non‐trivial (non‐Gaussian), and when the inverse problem is non‐linear. Here we demonstrate how to use a neural network to directly estimate posterior statistics of continuous or discrete features of the posterior distribution. The method is illustrated on a probabilistic inversion of airborne EM data from Morrill Nebraska, where the forward problem is nonlinear and the prior information is non‐Gaussian. Once trained the application of the network is fast, with results similar to those obtained using much slower sampling methods. Plain Language Summary: Probabilistic inversion is in principle ideal as a method for combining available information about geo‐models, in a way that will allow detailed risk analysis and hypothesis testing based on available information. However, practical use of such methods has historically been limited because they (a) require computationally expensive numerical algorithms and (b) typically rely on relatively simple assumptions about the model. Machine learning‐based methods, such as neural networks, provide an alternative approach to probabilistic inversion. We discuss using neural networks to estimate in principle any statistics about continuous or discrete statistical features of the combined information, such as "What is the probability that a specific lithology exists below a certain depth?". A focus is on the use of realistic/complex assumptions. As an example, the method is demonstrated on a probabilistic inversion of airborne electromagnetic data, and it is demonstrated as accurate, fast, and allows analysis of many (>100.000) 1D soundings per second, making it applicable to very large data sets. Key Points: A machine learning approach for the probabilistic solution of inverse problems by directly estimating posterior statistics of any continuous or discrete feature of the posterior distribution Allows the use of complex prior information and noise models Demonstrated non‐linear probabilistic inversion of airborne electromagnetic; enables analysis of more than 10 5 1D soundings per second