Geophysical inversion versus machine learning in inverse problems

Abstract

Geophysical inversion and machine learning both provide solutions for inverse problems in which we estimate model parameters from observations. Geophysical inversions such as impedance inversion, amplitude-variation-with-offset inversion, and traveltime tomography are commonly used in the industry to yield physical properties from measured seismic data. Machine learning, a data-driven approach, has become popular during the past decades and is useful for solving such inverse problems. An advantage of machine learning methods is that they can be implemented without knowledge of physical equations or theories. The challenges of machine learning lie in acquiring enough training data and selecting relevant parameters, which are essential in obtaining a good quality model. In this study, we compare geophysical inversion and machine learning approaches in solving inverse problems and show similarities and differences of these approaches in a mathematical form and numerical tests. Both methods aid in solving ill-posed and nonlinear problems and use similar optimization techniques. We take reflectivity inversion as an example of the inverse problem. We apply geophysical inversion based on the least-squares method and artificial neural networks as a machine learning approach to solve reflectivity inversion using 2D synthetic data sets and 3D field data sets. A neural network with multiple hidden layers successfully generates the nonlinear mapping function to predict reflectivity. For this inverse problem, we test different L1 regularizers for both approaches. L1 regularization alleviates effects of noise in seismic traces and enhances sparsity, especially in the least-squares method. The 2D synthetic wedge model and field data examples show that neural networks yield high spatial resolution.

An iterative process for efficient optimisation of parameters in geoscientific models: a demonstration using the Parallel Ice Sheet Model (PISM) version 0.7.3

“…- Kingslake et al (2018) simulate the evolution of the AIS over the past 205 000 years using a horizontal resolution of 15 km. An ensemble approach is used to sample uncertain parameters, with the ranges used for optimisation, and the final reference state selected, shown in Table 1.…”

“…We are only aware of one previous study that has varied the effective till pressure scaling factor parameter: Kingslake et al (2018) explored values in the range 0.02-0.05, with a reference value of 0.04. We use the range 0.01-0.05 as the initial range in this study.…”

Massive database generation for 2.5D borehole electromagnetic measurements using refined isogeometric analysis

“…Jon Ander Rivera: Investigation, methodology, software; David Pardo: Funding acquisition, project administration, resources, supervision, writing-review & editing. 2007; Shen et al, 2020), and artificial intelligence based methods (Kim and Nakata, 2018;Liu and Grana, 2019;Yang and Ma, 2019;Li et al, 2020). In geosteering EM measurements, deep learning (DL) methods with advanced encoder-decoder neural networks have recently demonstrated to be suitable to solve inverse problems (Shahriari et al, 2020a,b).…”

An iterative process for efficient optimisation of parameters in geoscientific models: a demonstration using the Parallel Ice Sheet Model (PISM) version 0.7.3

“…Machine learning techniques aim to enumerate unspecified relationships between input and output datasets, without requiring any understanding of the underlying physical processes (e.g. DeVries et al, 2017; Kim and Nakata, 2018). This allows for the discovery and utilisation of previously-unknown relationships, but does raise questions regarding the applicability for states that lie outside the range spanned by the training datasets.…”