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The mixed Lp-norm, 0 ≤ p ≤ 2, stabilization algorithm is flexible for constructing a suite of subsurface models with either distinct, or a combination of, smooth, sparse, or blocky structures. This general purpose algorithm can be used for the inversion of data from regions with different subsurface characteristics. Model interpretation is improved by simulta- neous inversion of multiple data sets using a joint inversion approach. An effective and general algorithm is presented for the mixed Lp-norm joint inversion of gravity and magnetic data sets. The imposition of the structural cross-gradient enforces similarity between the reconstructed models. For efficiency the implementation relies on three crucial realistic details; (i) the data are assumed to be on a uniform grid providing sensitivity matrices that decompose in block Toeplitz Toeplitz block form for each depth layer of the model domain and yield efficiency in storage and computation via 2D fast Fourier transforms; (ii) matrix-free implementation for calculating derivatives of parameters reduces memory and computational overhead; and (iii) an alternating updating algorithm is employed. Balancing of the data misfit terms is imposed to assure that the gravity and magnetic data sets are fit with respect to their individual noise levels without overfitting of either model. Strategies to find all weighting parameters within the objective function are described. The algorithm is validated on two synthetic but complicated models. It is applied to invert gravity and magnetic data acquired over two kimberlite pipes in Botswana, producing models that are in good agreement with borehole information available in the survey area.
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A machine learning approach to joint gravity and cosmic-ray muon inversion at Mt Usu, Japan
SUMMARY The ability to accurately and reliably obtain images of shallow subsurface anomalies within the Earth is important for hazard monitoring and a fundamental understanding of many geologic structures, such as volcanic edifices. In recent years, machine learning (ML) has gained increasing attention as a novel approach for addressing complex problems in the geosciences. Here we present an ML-based inversion method to integrate cosmic-ray muon and gravity data sets for shallow subsurface density imaging at a volcano. Starting with an ensemble of random density anomalies, we use physics-based forward calculations to find the corresponding set of expected gravity and muon attenuation observations. Given a large enough ensemble of synthetic density patterns and observations, the ML algorithm is trained to recognize the expected spatial relations within the synthetic input–output pairs, learning the inherent physical relationships between them. Once trained, the ML algorithm can then interpolate the best-fitting anomalous pattern given data that were not used in training, such as those obtained from field measurements. We test the validity of our ML algorithm using field data from the Showa-Shinzan lava dome (Mt Usu, Japan) and show that our model produces results consistent with those obtained using a more traditional Bayesian joint inversion. Our results are similar to the previously published inversion, and suggest that the Showa-Shinzan lava dome consists of a relatively high-density (2200–2400 km m–3) cylindrical anomaly, about 300 m in diameter. Adding noise to synthetic training and testing data sets shows that, as expected, the ML algorithm is most robust in areas of high sensitivity, as determined by the forward kernels. Overall, we discover that ML offers a viable alternate method to a Bayesian joint inversion when used with gravity and muon data sets for subsurface density imaging.
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- Award ID(s):
- 2120812
- PAR ID:
- 10391769
- Publisher / Repository:
- Oxford University Press
- Date Published:
- Journal Name:
- Geophysical Journal International
- Volume:
- 233
- Issue:
- 2
- ISSN:
- 0956-540X
- Format(s):
- Medium: X Size: p. 1081-1096
- Size(s):
- p. 1081-1096
- Sponsoring Org:
- National Science Foundation
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