Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

2D Basement Relief Inversion using Sparse Regularization

Francisco Márcio Barboza, Arthur Anthony da Cunha Romão E Silva, Bruno Motta de Carvalho

Abstract

Basement relief gravimetry is crucial in geophysics, especially for oil exploration and mineral prospecting. It involves solving an inverse problem to infer geological model parameters from observed data. The model represents basement relief with constant-density prisms, and the data reflect gravitational anomalies from these prisms. Inverse problems are often ill-posed, meaning small data changes can lead to large solution variations. To mitigate this, regularization techniques like Tikhonov's are used to stabilize solutions. This study compares regularization methods applied to gravimetric inversion, including Smoothness Constraints, Total Variation, Discrete Cosine Transform (DCT), and Discrete Wavelet Transform (DWT) using Daubechies D4 wavelets. Optimization, particularly with Genetic Algorithms (GA), is used to find prism depths that best match observed anomalies. GA, inspired by natural selection, selects the best solutions to minimize the objective function. The results, evaluated through fit metrics and error analysis, show the effectiveness of all regularization methods and GA, with the Smoothness constraint performing best in synthetic models. For the real data model, all methods performed similarly.

2D Basement Relief Inversion using Sparse Regularization

Abstract

Basement relief gravimetry is crucial in geophysics, especially for oil exploration and mineral prospecting. It involves solving an inverse problem to infer geological model parameters from observed data. The model represents basement relief with constant-density prisms, and the data reflect gravitational anomalies from these prisms. Inverse problems are often ill-posed, meaning small data changes can lead to large solution variations. To mitigate this, regularization techniques like Tikhonov's are used to stabilize solutions. This study compares regularization methods applied to gravimetric inversion, including Smoothness Constraints, Total Variation, Discrete Cosine Transform (DCT), and Discrete Wavelet Transform (DWT) using Daubechies D4 wavelets. Optimization, particularly with Genetic Algorithms (GA), is used to find prism depths that best match observed anomalies. GA, inspired by natural selection, selects the best solutions to minimize the objective function. The results, evaluated through fit metrics and error analysis, show the effectiveness of all regularization methods and GA, with the Smoothness constraint performing best in synthetic models. For the real data model, all methods performed similarly.

Paper Structure

This paper contains 13 sections, 9 equations, 13 figures, 3 tables, 1 algorithm.

Table of Contents

  1. INTRODUCTION
  2. METHODOLOGY
  3. Inverse Problem
  4. Regularization
  5. Smoothness
  6. Total Variation
  7. Sparsity
  8. Genetic Algorithms
  9. RESULTS AND DISCUSSION
  10. Isolated Graben
  11. Two Sub-basins
  12. Bridge of the Poema
  13. CONCLUSION

Figures (13)

  • Figure 1: (a) Gravimetric anomaly and (b) sedimentary basin showing basement topography $S$ and an interpretive model formed by a set of $M$ juxtaposed 2D rectangular prisms with height $p_{j}$. Source: santos2013inversao
  • Figure 2: (a) True synthetic model of isolated graben and (b) observed gravimetric data set from the model in question.
  • Figure 3: Result of the average of 10 inversions of the isolated graben model using constraint (a) DCT, (b) DWT, (c) SV, and (d) VT.
  • Figure 4: Relative error between the data from the true isolated graben model and the average of 10 inversions in each addressed constraint.
  • Figure 5: Convergence curve of the functional with the constraints used in the inversion of gravimetric data from the isolated graben model.
  • ...and 8 more figures