Theories and methods of inverse problems are driven by applied issues in science and engineering. The study of inverse problems has been an exciting and appealing topic in recent decades. Inverse problems are of particular importance in the field of natural sciences, as it is an interdisciplinary discipline related to mathematics, physics, chemistry, astronomy, geosciences, biology, finance, business, life sciences, computational technology, and engineering. Geophysical inverse problems are pivotal branches in inversion community, which possess both theoretical characteristics of the inverse problem itself and practical difficulties of engineering applications. The advantages and disadvantages of the inversion are the keys to the success of inversion methods. Therefore, it is of great significance and necessity to carry out the research regarding practical and reliable numerical methods of the geophysical inversion.
Geophysical inverse problems face a lot of issues to be solved:
1. Data noise: General data records contain a lot of noise due to various factors in the excitation, propagation, and reception processes, and are generally band-limited, making it difficult to fully restore the true appearance of the model medium as inversion results.
2. Model selection: The real medium is often very complex, in order to facilitate the solution, so that we generally have to simplify physical equations, as this simplification will inevitably bring model errors leading to difficulty in practical applications.
3. Ill-posed nature: The inversion process is a complex nonlinear problem, and actual inverse problems are often ill-posed with the empirical selection of initial guess, which causes multiple solutions and low resolution of inversion results.
4. Large scale computing: The media model in the actual calculation is very large, and it is usually essential to implement numerical discretization of original continuous problems and carry out finite dimensional approximation, due to the dimensionality effect, we need to solve a large algebraic system of equations, which leads to a huge amount of computation and storage for solving ill-posed nonlinear problems.
Geophysical inverse problems are typically ill-posed in the sense that three items relating to the solution, namely existence, uniqueness, and stability, are challenging to be satisfied simultaneously. In addition, even a solution exists, its uncertainty still needs to be quantified. Standard methods for inverse problems are regularization methods, whereas optimization methods are widely employed in science and engineering fields. Consequently, in this Research Topic, we focus on computational methods for geophysical inverse problems. More advanced techniques and novel applications in earth science are particularly welcome.
Potential contributions include, but are not limited to:
• Theories of inverse and ill-posed problems
• Regularization techniques and recent development
• Optimization theories and methods in geophysics
• Statistical inversion in geophysics
• Big data and machine learning in geophysics
• High performance computing
• Case studies in geophysical exploration
Theories and methods of inverse problems are driven by applied issues in science and engineering. The study of inverse problems has been an exciting and appealing topic in recent decades. Inverse problems are of particular importance in the field of natural sciences, as it is an interdisciplinary discipline related to mathematics, physics, chemistry, astronomy, geosciences, biology, finance, business, life sciences, computational technology, and engineering. Geophysical inverse problems are pivotal branches in inversion community, which possess both theoretical characteristics of the inverse problem itself and practical difficulties of engineering applications. The advantages and disadvantages of the inversion are the keys to the success of inversion methods. Therefore, it is of great significance and necessity to carry out the research regarding practical and reliable numerical methods of the geophysical inversion.
Geophysical inverse problems face a lot of issues to be solved:
1. Data noise: General data records contain a lot of noise due to various factors in the excitation, propagation, and reception processes, and are generally band-limited, making it difficult to fully restore the true appearance of the model medium as inversion results.
2. Model selection: The real medium is often very complex, in order to facilitate the solution, so that we generally have to simplify physical equations, as this simplification will inevitably bring model errors leading to difficulty in practical applications.
3. Ill-posed nature: The inversion process is a complex nonlinear problem, and actual inverse problems are often ill-posed with the empirical selection of initial guess, which causes multiple solutions and low resolution of inversion results.
4. Large scale computing: The media model in the actual calculation is very large, and it is usually essential to implement numerical discretization of original continuous problems and carry out finite dimensional approximation, due to the dimensionality effect, we need to solve a large algebraic system of equations, which leads to a huge amount of computation and storage for solving ill-posed nonlinear problems.
Geophysical inverse problems are typically ill-posed in the sense that three items relating to the solution, namely existence, uniqueness, and stability, are challenging to be satisfied simultaneously. In addition, even a solution exists, its uncertainty still needs to be quantified. Standard methods for inverse problems are regularization methods, whereas optimization methods are widely employed in science and engineering fields. Consequently, in this Research Topic, we focus on computational methods for geophysical inverse problems. More advanced techniques and novel applications in earth science are particularly welcome.
Potential contributions include, but are not limited to:
• Theories of inverse and ill-posed problems
• Regularization techniques and recent development
• Optimization theories and methods in geophysics
• Statistical inversion in geophysics
• Big data and machine learning in geophysics
• High performance computing
• Case studies in geophysical exploration