Developments in mathematics are fundamental driving forces for all geophysical studies but are often overlooked. New algorithms in harmonic analysis, dimensionality reduction, dictionary learning, deep learning, and other fields always lead to significant advancements in geophysical data processing, imaging, and inversion. In the past decade, we have witnessed considerable progress in machine learning and its successful applications to geophysics.

The demand for advanced mathematical methods in geophysics is continuously increasing. New acquisition techniques provide high-density and large-volume data that keep challenging the capacity of existing methods. Modern quantitative analysis requires high-resolution estimation of multiple parameters, including rock and fluid properties,...

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