Seismic inversion is the process of transforming seismic data generated by active or passive sources into a quantitative description of the subsurface properties of the earth. It addresses important problems related to our energy needs, to hazards such as earthquakes and volcanic eruptions, and to the general study of Earth's interior on a planetary scale. It draws extensively from the mathematical sciences by applying tools from signal processing, elastic and electromagnetic theory, partial differential equations, harmonic analysis, inverse-problem theory, numerical analysis, optimization, and statistics.

The sheer volume of seismic data also makes it arguably the oldest area with "big data." Theoretical and engineering developments have advanced this field tremendously in the past several decades; however, there remain many fundamental open questions, ranging from uniqueness and uncertainty through the nonlinear nature of these problems.

This cluster will bring together academic and industrial researchers with the goal of addressing some of the key challenges in the analysis of inverse problems, with emphasis on reconstruction, big data and fast algorithms. Thematic topics include:

• Fast and massively parallel algorithms for the propagation and scattering of seismic waves, direct and iterative solvers and preconditioners, source dynamics.


• Stability analysis of seismic inverse problems and optimization, referred to as full waveform inversion in exploration seismology.


• Numerical techniques cutting across direct and inverse problems: multiscale and spectral finite elements, regularization, numerical homogenization, reduced-order model methods, multiscale time stepping, hybrid methods combining high frequency asymptotics with standard numerical discretization.


• Direct inverse methods in time-harmonic, time-dependent, and reduced-order model formulations.


• Data filtering and reduction for imaging a particular target (partial data analysis, redundancy), learning.