Our research program, with connections outlined in the mind map, involves the following main components:

Seismic data acquisition — where we leverage recent developments in compressive sensing towards the development of new (randomized) seismic acquisition and recovery schemes that include

  • simultaneous marine acquisition with jittered sampling and randomly placed ocean bottom nodes yielding a new sampling scheme that reduces acquisition costs and improves sampling rates of full-azimuthal sampling.
  • 4-D seismic data acquisition with less reliance on repeatability in acquisition.

Objectives. Design and implementation of new seismic-data acquisition methodologies that reduce costs by exploiting structure in seismic data.

Outcomes. Development of a new paradigm for seismic data acquisition and sparsity/low-rank-promoting recovery that will allow us to acquire high-resolution wide azimuth seismic data volumes at significantly reduced costs. Our technology will be a key enabler for full-waveform inversion by pushing access to both the low and high end of the spectrum.

Seismic data processing — where we leverage recent developments in sparse and rank-revealing optimization methods that include

  • curvelet-based missing-trace interpolation with co-sparsity promotion, which improves recovery for certain redundant transforms.
  • extension of estimation of primaries by sparse inversion to 3-D, which is an alternative formulation to SRME and that is computationally affordable.
  • missing trace-trace interpolation with matrix or tensor factorizations, which is computationally affordable while avoiding redundancy of transform-domain methods such as curvelets.

Objectives. Wave-equation-based mitigation of the free surface by sparse inversion and recovery of incomplete data.

Outcomes. A robust framework for the estimation of surface-free Green’s functions (multiple-free data) and source signatures that serve as input to imaging, migration-velocity analysis, and full-waveform inversion.

Seismic modelling — where we leverage recent developments wave simulators and streaming field-programmable gate-array (FPGA) hardware that include

  • optimized (on FPGA) preconditioner for the time-harmonic Helmholtz solver for frequency domain solvers yielding a computationally efficient solver suitable for reverse-time migration and full-waveform inversion.
  • optimized (on FPGA) time-stepping method for wave-equation solvers yielding a computationally efficient solver suitable for reverse-time migration and full-waveform inversion.

Objectives. Design and implementation of efficient wavefield simulators in 2- and 3-D.

Outcomes. Concrete implementation of a scalable virtually parameter-free object-oriented parallel simulation framework in 2- and 3-D for time-harmonic wave equations including explicit control of simulation accuracy, matrix-free definition of the linearized Born scattering operator (the Jacobian) and its adjoint the reverse-time migration operator (adjoint of the Jacobian).

Seismic wave-equation based imaging—where we leverage recent developments in sparse recovery and imaging with multiples that includes

  • extension of fast sparsity-promoting imaging to 3D yielding a formulation for least-squares reverse-time migration in 3D that has roughly the cost of a single migration.
  • extension of imaging with surface-related multiples to 3D yielding an imaging scheme that is fast, images surface-related multiples and that estimates the source function on the fly.
  • migration-velocity analysis with the double two-way wave equation yielding an automatic velocity model building technology that uses both reflected and turning waves.

Objectives. Design and implementation of an efficient and robust wave-equation based inversion framework leveraging recent developments in machine learning, sparse recovery, robust statistics, and optimization.

Outcomes. An efficient, concrete, and versatile imaging framework accelerated by message passing and improved by curvelet-domain sparsity promotion by leveraging the free surface and properties of extended image volumes.

Seismic full-waveform inversion (FWI) —where we leverage recent developments in machine learning and PDE constrained optimization that include

  • Extension of our efficient badging techniques for 3-D FWI to multiparameter (anisotropic, elastic, etc.) case, yielding a fast implementation based on our fast wave simulators.
  • New workflows for FWI that allow us to work with elastic data, which include the use of curvelets for signal separation, yielding a robust scheme for the inversion of elastic data with an incomplete (e.g. acoustic) wave simulator.
  • Extension of our new penalty formulation to 3-D and to more general wave physics, yielding a scheme for FWI that requires less accurate initial models to guarantee convergence.

Objectives. Development of a fast and versatile framework for FWI.

Outcomes. A fast and robust framework for full-waveform inversion that removes some of the impediments of computational complexity, by using randomized dimensionality-reduction techniques, some of reliance on accurate wave physics, by using misfit functionals derived from robust statistics, and some of the reliance of accurate starting models by enlarging the search space of the optimization.

Case studies: Wave-equation based inversion on industrial data–where we leverage our tools to solve industry-scale problems in above areas of exploration seismology.

SINBAD—DNOISE: a step-change from 2D to 3D seismic.

The document, which outlines the future research plans including getting access to HPC equipment, is available upon request from Felix Herrmann.