Fast and accurate solutions of the eikonal and transport equations for seismic imaging

Seismic imaging is used in industrial explorations for oil and gas to investigate, visualize and build geological models of the subsurface. The key challenge in industrial seismic imaging and processing is to improve accuracy and reduce computational costs so that decisions can be made rapidly and optimally. Recently, new methods were developed to calculate the travel time of a wave front. The methods make use of parallel computer architectures and offer a new level of computing time and accuracy. Moreover, the new approach offers possibilities for faster and more accurate amplitude computation of the seismic wave. Travel times and amplitudes could be used to model the entire wave field significantly faster than with conventional methods. The new approaches can be used to make travel time and waveform inversion faster and more practicable for frequent use. This applies to complex regions with many boundary layers or featuring inhomogeneous and anisotropic media. In addition, the improved computational efficiency could be used to optimize a subsurface model more efficiently. Faster and more accurate seismic imaging will allow for better risk analysis of potential reservoirs and continue to be a competitive driver in the oil industry. In addition, a new wave equation solver was developed which allows for efficient wave motion computations on super computer architecture. Also a novel optimization strategy was developed to bridge the gap between forward model and images of the sub surface.

This PhD project treats fundamental research questions in seismic imaging. Presently, Kalkulo has portfolio in the mathematical modelling of folds and faults in the subsurface. These methods involve mapping geological properties to 3D volumes by utilising mathematical representation of geological structures. Here, the eikonal equation is used to propagate geological surfaces through a volume. The mappings can then be used to successively undo the folding and faulting transformations on such properties, re constructing how the volume looked like prior to a particular event. In a previous PhD project funded by this scheme, strategies for efficiently solving the eikonal equation on parallel architectures, such as the graphics processing unit or GPU, were cons tructed. The project description details how the eikonal equation and derivations of it can also be used to solve both the direction that seismic rays propagate through the domain as well as the how the energy attenuates in the domain. Since 2005, Kalku lo has been developing the mathematical kernel for the Compound Earth Simulator (CES) for the construction and analysis of advanced geological models. The work on CES has raised research questions about the applicability of the methods for seismic imaging . The depth of the required research is suitable for a PhD study and detailed in the Project Description. During the PhD period, the student will focus on how the eikonal and transport equations can be used to obtain the Greens function in complex geologi cal structures, such as those found in real exploration environments. In addition, the research will focus on how such equations and associated data structures can be manipulated to allow for fast solutions on parallel architectures, such as supercomputer s and GPUs. The expected result is that this method will prove useful in seismic imaging for fast and high resolution solutions and allow Kalkulo to increase its project portfolio.