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Abstract: Accurately capturing topographic effects in wave-equation based seismic imaging algorithms such as RTM and FWI enhances their kinematic accuracy in land settings, improving imaging quality1. By representing free surface topography as an immersed boundary, complex geometries can be accurately captured whilst retaining use of cartesian, structured FD methods2. Eschewing curvilinear or unstructured grids, immersed boundaries are readily compatible with existing propagators and overarching imaging frameworks. However, devising a suitable boundary treatment and implementing the associated routines in the underlying kernel represents a substantial effort, whilst introducing additional complexity and potential technical debt.
To date, immersed boundary implementations, particularly in seismic contexts, have focussed on specific equations and boundary conditions. This specificity hinders extension to new equations, particularly when application-specific approximations are used. Furthermore, because these implementations rely on low-level interventions within the kernel itself, the cost of implementing such treatments rapidly becomes a barrier to practical deployment.
Constructing a framework which leverages symbolic computation to generate suitable immersed boundary treatments from a high-level specification of boundary geometry and conditions introduces a layer of abstraction between the user and underlying numerics. By avoiding major modifications to the underlying numerical methods and encapsulating the boundary treatment within a powerful abstraction, topography can be treated as a module of the propagator framework, avoiding the need for fundamental or extensive reworking to include topography. This facilitates topography implementation in overarching imaging and inversion workflows, whilst enabling code reuse across applications. Integration with Devito3, a DSL and compiler for stencil computations further reduces barriers to entry.
Using this framework, FWI workflows can be straightforwardly implemented, and we have successfully constructed tomographic gradients in settings featuring over a kilometre of irregular topographic variation. Furthermore, it was found that a topographic free surface results in improved illumination balance over that observed in a comparable flat-surface case or where topography is implemented as a damping surface.
By managing complexity through abstraction layers, whilst enabling generalisation of immersed boundary treatments across a wide range of physics, the approach developed represents a powerful means of handling the emerging challenge of topography in land seismic imaging.
Speaker: Edward Caunt, PhD - Research Scientist, Devito CodesBio: Dr Edward Caunt is a Research Scientist at Devito Codes, developing novel abstractions for finite-difference methods with a focus on seismic modelling and imaging applications. His PhD thesis explored the development of a generalised mathematical approach to immersed boundary implementation, enabling the automatic generation of numerical treatments for complex topography across a wide range of seismic applications. Applications of this work have been published in Geophysics, alongside presentations at numerous academic and industry conferences. His ongoing research and development work focuses on domain-specific languages (DSLs) and code generation for high-performance, high-productivity geophysical model development.
Authors: Edward Caunt( Devito Codes), Rhodri Nelson (Imperial College London), Fabio Luporini (Devito Codes), Mathias Louboutin (Devito Codes), Gerard Gorman (Imperial College London)
