We present a methodology providing a new perspective on modeling and inversion of wave propagation satisfying time-reversal invariance and reciprocity in generally inhomogeneous media. The approach relies on a representation theorem of the wave equation to express the Green function between points in the interior as an integral over the response in those points due to sources on a surface surrounding the medium. Following a predictable initial computational effort, Green's functions between arbitrary points in the medium can be computed as needed using a simple cross-correlation algorithm.

Time reversal of arbitrary, elastodynamic wavefields in partially open media can be achieved by measuring the wavefield on a surface surrounding the medium and applying the time reverse of those measurements as a boundary condition. We use a representation theorem to derive an expression for the time-reversed wavefield at arbitrary points in the interior. When this expression is used to compute, in a second point, the time-reversed wavefield originating from a point source, the time-reversed Green's function between the two points is observed. By invoking reciprocity, we obtain an expression that is suitable for modeling of wave propagation through the medium. From this we develop an efficient and flexible twostage modeling scheme. In the initial phase, the model is illuminated systematically from a surface surrounding the medium using a sequence of conventional forward-modeling runs. Full waveforms are stored for as many points in the interior as possible. In the second phase, Green's functions between arbitrary points in the volume can be computed by crosscorrelation and summation of data computed in the initial phase. We illustrate the method with a simple acoustic example and then apply it to a complex region of the elastic Pluto model. It is particularly efficient when Green's functions are desired between a large number of points, but where there are few common source or receiver points. The method relies on interference of multiply scattered waves, but it is stable. We show that encoding the boundary sources using pseudonoise sequences and exciting them simultaneously, akin to daylight imaging, is inefficient and in all explored cases leads to relatively high-noise levels.

An exact boundary condition is presented for scattering problems involving spatially limited perturbations of arbitrary magnitude to a background model in generally inhomogeneous acoustic media. The boundary condition decouples the wave propagation on a perturbed domain while maintaining all interactions with the background model, thus eliminating the need to regenerate the wave field response on the full model. The method, which is explicit, relies on a Kirchhoff-type integral extrapolation to update the boundary condition at every time step of the simulation. The Green’s functions required for extrapolation through the background model are computed efficiently using wave field interferometry.

Many applications in computational geophysics involve the modeling of seismic wave propagation on a set of closely related subsurface models. In such scenarios, it is of interest to recompute the seismic wavefields locally (only in the regions of change), instead of in the full subsurface model. We have developed a method for local acoustic wavefield recomputation that makes it possible to fully immerse a local modeling domain within a larger domain of arbitrary extent and complexity, such that the wave propagation in the full domain is completely accounted for. The method enables wavefield modeling on much smaller local domains, while relying on the up-front generation of a large number of Green’s functions and a wavefield extrapolation step at each time step of the simulation. A Kirchhoff-Helmholtz extrapolation integral is used to predict the interaction of the wavefield leaving the local domain with the exterior domain. The outward propagating wavefield and the wavefield reentering the local domain are applied as a boundary condition along the edges. Thanks to these dynamically calculated boundary conditions, all higher order long-range interactions between the two domains are fully accounted for. We have implemented the method in a conventional finite-difference time-domain scheme and determined that the locally calculated wavefields are equal to wavefields generated on the full domain to within numerical precision. The efficiency of the local modeling algorithm will greatly depend on the nature and size of the problem.

A wave propagation laboratory is proposed which enables the study of the interaction of broadband signals with complex materials. A physical experiment is dynamically linked to a numerical simulation in real time through transmitting and recording transducer surfaces surrounding the target. The numerical simulation represents an arbitrarily larger domain, allowing experiments to be performed in a total environment much greater than the laboratory experiment itself. Specific applications include the study of non-linear effects or wave propagation in media where the physics of wave propagation is not well understood such as the effect of fine scale heterogeneity on broadband propagating waves.

We present a fundamentally new approach to laboratory acoustic and seismic wave experimentation that enables full immersion of a physical wave propagation experiment within a virtual numerical environment. Using a recent theory of immersive boundary conditions that relies on measurements made on an inner closed surface of sensors, the output of numerous closely spaced sources around the physical domain is continuously varied in time and space. This allows waves to seamlessly propagate back and forth between both domains, without being affected by reflections at the boundaries between both domains, which enables us to virtually expand the size of the physical laboratory and operate at much lower frequencies than previously possible (sonic frequencies as low as 1 kHz). While immersive boundary conditions have been rigorously tested numerically, here we present the first proof of concept for their physical implementation with experimental results from a one-dimensional sound wave tube. These experiments demonstrate the performance and capabilities of immersive boundary conditions in canceling boundary reflections and accounting for long-range interactions with a virtual domain outside the physical experiment. Moreover, we introduce a unique high-performance acquisition, computation, and control system that will enable the real-time implementation of immersive boundary conditions in three dimensions. The system is capable of extrapolating wave fields recorded on 800 simultaneous inputs to 800 simultaneous outputs, through arbitrarily complex virtual background media with an extremely low total system latency of 200 μs. The laboratory allows studying a variety of long-standing problems and poorly understood aspects of wave physics and imaging. Moreover, such real-time immersive experimentation opens up exciting possibilities for the future of laboratory acoustic and seismic experiments and for fields such as active acoustic cloaking and holography.

Three-component measurements of particle motion would bring significant benefits to towed-marine seismic data if processed in conjunction with the pressure data. We show that particle velocity measurements can increase the effective Nyquist wavenumber by a factor of two or three, depending on how they are used. A true multicomponent streamer would enable accurate data reconstruction in the crossline direction with cable separations for which pressure-only data would be irrecoverably aliased. We also show that conventional workflows aimed at reducing these aliasing effects, such as moveout correction applied before interpolation, are compatible with multicomponent measurements. Some benefits of velocity measurements for deghosting data are well known. We outline how the new measurements might be used to address some long-standing deghosting challenges of particular interest. Specifically, we propose methods for recovering de-ghosted data between streamers and for 3D deghosting of seismic data at the streamer locations.

Computation of the 3D upgoing/downgoing separated wavefield at any desired position within a marine streamer spread is enabled by multicomponent streamers that can measure the crossline and vertical components of water-particle motion in addition to the pressure. We introduce the concept of simultaneous interpolation and deghosting and describe a new technique, generalized matching pursuit (GMP), to achieve this. This method is based on the matching-pursuit technique and iteratively reconstructs the signal as a combination of optimal basis functions. In the GMP method, the basis functions describing the unknown 3D upgoing wavefield are filtered by appropriate forward ghost operators before being matched to the multicomponent measurements. As a data-dependent method, GMP can operate on data samples that are highly aliased in the crossline direction without relying on assumptions about seismic events such as linearity. The technique is naturally suitable for data with only a small number of samples that may be irregularly spaced. We demonstrate the efficacy and robustness of the GMP method on several synthetic data sets of increasing complexity and in the presence of noise.