A field expansions method for scattering by periodic multilayered media

The interaction of acoustic and electromagnetic waves with periodic structures plays an important role in a wide range of problems of scientific and technological interest. This contribution focuses upon the robust and high-order numerical simulation of a model for the interaction of pressure waves generated within the earth incident upon layers of sediment near the surface. Herein is described a Boundary Perturbation Method for the numerical simulation of scattering returns from irregularly shaped periodic layered media. The method requires only the discretization of the layer interfaces (so that the number of unknowns is an order of magnitude smaller than Finite Difference and Finite Element simulations), while it avoids not only the need for specialized quadrature rules but also the dense linear systems characteristic of Boundary Integral/Element Methods. The approach is a generalization to multiple layers of Bruno & Reitich's "Method of Field Expansions" for dielectric structures with two layers. By simply considering the entire structure simultaneously, rather than solving in individual layers separately, the full field can be recovered in time proportional to the number of interfaces. As with the original Field Expansions method, this approach is extremely efficient and spectrally accurate.National Science Foundation (U.S.) (grant No. DMS–0810958)United States. Dept. of Energy (Award No. DE–SC0001549)Massachusetts Institute of Technology. Earth Resources Laborator

SVD enhanced seismic interferometry for traveltime estimates between microquakes

In general, Green’s functions obtained with seismic interferometry are only estimates of the true Green’s function, introducing uncertainties to the information recovered from them. However, there are still many cases in which the source-receiver geometries are suitable for seismic interferometry, usually allowing the recovery of kinematic information. Here we show how to use the singular value decomposition to re-enforce the accuracy of traveltimes obtained from interferometric Green’s functions. We apply the combination of seismic interferometry and the singular value decomposition to obtain physically accurate inter-event traveltimes for microquake pairs at a geothermal reservoir. With a synthetic example, we show that the P-wave phase and coda-wave energy information are closer to correct with the singular value decomposition than without. These traveltimes could be used for velocity tomography and event location algorithms to obtain more accurate event locations and locally accurate velocity models.United States. Dept. of Energy (Grant DE-FG36-08GO18197); Massachusetts Institute of Technology. Earth Resources Laborator

A multi-pass one way method to include turning waves and multiples

Conventional one way migration methods exclude turning waves and multiples. We propose an algorithm that uses multiple passes to extend the one way method to efficiently include these wavepaths. A comparison of the images produced by the regular one way algorithm, RTM, and the new method, shows that this new method can significantly improve the image in regions of interest, and in certain situations may even provide more useful information than RTM. The runtime is demonstrated to be in between that of regular one way and RTM, while the physical memory required is considerably lower than that of RTM

Reverse Time Migration in the presence of known sharp interfaces

We propose using the forward propagated source wave to create synthetic receiver data on the surfaces of the computational domain where real receiver data is not available as a means of exploiting known information about reflector locations in Reverse Time Migration. The inclusion of synthetic boundary data can make true amplitude imaging possible, and reduce the artifacts associated with the inclusion of multiples. Here, we describe the new method, present synthetic examples, and propose an appropriate imaging condition

Microquake seismic interferometry with SVD-enhanced Green's function recovery

The conditions under which seismic interferometry (SI) leads to the exact Green's function (GF) are rarely met in practice. As a result, we generally recover only estimates of the true GF. This raises the questions: How good an approximation to the GF can SI give? Can we improve this estimated GF?United States. Dept. of Energy (Grant DE-FG36-08GO18197)Massachusetts Institute of Technology. Earth Resources Laboratory (Grant)ChevronTexaco (Firm) (Grant

Detecting medium changes from coda by interferometry

In many applications, sequestering CO[subscript 2] underground for example, determining whether or not the medium has changed is of primary importance, with secondary goals of locating and quantifying that change. We consider an acoustic model of the Earth as a sum of a smooth background velocity, isolated velocity jumps and random small scale fluctuations. Although the first two parts of the model can be determined precisely, the random fluctuations are never known exactly and are thus modeled as a realization of a random process with assumed statistical properties. We exploit the so-called coda of multiply scattered energy recorded in such models to monitor for change and to localize and quantify that change, by examining the shape and frequency content of correlations of the coda produced by different parts in the medium. These ideas build upon past work in time-reversal detection methods that have often been limited to theoretical regimes in which the scales of scattering and reflection are strictly separated. This results in an application of time-reversal detection methods to non-theoretical regimes in which the separation of scales is not strictly satisfied, opening up the possibility, discussed here, of using such techniques to monitor CO[subscript 2] sequestration sites for leakage.Massachusetts Institute of Technology. Earth Resources Laborator

Interferometric imaging of multiples in an RTM approach

It is well known that reverse-time migration is capable of correctly imaging multiply scattered energy. To do this, one of the interfaces from which the waves scatter must be included in the background velocity model. In a one-way framework this requirement is avoided by iteratively forming images of higher-order scattered waves. These techniques use an image made with singly scattered waves to estimate the locations of some of the reflection points in a multiply-scattered wave, from which the location of an additional scattering point is determined through standard imaging techniques. This removes the requirement that a single multiple-generating interface be identified. Here we extend this technique to reverse-time migration using results from several recent studies linking standard and extended imaging conditions to interferometry. This results in a method to generate images with multiply-scattered waves using the full-waveform imaging techniques of reverse-time migration and the iterative imaging formulations of scattering series in a one-way framework.Geo-Mathematical Imaging GroupTOTAL (Firm)Massachusetts Institute of Technology. Earth Resources Laborator

Monitoring Seismic Attenuation Changes Using a 4D Relative Spectrum Method in Athabsca Heavy Oil Reservoir, Canada

Heating heavy oil reservoirs is a common method for reducing the high viscosity of heavy oil and thus increasing the recovery factor. Monitoring these changes in the reservoir is essential for delineating the heated region and controlling production. In this study, we measure the changes in the seismic wave attenuation of a heavy oil reservoir by constructing time-lapse Q[superscript -1] factor maps using a 4D-relative spectrum method. This method estimates seismic attenuation from surface reflection seismic surveys by calculating, for each trace in each survey, the attenuation (Q[superscript -1]) using the spectral ratio (Toksoz et al. (1979)) between a reference reflector above the reservoir and a second reflector below the reservoir. The results of our study on a real data set exhibit alignment along the injection wells, indicating that seismic attenuation can be used to monitor changes in a heavy oil reservoir

Seismic Imaging and Illumination with Internal Multiples

If singly scattered seismic waves illuminate the entirety of a subsurface structure of interest, standard methods can be applied to image it. It is generally the case, however, that with a combination of restricted acquisition geometry and imperfect velocity models, it is not possible to illuminate all structures with only singly scattered waves. We present an approach to use multiply scattered waves to illuminate structures not sensed by singly scattered waves. It can be viewed as a refinement of past work in which a method to predict artifacts in imaging with multiply scattered waves was developed. We propose an algorithm and carry out numerical experiments, representative of imaging of the bottom and flanks of salt, demonstrating the effectiveness of our approach.Dutch National Science Foundation (grant number NWO:VIVI865.03.007)StatoilHydroNorwegian Research Council (ROSE project)Geo-Mathematical Imaging Grou

Efficient stochastic Hessian estimation for full waveform inversion

In this abstract we present a method that allows arbitrary elements of the approximate Hessian to be estimated simultaneously. Preliminary theoretical and numerical investigations suggest that the number of forward models required for this procedure does not increase with the number of shots. As the number of shots increases this means that the cost of estimating these approximate Hessian entries becomes negligible relative to the cost of calculating the gradient. The most obvious application would be to estimate the diagonal of the approximate hessian. This can then be used as a very inexpensive preconditioner for optimization procedures, such as the truncated Newton method