Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

Cross-correlation of 1 month of ambient seismic noise recorded at USArray stations in California yields hundreds of short-period surface-wave group-speed measurements on interstation paths. We used these measurements to construct tomographic images of the principal geological units of California, with low-speed anomalies corresponding to the main sedimentary basins and high-speed anomalies corresponding to the igneous cores of the major mountain ranges. This method can improve the resolution and fidelity of crustal images obtained from surface-wave analyses.

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High-resolution surface-wave tomography from ambient seismic noise.

/pdf/statistical-theory-of-communication-4wy4yg9ato.pdf

Statistical Theory of Communication

The term seismic interferometry refers to the principle of generating new seismic responses by crosscorrelating seismic observations at different receiver locations. The first version of this principle was derived by Claerbout (1968), who showed that the reflection response of a horizontally layered medium can be synthesized from the autocorrelation of its transmission response. For an arbitrary 3D inhomogeneous lossless medium it follows from Rayleigh's reciprocity theorem and the principle of time-reversal invariance that the acoustic Green's function between any two points in the medium can be represented by an integral of crosscorrelations of wavefield observations at those two points. The integral is along sources on an arbitrarily shaped surface enclosing these points. No assumptions are made with respect to the diffusivity of the wavefield. The Rayleigh-Betti reciprocity theorem leads to a similar representation of the elastodynamic Green's function. When a part of the enclosing surface is the earth's free surface, the integral needs only to be evaluated over the remaining part of the closed surface. In practice, not all sources are equally important: The main contributions to the reconstructed Green's function come from sources at stationary points. When the sources emit transient signals, a shaping filter can be applied to correct for the differences in source wavelets. When the sources are uncorrelated noise sources, the representation simplifies to a direct crosscorrelation of wavefield observations at two points, similar as in methods that retrieve Green's functions from diffuse wavefields in disordered media or in finite media with an irregular bounding surface.

/pdf/green-s-function-representations-for-seismic-interferometry-53cireml6q.pdf

Green's function representations for seismic interferometry

[1] It has been demonstrated experimentally and theoretically that an estimate of the Green's function between two seismic stations can be obtained from the time-derivative of the long-time average cross correlation of ambient noise between these two stations. This TDGF estimate from just the noise field includes all tensor components of the Green's function and these Green's function estimates can be used to infer Earth structure. We have computed cross correlations using 1 to 30 continuous days of ambient noise recorded by over 150 broadband seismic stations located in Southern California. The data processing yielded thousands of cross-correlation pairs, for receiver separations from 4–500 km, which clearly exhibit coherent broadband propagating dispersive wavetrains across frequency band 0.1–2 Hz.

/pdf/extracting-time-domain-green-s-function-estimates-from-23y2zfok4r.pdf

Extracting time-domain Green's function estimates from ambient seismic noise

The recovery of elastic properties from seismic data often requires the iterative use of seismic modeling. Finite-difference (FD) simulation is a common component in seismic modeling, and i...

Reduced memory implementation of a local elastic finite-difference solver

Time-lapse full-waveform inversion using Hamiltonian Monte Carlo: A proof of concept

Multi-component elastic seismic data collected at large offsets have the potential to be used in micro seismic imaging and monitoring. However, types of receiver surface deployments used for micro-seismic monitoring are generally very sparse, and thus the data used for imaging from these receivers cause receiver-migration-operator artifacts that severely contaminate the shallow part of the image. In this study, we present a data-driven method that alleviates these imaging artifacts. The method is based on converted-phase elastic seismic migration and de-migration. We show that despite the spatial aliasing of the recorded data, we are able to suppress the receiver migration-operator artifacts and reconstruct the shallow part of the image. The merit of this approach is that it is elastic, fully data-driven (i.e, independent of source parameters), and does not suffer from migration operator source aliasing, when a small number of shots or micro-seismic events are used. We present a derivation of the method and test it with a synthetic model and a field data set from a geothermal reservoir with abundant natural and induced seismicity.

/pdf/migration-based-seismic-trace-interpolation-of-sparse-19h4tk8hb2.pdf

Migration-Based Seismic Trace Interpolation of Sparse Converted Phase Micro-Seismic Data

As more and more resources are extracted from unconventional reservoirs, an understanding of the microstructure of reservoir rocks is of increasing importance. Many conventional techniques struggle to sense variations in the micro-structure and pore-fluids of rock samples. The nonlinear coupling of two elastic waves is known to be sensitive to these parameters, however, and so is a natural candidate to improve our understanding of these structures. Here, we develop an experimental technique to sense the nonlinear interaction of two propagating waves: a strong S-wave pump that changes (minutely) the elastic properties of the sample and a weaker P-wave probe that senses those changes. By measuring the delay in the P-wave probe traveltime induced by the S-wave pump, we show that this signal is significant in a Berea sandstone sample and absent in Aluminum and Plexiglass samples. The polarization of the S-wave (particle motion aligned or perpendicular to the P-wave probe) has a large impact on the measured response; this is evidence that the signal we measure is sensitive to the micro-structure of the rock. We show that the method is sensitive to fluids by imaging the variations in two specific nonlinear parameters, caused by the introduction of fluid into a Berea sandstone sample.

/pdf/nonlinear-interaction-of-seismic-waves-in-the-lab-a-2oypvx0y7a.pdf

Alison Malcolm

Papers

Reduced memory implementation of a local elastic finite-difference solver

Time-lapse full-waveform inversion using Hamiltonian Monte Carlo: A proof of concept

Migration-Based Seismic Trace Interpolation of Sparse Converted Phase Micro-Seismic Data

Nonlinear interaction of seismic waves in the lab: A potential tool for characterizing pore structure and fluids

Improved well log classification using semi-supervised algorithms