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.

/pdf/high-resolution-surface-wave-tomography-from-ambient-seismic-2rxarxopq3.pdf

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

A ballistic pulse launched in a strongly scattering random medium becomes diffusive after a few mean-free times. In this regime of diffusive propagation there is a net flux of energy away from the source. Eventually the flux goes to zero, in the equipartitioned regime, in which the signal consists of equal amounts of energy propagating in all directions. In this regime the two-point, two-time correlation of the wave-field should equal the sum of the advanced and retarded Green functions associated with the average medium. We observe the emergence of the Green function from this correlation at about 9 mean-free times in a highly heterogeneous rock sample.

/pdf/extracting-the-green-function-from-diffuse-equipartitioned-c7t9gooszk.pdf

Extracting the Green function from diffuse, equipartitioned waves.

SUMMARY 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 artefacts 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.

/pdf/seismic-imaging-and-illumination-with-internal-multiples-4ay5u4bow5.pdf

Seismic Imaging and Illumination with Internal Multiples

Lasers can be used to excite and detect ultrasonic waves in a wide variety of materials. This allows the measurement of absolute particle motion without the mechanical disturbances of contacting transducers. In an ultrasound transmission experiment, the wave field is usually accessible only on the boundaries of a sample. Using optical methods, one can measure the surface wave field, in effect, within the scattering region. Here, we describe noncontacting (laser source and detector) measurements of ultrasonic wave propagation in randomly heterogeneous rock samples. By scanning the surface of the sample, we can directly visualize the complex dynamics of diffraction, multiple scattering, mode conversion, and whispering gallery modes. We will show measurements on rock samples that have similar elastic moduli and intrinsic attenuation, but different grain sizes, and hence, different scattering strengths. The intensity data are well fit by a radiative transfer model, and we use this fact to infer the scattering mean free path.

/pdf/laser-characterization-of-ultrasonic-wave-propagation-in-2mvo9sscyp.pdf

Laser characterization of ultrasonic wave propagation in random media

Wave front healing, in which diffractions interfere with directly travelling waves causing a reduction in recorded traveltime delays, has been postulated to cause a bias towards faster estimated earth models. This paper reviews the theory from the mathematical physics community that explains the properties of diffractions and applies it to a suite of increasingly complicated numerical examples. We focus in particular on the elastic case and on the differences between P and S healing. We find that rather than introducing a systemic fast bias, wave front healing gives a more complicated bias in the results of traveltime tomography, with fast anomalies even manifesting themselves as slow anomalies in some situations. Of particular interest, we find that a negative correlation between the bulk and shear or compressional velocities may result to a large extend from healing.

Tomographic errors from wave front healing: more than just a fast bias

Knowledge of changes in reservoir properties resulting from extracting hydrocarbons or injecting fluid is critical to future production planning. Full-waveform inversion (FWI) of time-lapse seismic data provides a quantitative approach to characterize the changes by taking the difference of the inverted baseline and monitor models. The baseline and monitor data sets can be inverted either independently or jointly. Time-lapse seismic data collected by ocean-bottom cables (OBCs) in the Valhall field in the North Sea are suitable for such time-lapse FWI practice because the acquisitions are of a long offset, and the surveys are well-repeated. We have applied independent and joint FWI schemes to two time-lapse Valhall OBC data sets, which were acquired 28 months apart. The joint FWI scheme is double-difference waveform inversion (DDWI), which inverts differenced data (the monitor survey subtracted by the baseline survey) for model changes. We have found that DDWI gave a cleaner and more easily interpr...

/pdf/time-lapse-full-waveform-inversion-with-ocean-bottom-cable-m16twolgo0.pdf

Alison Malcolm

Papers

Extracting the Green function from diffuse, equipartitioned waves.

Seismic Imaging and Illumination with Internal Multiples

Laser characterization of ultrasonic wave propagation in random media

Tomographic errors from wave front healing: more than just a fast bias

Time-lapse full-waveform inversion with ocean-bottom-cable data: Application on Valhall field