355 research outputs found
Approximate inversion of the wave-equation Hessian via randomized matrix probing
We present a method for approximately inverting the Hessian of full waveform inversion as a dip-dependent and scale-dependent amplitude correction. The terms in the expansion of this correction are determined by least-squares fitting from a handful of applications of the Hessian to random models — a procedure called matrix probing. We show numerical indications that randomness is important for generating a robust preconditioner, i.e., one that works regardless of the model to be corrected. To be successful, matrix probing requires an accurate determination of the nullspace of the Hessian, which we propose to implement as a local dip-dependent mask in curvelet space. Numerical experiments show that the novel preconditioner fits 70% of the inverse Hessian (in Frobenius norm) for the 1-parameter acoustic 2D Marmousi model.National Science Foundation (U.S.); Alfred P. Sloan Foundatio
Hierarchical model for the scale-dependent velocity of seismic waves
Elastic waves of short wavelength propagating through the upper layer of the
Earth appear to move faster at large separations of source and receiver than at
short separations. This scale dependent velocity is a manifestation of Fermat's
principle of least time in a medium with random velocity fluctuations. Existing
perturbation theories predict a linear increase of the velocity shift with
increasing separation, and cannot describe the saturation of the velocity shift
at large separations that is seen in computer simulations. Here we show that
this long-standing problem in seismology can be solved using a model developed
originally in the context of polymer physics. We find that the saturation
velocity scales with the four-third power of the root-mean-square amplitude of
the velocity fluctuations, in good agreement with the computer simulations.Comment: 7 pages including 3 figure
Detection and imaging in strongly backscattering randomly layered media
Abstract. Echoes from small reflectors buried in heavy clutter are weak and difficult to distinguish from the medium backscatter. Detection and imaging with sensor arrays in such media requires filtering out the unwanted backscatter and enhancing the echoes from the reflectors that we wish to locate. We consider a filtering and detection approach based on the singular value decomposition of the local cosine transform of the array response matrix. The algorithm is general and can be used for detection and imaging in heavy clutter, but its analysis depends on the model of the cluttered medium. This paper is concerned with the analysis of the algorithm in finely layered random media. We obtain a detailed characterization of the singular values of the transformed array response matrix and justify the systematic approach of the filtering algorithm for detecting and refining the time windows that contain the echoes that are useful in imaging
openWAR: An Open Source System for Evaluating Overall Player Performance in Major League Baseball
Within baseball analytics, there is substantial interest in comprehensive
statistics intended to capture overall player performance. One such measure is
Wins Above Replacement (WAR), which aggregates the contributions of a player in
each facet of the game: hitting, pitching, baserunning, and fielding. However,
current versions of WAR depend upon proprietary data, ad hoc methodology, and
opaque calculations. We propose a competitive aggregate measure, openWAR, that
is based upon public data and methodology with greater rigor and transparency.
We discuss a principled standard for the nebulous concept of a "replacement"
player. Finally, we use simulation-based techniques to provide interval
estimates for our openWAR measure.Comment: 27 pages including supplemen
Time reversal methods in acousto-elastodynamics
The aim of the article is to solve an inverse problem in order to determine the presence and some properties of an elastic “inclusion” (an unknown object, characterized by elastic properties discriminant from the surrounding medium) from partial observa- tions of acoustic waves, scattered by the inclusion. The method will require developing techniques based on Time Reversal methods. A finite element method based on varia- tional acousto-elastodynamics formulation will be derived and used to solve to solve the forward, and then, the time reversed problem. A criterion, derived from the reverse time migration framework, is introduced, to help use to construct images of the inclusions to be determined. Our approach will be applied to configurations modeling breast cancer detection, using simulated ultrasound waves
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