Noise cross-correlation sensitivity kernels

Jeroen Tromp, Yang Luo, Shravan Hanasoge, Daniel Peter

    Research output: Contribution to journalArticle

    Abstract

    We determine finite-frequency sensitivity kernels for seismic interferometry based upon noise cross-correlation measurements. Under the assumptions that noise is spatially uncorrelated but non-uniform, we determine ensemble-averaged cross correlations between synthetic seismograms at two geographically distinct locations. By minimizing a measure of the difference between observed and simulated ensemble cross correlations-subject to the constraint that the simulated wavefield satisfies the seismic wave equation-we obtain ensemble sensitivity kernels. These ensemble kernels reflect the sensitivity of ensemble cross-correlation measurements to variations in model parameters, for example, mass density, shear and compressional wave speeds and the spatial distribution of noise. Ensemble kernels are calculated based upon the interaction between two wavefields: an ensemble forward wavefield and an ensemble adjoint wavefield. To obtain the ensemble forward wavefield, one first calculates a generating wavefield obtained by inserting a signal determined by the characteristics of the noise at the location of the first receiver, saving the results of this calculation at locations where noise is generated, that is, typically on (a portion of) the Earth's surface. Next, one uses this generating wavefield as the source of the ensemble forward wavefield associated with the first receiver. The ensemble adjoint wavefield is obtained by using measurements between simulated and observed ensemble cross correlations as a seismic source located at the second receiver. The interaction between ensemble forward and adjoint wavefields 'paints' ensemble sensitivity kernels. We illustrate the construction of ensemble kernels and their nature in two and three dimensions using a spectral-element method. In addition to a 'banana-doughnut' feature connecting the two receivers, as in traditional finite-frequency earthquake tomography, some noise cross-correlation sensitivity kernels exhibit hyperbolic 'jets' protruding from each receiver in a direction away from the other receiver. Ensemble sensitivity kernels for long-period (T > ~ 50 s) non-uniform noise in global models exhibit sensitivity along the minor and major arcs. These kernels reflect the fact that measurements typically involve long time-series that include multi-orbit surface waves. Like free oscillations, such measurements are sensitive to structure along the great circle through the two receivers. From the perspective of noise cross-correlation tomography, we discuss strategies for inversions in terrestrial and helioseismology.

    Original languageEnglish (US)
    Pages (from-to)791-819
    Number of pages29
    JournalGeophysical Journal International
    Volume183
    Issue number2
    DOIs
    StatePublished - Nov 1 2010

    Fingerprint

    cross correlation
    receivers
    sensitivity
    Tomography
    Seismic waves
    tomography
    Wave equations
    Interferometry
    Paint
    Surface waves
    Spatial distribution
    great circles
    Time series
    Earthquakes
    Orbits
    helioseismology
    Earth (planet)
    synthetic seismogram
    free vibration
    seismograms

    Keywords

    • Computational seismology
    • Interferometry
    • Seismic tomography
    • Theoretical seismology

    ASJC Scopus subject areas

    • Geophysics
    • Geochemistry and Petrology

    Cite this

    Noise cross-correlation sensitivity kernels. / Tromp, Jeroen; Luo, Yang; Hanasoge, Shravan; Peter, Daniel.

    In: Geophysical Journal International, Vol. 183, No. 2, 01.11.2010, p. 791-819.

    Research output: Contribution to journalArticle

    Tromp, J, Luo, Y, Hanasoge, S & Peter, D 2010, 'Noise cross-correlation sensitivity kernels', Geophysical Journal International, vol. 183, no. 2, pp. 791-819. https://doi.org/10.1111/j.1365-246X.2010.04721.x
    Tromp, Jeroen ; Luo, Yang ; Hanasoge, Shravan ; Peter, Daniel. / Noise cross-correlation sensitivity kernels. In: Geophysical Journal International. 2010 ; Vol. 183, No. 2. pp. 791-819.
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