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15444344024
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note
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Traditional stacking assumes that travel-time variation across the array is a linear function of the great-circle distance from the source. This is valid for small aperture arrays and teleseismic data but limits stacking to a single source or sources that are essentially co-located. Double-beam stacking (6) relaxes the latter restriction, stacking over receiver and source arrays and resulting in improved slowness and azimuth resolution. The source array aperture, however, must be small in comparison with epicentral distance. With an assumption of a target phase, we can use our approach to stack over large arrays.
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B. L. N. Kennett, Ed. Research School of Earth Sciences, Australian National University, Canberra, Australia
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B. L. N. Kennett, in International Association of Seismology and Physics of the Earth's Interior (IASPEI) 1991 Seismological Tables, B. L. N. Kennett, Ed. (Research School of Earth Sciences, Australian National University, Canberra, Australia, 1991), pp. 164-167. We modified the model by depressing the CMB 100 km while retaining the lowermost mantle velocity gradients. This allowed us to compute PcP and PdP times appropriate for a slow D″ velocity layer without having to alter the overlying velocity structure (for example, slow PcP would map as a reflector below the nominal CMB). Ellipticity corrections were applied to the predicted P and PdP times, the latter approximated by the tabulated correction for PcP. Because our focus was on the lowermost mantle, the error in this approximation was ≤0.01 s.
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(1991)
International Association of Seismology and Physics of the Earth's Interior (IASPEI) 1991 Seismological Tables
, pp. 164-167
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Kennett, B.L.N.1
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Stacking was preceded by alignment of P wave forms and deconvolution of the source-time function. Alignment of P reduced travel-time variability due to shallow velocity structure and source mislocation. Aligned wave forms were averaged to eliminate variable station-side contributions, leaving the source-time function convolved against a mean mantle response. This was deconvolved from the aligned wave forms, reducing interevent variation of wave form shape to <10% of peak amplitude.
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To obtain the synthetic stack, we generated raytheory synthetic data matching the distance distribution of the source region data set and consisting of P and PcP, the only phases occurring in the absence of a lower mantle reflector. The synthetic seismograms were convolved with the mean deconvolved P wave form (9) before they were stacked.
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Residual travel-time variability is parameterized as the standard deviation of a zero-mean Gaussian perturbation applied to delay time in the synthetics.
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Velocities above the reflector were fixed at IASP91 values for the mean discontinuity depth. We obtained the mean plane-layer reflection coefficient by averaging over the ray parameter weighted by the ray-parameter distribution of stacked data.
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Amplitudes of PdP are affected by variations in lowermost mantle attenuation, velocity heterogeneity, and reflector topography. The factor of 2 expansion of the acceptable range of R is intended to avoid the introduction of biases from these factors and from approximations inherent to ray theory. We also required that the resulting mean PcP reflection coefficient be positive and less than 0.42 (0.33 for SA) after we applied the same perturbations to velocity and density at the CMB. This constraint eliminates models with large compressional to shear velocity variation ratios. The maximum value for each source region is a factor of 3 greater than the largest accepted estimate (Table 1) to allow for unmodeled variations in geometric spreading and possibly severe attenuation within the LVL.
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Velocity and density vary linearly across the transition. To compute the mean reflection coefficient, we ok the magnitude of the complex reflection coefficient at peak frequency and ignored wave form distortion effects.
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p increases produce PdP and PcP reflection coefficients that are too large. Some Monte Carlo models had reversed-polarity PdP. Eliminating these and accepting only those triplets that predict normalpolarity PdP do not affect our conclusions.
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K. Aki and R. Dmowska, Eds., Geophysical Monograph Series American Geophysical Union, Washington, DC
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E. Knittle and R. Jeanloz, Science 251, 1438 (1991); F. Goarant, F. Guyot, J. Peyronneau, J.-P. Poirier, J. Geophys. Res. 97, 4477 (1992); R. Jeanloz, in Relating Geophysical Structures and Processes: The Jeffreys Volume, K. Aki and R. Dmowska, Eds., vol. 76 of Geophysical Monograph Series (American Geophysical Union, Washington, DC, 1993), pp. 121-127.
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note
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This research was supported by NSF and Lawrence Livermore National Laboratory, Institute of Geophysics and Planetary Physics. This is Institute of Tectonics contribution 308.
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