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Downward continuation of moveout-corrected seismograms
Geophysics, 1972Abstract Earlier work developed a method of migration of seismic data based on numerical solutions of partial differential equations. The method was designed for the geometry of a single source with a line of surface receivers. Here the method is extended to the geometry of stacked sections, or what is nearly the same thing, to the ...
Jon F. Claerbout, Stephen M. Doherty
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Downward continuation of heat flow data
Tectonophysics, 1989Abstract Downward continuation operators are derived and used to calculate the subsurface temperature from surface heat flow data. If the distribution of the shallow heat sources were known, their effect on the temperature field could be included in the downward continuation operator.
J.C. Mareschal, Y. Hamdani, D.M. Jessup
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Downward Continuation of the Gravitational Potential
1991Clerk Maxwell’s form of the attraction potential at an external point, distant r from an internal origin, can be written in the tensor form $$- \frac{V}{G} = \sum\limits_{{n = 0}}^{\infty } {\frac{{{{{( - 1)}}^{n}}}}{{n!}}} {{I}^{{stu \ldots (n)}}}{{\left( {\frac{1}{r}} \right)}_{{stu \ldots (n)}}},$$ (1) in which the lower indices imply ...
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Downward continuation of constrained potential fields
Journal of Geophysical Research, 1973Formal analytic solutions to a class of problems of downward continuation of potential fields into a homogeneous semi-infinite solid are given. The solid contains stationary sources below a fixed depth, and the potential field in the source-free slab is derived on the basis of given boundary values of the field and its vertical derivative.
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Comparative Study of the Spherical Downward Continuation
Surveys in Geophysics, 2015Downward continuation of the potential data (gravity or magnetic) helps to interpret contributing sources by transforming the physical signal to their neighborhood. This paper applies three continuation approaches (Landweber’s iteration, the direct method and the inverse-matrix approach with Tikhonov’s regularization), based on the Poisson integral ...
Josef Sebera +3 more
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Solution of the downward continuation problem by collocation
Bulletin géodésique, 1975The modern satellite techniques enable to measure the gravity acceleration in space. The downward continuation of this measurements to the earth's surface is by the closed theory practically impossible. Using the method of collocation we can estimate the values of Δ g in the limited region underneath the observation with a little loss of accuracy ...
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Upward and downward continuations in the geopotential determination
Bulletin Géodésique, 1979The geopotential on and outside the earth is represented as a series in surface harmonics. The principal terms in it correspond to the solid harmonics of the external potential expansion with the coefficients being Stokes’ constantsCnm andSnm. The additional terms which occur near the earth’s surface due to its non-sphericity and topography are ...
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The Downward Continuation of Potential Field Data
Proceedings, 2018Summary Aeromagnetic data from ensemble and dyke models (and their derivatives) can be pseudo-downward continued by a factor alpha by raising the amplitude of the Fourier coefficients to a power alpha.
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Regularization of downward heat flow continuation
Studia Geophysica et Geodaetica, 1987Some regularization approaches to downward heat flow continuation from the Earth's surface to the depth of interest are presented, provided the heat transfer is described by the homogeneous steady-state equation. The Fourier transform of horizontal coordinates is used and the relation between the regularization of the heat flow spectrum and the ...
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A continuing downward trend in intergenerational mobility? [PDF]
Jo Blanden and Stephen Machin look at evidence on the life chances of children born into poor families since 1970.
Jo Blanden, Stephen Machin
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