By Guust Nolet
The 1st textbook to supply an intensive creation to seismic tomography for complex scholars and examine practitioners.
Read or Download A Breviary of Seismic Tomography: Imaging the Interior of the Earth and Sun PDF
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Additional resources for A Breviary of Seismic Tomography: Imaging the Interior of the Earth and Sun
6 Show that the elements of the vector p are equal to the direction cosines γi ≡ xi /r of the ray path scaled by the velocity c. 6 Ray solutions in layered and spherical systems In a medium with horizontal stratification, where c(x, y, z) = c(z), we may without loss of generality choose our x-axis in the direction of propagation. e. with py = 0). 4). In the case of horizontal layering the subscript x on px is usually omitted. The horizontal slowness p is measured in s/m or s/km. The constant p is also known as the ‘ray parameter’.
49) The right-hand side disappears at the surface of the Sun or ocean, where the pressure is zero. In general, for homogeneous boundary conditions on S, the volume integral equals zero. So far, we have simply manipulated equations for arbitrary wavefields and sources. 10 Huygens, Fresnel and Green 33 sources. This was recognized by George Green (1793–1841), a British amateur mathematician, who published his essay privately in 1828 because he ‘felt that it was presumptuous to submit his paper to a journal’ and who was not fully appreciated until his work was rediscovered by Lord Kelvin .
47) where ds = |dr| is small enough so that we make only a small error by replacing the velocity c along the segment by its average over dr. If we perturb the ray location such that dr → d(r + δr), the ray encounters a different velocity c + δc and: dt + δdt = |dr + dδr| |dr + dδr| δc ≈ 1− c + δc c c ≈ |dr + dδr| 1 1 +δ c c . By writing out, one verifies that: |dr + dδr| = |dr| + dr · dδr = nˆ · (dr + dδr) , |dr| where nˆ = dr/|dr| = dr/ds, a unit vector along the ray, so that (to first order): δdt = 1 1 nˆ · dδr + δ nˆ · dr .
A Breviary of Seismic Tomography: Imaging the Interior of the Earth and Sun by Guust Nolet