Mathematics of Multidimensional Seismic Imaging, Migration, by N. Bleistein, J.K. Cohen, John W. Jr. Stockwell

By N. Bleistein, J.K. Cohen, John W. Jr. Stockwell

In the final forty years geophysicists have chanced on that it truly is attainable to build photographs or even confirm vital actual features of rocks that may yield information regarding oil and fuel bearing buildings within the earth. To make those photographs and extract this knowledge calls for the applying of a sophisticated realizing of the mathematical physics of wave propagation. The oil and fuel labels a huge choice of the required seismic information processing tools via the identify seismic "migration".
This textual content ist the 1st to regard many varieties of migration in a unified mahtematical means. The viewers is mathematically orientated geophysicists or utilized mathematicians operating within the box of "inverse scattering imaging". The textual content can function a bridge among the utilized math and geophysics neighborhood through proposing geophysicists with a pragmatic advent to complicated engineering arithmetic, whereas offering mathematicians with a window into the realm of the mathematically sophistiated geophysicist.

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Previously, we spoke of the hierarchy of complexity of propagation speeds. Now we consider another hierarchy of complexity, that of recording and data sorting geometries. Seismic surveys are limited to ensembles of experiments with a nonzero offset between sources and their respective receivers. Each of the experiments composing the ensemble usually consists of an arrangement involving one source and many receivers, all in a line, or in a surface array, called a shot profile. 2. Schematic for a common-source (-shot) seismic profile.

We can deduce the approximate appearance of the recorded data by applying the rules of geometrical optics, which describe waves through the geometrical constructions of raypaths and wavefront surfaces-all highfrequency concepts. Under these rules, the reflections from smooth portions of reflector surface differ markedly from those from "corners" or discontinuities of the slope of the reflector surface. The requirement that incident and reflected ray angles must be equal means that only rays normally (per5 See Dobrin [1976] or Telford et.

These data may be measurements of a time-independent quantity made in one spatial dimension, or may consist of measurements of a temporally variable quantity that is spatially independent. Historically, lD models have played an important role in mathematical physics by providing a starting point for solving higher-dimensional problems; this is how we will employ them here. 1 The 1D Model in a Geophysical Context Geophysics has two ready examples of such lD data sets. A well log is an example of a lD spatially variable, but time-independent data set.

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