# Seismic Imaging and Inversion: Volume 1: Application of by Stolt D.R.H., Weglein P.A.B.

By Stolt D.R.H., Weglein P.A.B.

Extracting details from seismic info calls for wisdom of seismic wave propagation and mirrored image. the generally used procedure includes fixing linearly for a reflectivity at each element in the Earth, yet this booklet follows an alternate strategy which invokes inverse scattering thought. via constructing the idea of seismic imaging from simple ideas, the authors relate different types of seismic propagation, mirrored image and imaging - hence supplying hyperlinks to reflectivity-based imaging at the one hand and to nonlinear seismic inversion at the different. the great and bodily whole linear imaging origin built offers new effects on the cutting edge of seismic processing for aim situation and identity. This e-book serves as a primary consultant to seismic imaging rules and algorithms and their beginning in inverse scattering thought and is a worthy source for operating geoscientists, clinical programmers and theoretical physicists

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**Sample text**

The flat portions of the reflecting boundary do not appear to be exactly zero phase, suggesting some phase has been induced by the imposed boundary conditions. Distances are in feet and time in seconds. 20 Reverse time migration of the faulted boundary data. The structure of the boundary, including the steeply dipping fault, is well recovered. The boundary image is zero phase – the phase induced in the image by the forward time operator has been removed by the reverse time operator, not too surprising in that the two operators used the same boundary conditions.

14) This suggests a simple migration algorithm: first, identify the reflectors and measure the apparent dips αapp . For each source–receiver location, draw a circle centered on the source–receiver location, with radius equal to the distance to the reflector. The point on the circle tangent to a line dipping at angle αtrue = arcsin(tan αapp ) is the true reflector location. This geometrical migration algorithm can be generalized to variable velocity, and is relatively simple to implement. In fact, its use pre-dates digital computers.

In fact, its use pre-dates digital computers. One should acknowledge, however, some limitations. First, it only works where reflections can be identified and dip measured prior to migration. Second, the geometrical argument does not tell us what to do about amplitudes. However incomplete, the concept is useful for understanding migration as an attempt to move events up dip to their true locations. What happens to this concept if the migrated image is a point instead of a line? Since the unmigrated image of a reflecting point is a hyperbola, its apparent dip is spatially variable.