## LSU Historical Dissertations and Theses

1987

Dissertation

#### Degree Name

Doctor of Philosophy (PhD)

#### Abstract

A ray theoretical traveltime inversion method in two dimensional arbitrarily dipping layers has been developed and applied to synthetic and real field data. The method is based on Durbaum's formula and may be applied to single-fold as well as CMP raw data. The advantage of Durbaum's formula is that we can estimate dipping angles as well as accurate velocities in dipping layers. In addition, the number of traces which can be utilized for velocity estimations is drastically increased. Also, a statistical method can be used to estimate normal incident times (t$\sb{\rm o}$) and the take-off angles at the surface (B$\sb{\rm o}$) which are measured manually from a stacked section in other methods. Basically, two different statistical ways of interval parameter estimations are discussed. One is Gauss-Newton's nonlinear least squares which applies to sampled traveltime data. The other is the coherency measures technique which does not need picking. To visualize the coherency measures, three different types of plotting are proposed depending on which parameter is fixed with respect to the others. The velocity-B$\sb{\rm o}$ analysis display which plots semblance coefficients on the axes of Vnmo and B$\sb{\rm o}$ at a fixed t$\sb{\rm o}$ is the most efficient method of presentation. An analytical method and an iterative method for velocity inversion from interval parameters are discussed. A computer algorithm to trace rays efficiently in arbitrarily dipping plane layers is also presented because both inversion methods need ray tracing to solve the inversion equation. The accuracy of inversion is studied through models. This study shows that velocity-B$\sb{\rm o}$ analysis is superior to Dix's and Hubral's method for estimating the interval velocities, depths, and dipping angles. Even in the presence of random errors, the method gives a better prediction than the others. The inversion from curved layers and the effect of multiples and diffractions on velocity-B$\sb{\rm o}$ analysis are examined. Application of Velocity-B$\sb{\rm o}$ analysis to real seismic data shows that it successfully predicts both velocity and dipping angle. These accurate velocities and dipping angles are essential in subsequent processing stages.

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