# Institute for Geophysics Theses and Dissertations

Permanent URI for this collectionhttps://hdl.handle.net/2152/123395

This collection is updated each semester. For the most complete record of theses and dissertations, please see the

__ETD Collection__.## Browse

# Browsing Institute for Geophysics Theses and Dissertations by Author "Backus, Milo M., 1932-"

Now showing 1 - 3 of 3

- Results Per Page
- Sort Options

Item Practical seismic inversion(1994) Simmons, James L., Jr.; Backus, Milo M., 1932-Seismic data contain information regarding the phase and amplitude of reflected events. Variations in amplitude, traveltime, and waveform as a function of offset are controlled by changes in the subsurface elastic properties. Analysis of prestack seismic data provides the opportunity to distinguish between changes in compressional-wave velocity, shear-wave velocity, and density, in the context of an isotropic, locally one-dimensional earth. A practical approach to prestack seismic inversion is developed and applied to a portion of a real data set. As a data preprocessing step, a predictive deconvolution algorithm is devised which incorporates the angle, time, and spatial dependence of the reverberation period into the deconvolution operator. An impedance model is obtained by use of a matched filter which represents the data as a superposition of simple-interface and thin-layer reflections. The inversion results are used to substantiate a modification to the statistically estimated seismic wavelet for a nonwhite reflectivity spectrum. One-dimensional velocity estimation is cast as a linear inverse problem. An initial velocity model, which is parameterized as a superposition of cubic B-splines, is adjusted to account for the residual moveout of selected events. The velocity analysis is fully automated. Residual moveout estimates are obtained implicitly without picking, and the resulting velocity function is guaranteed to be smooth. Primaries-only ray tracing, in which the linearized approximation to the Zoeppritz equations describes the reflection coefficients, serves as the forward modeling algorithm. The linear prestack inversion is based on the three-term linearized approximation to the Zoeppritz equations. This expression is reformulated so that one term incorporates the apriori relationships between the elastic properties and the other two represent perturbations from the apriori assumptions. Effects of thin layering, the seismic wavelet, and normal moveout stretch are incorporated into the Frechet derivatives. A single-iterate maximum-likelihood solution estimates the model parameter perturbations relative to the smooth starting model. Real data results illustrate the importance of a judicious selection of the data and model covariance matrices. Known hydrocarbon accumulations are detected as perturbations relative to the apriori assumptions.Item Seismic traveltime inversion in three-dimensional heterogeneous media(1990) Finn, Christopher Jude, 1960-; Backus, Milo M., 1932-The measured traveltimes of specular reflection events are inverted to obtain a low spatial frequency, three-dimensional model of the reflector geometry and the compressional wave propagation speed. B-spline functions are used to describe the shapes of the interfaces and the lateral variations in velocity. The inversion is performed by optimizing a maximum likelihood criterion using a Newton based iteration. Model updates are obtained by iterative forward modeling and solution of the linearized equation set derived from the maximum likelihood criterion. In the forward problem, the ray tracing equations are solved as a two point boundary value problem with appropriate internal boundary conditions at velocity discontinuities. Analytic expressions for the Frechet derivatives necessary to obtain the model updates are given. Conventional methods are compared to the traveltime inversion technique using synthetic examples. For a relatively simple earth model containing only moderate lateral velocity variations hyperbolic moveout analysis followed by a Dix inversion produces a biased estimate of the velocity and depth. This is a consequence of the simplifying assumptions of the method. In this case, the more general traveltime analysis provides a better result. This is also true for a more complex earth model containing lateral velocity variations and interfaces with large dips and curvatures where the conventional methods fail badly. Picked traveltimes are used as the data in the inversion although the use of the data semblance or the stack power along the predicted traveltime trajectory is also explored. These criterion are shown to be more nonlinear than the least-squares data residual measure. Thus, it is difficult to converge to a global minimum using these criterion and more accurate initial guesses are necessary. An application of the traveltime inversion technique to a 3D marine data set is presented. In this application the effects of the seismic source and the recording system on the measured traveltimes are estimated. The time delay between the first break and the main pulse of the minimum phase source wavelet and the effect of the ghost reflections from the free surface are compensated for in the prediction of the measured traveltimesItem Traveltime inversion for a 3-D near surface velocity model(1987) Simmons, James Layton, 1957-; Backus, Milo M., 1932-The near surface environment is often the source of the most severe lateral velocity variations present in the seismic section. Near surface lateral velocity variations distort the traveltimes of deeper events and are the most serious limitation in achieving accurate structural maps. This work discusses the development of a near surface velocity model for a shallow marine data set. The near surface model consists of three components. The first is a model of the laterally variable seafloor depth and topography. Below the seafloor, the model consists of the compressional wave velocity as a function of depth which reaches a maximum depth of approximately 500 meters. The presence of vertical and lateral velocity gradients is recognized. Embedded within this slowly varying background velocity field are a number of local lens-like velocity anomalies. The lens anomalies represent the major lateral velocity variations present in the near surface. Autocorrelograms of the deeper pre-stack data are used to obtain the seafloor model. The period of the first water layer reverberation is used to estimate the water depth. These data are enhanced by a deconvolution algorithm which improves the agreement at the line intersections. Measured first arrival times from the pre-stack data are used to develop the subseafloor velocity model. A multichannel filter algorithm is devised to estimate the traveltime deviations produced by the lens anomalies and the common shot statics. These traveltime deviations are the higher spatial frequency components of the first arrival times and are produced by the higher spatial frequency components of the velocity model. The output from the algorithm consists of a sixteen layer traveltime (velocity) perturbation model. The estimates of the lens anomaly and shot static produced traveltime deviations are subtracted from the first arrival times to isolate the slowly varying background components. These data are then inverted using the Generalized Linear Inversion and Tausum algorithms to obtain the laterally varying background velocity model.