Albert J. Rudman

Least-squares fit of an ellipse to anisotropic polar data: Application to azimuthal resistivity surveys in karst regions

Abstract Polar plots of various types of anisotropic data are often approximated by ellipses and used by earth scientists as part of the interpretation process. FITELLIPSE, a code to calculate the orientation and values of the major and minor axes of a best-fit ellipse to anisotropic data, is written using Maple, a standard commercial software. A nonlinear statistical parameter is calculated to evaluate the goodness-of-fit. Application to azimuthal resistivity in karst of Indiana demonstrates the direction and degree of the anisotropy.

Correlation of geologic logs with spectral methods

Spectral studies of geologic logs demonstrate that automatic well—log correlation can be processed more efficiently in the frequency domain. Cross correlation of the power spectra of well logs identifies the direction and degree of thickening of stratigraphic sequences between two wells. Given the stretch, the displacement between logs is computed by correlation processes without relying on iterative procedures. Beginning with digitized log data of unequal lengths, power spectra are computed. The stretch factor between the two logs is observed as a difference in frequency scaling. A transform to logarithmic frequencies converts the spectra to a form that reduces the scaling effect of the frequencies to a simple displacement between the plots. A Lagrange interpolation procedure permits cross correlation of the two spectra with a variable window size. The peak value of the resultant correlation function identifies the displacement between the spectra and this, in turn, permits calculation of the stretch factor.

Geophysical analysis in central Indiana using potential field continuation

Seismic, gravity, and total, vertical, and horizontal magnetic surveys were conducted over a prominent basement anomaly in Hamilton County, Indiana, as part of a statewide effort to understand the nature of the basement complex. Application of Poisson’s relationship between the gravity and horizontal magnetic fields demonstrates that the source is not a single, vertically sided prism, but is a body whose outline (shape) varies with depth. Digital model studies support the suggestion that continuation of the fields observed at the surface to levels below the upper surface of the source can be useful in defining the shape of certain sources. Application of this technique was successful in defining a model whose fields closely match those observed in Hamilton County. Geologically, the final model resembles a vertical pipe associated with a succession of overlying flows, a model that is consistent with our present understanding of basement geology in midwestern United States.

A geophysical study of a basement anomaly in Indiana

Seismic, gravity, aeromagnetic, vertical, and horizontal magnetic surveys were made in Indiana as part of a statewide effort to study the basement complex. These surveys were interpreted collectively in a prescribed sequence that led to information ordinarily not obtained individually from such surveys. Prominent seismic reflections and sharp, coincident magnetic and gravity anomalies in Pulaski County, Indiana, were interpreted to show the depth, geometry, and rock type of an anomalous body within the basement complex. Seismic reflection data show the top of the anomalous body to be at a depth of 1.4 km. Analysis of the aeromagnetic anomaly indicates that the body can be approximated by a thick, vertical prism polarized along the earth’s field. Second derivative analysis of the vertical magnetic anomaly outlines the body as roughly circular and 29km2 in area. Curve‐fitting between the observed vertical magnetic anomaly and an anomaly computed for the prismatic model readily shows that the body has a vert...

Workstation computation of synthetic seismograms for vertical and horizontal profiles: a full wavefield response for a two-dimensional layered half-space

Abstract FORTRAN code for generation of full wavefield synthetic seismograms is presented for two-dimensional horizontally layered models bounded by a free surface and a half space. Model layers are user defined by compressional and shear velocities, Q factors, densities and thicknesses. The algorithm is based on the reflectivity method and uses the propagator matrix approach. Explosion (point) and double couple (fault) sources are generated with a moment tensor representation. As evaluation of the slowness integrals involves time consuming numerical Hankel transforms, these computations are made with a generalized Filon method that saves computational time. The architecture of the program is unusual because the outermost loop is over temporal frequency and the innermost loop is over slowness. This permits the use of frequency-dependent seismic velocities, necessary for causality, while giving a factor of seven speed-up from vectorization. The codes are applicable for both vector computers and workstations. Two test cases demonstrate successful applications of the codes for both horizontal seismic profiles (receivers at one depth at successively larger offsets) and for vertical seismic profiles (receivers arranged in a vertical array at any offset). Receivers and source may be positioned within any layer. The seismograms display direct, refracted, reflected, and head-wave arrivals and their multiples. Mode converted events of compressional and shear propagation are generated and identified. The code generates seismograms for pressure, vertical and horizontal displacement sensors and for models combining acoustic and elastic layers.

Computer Prediction of Changes in Stratigraphic Intervals: ABSTRACT

Computer correlation of well-log data usually presumes some prior knowledge of the direction and degree of stratigraphic thickening. Model studies, however, show that power spectra can identify the relative changes in stratigraphic intervals between wells. Given the stretch factor, the displacement between logs is computed without relying on iterative procedures. Study of real data shows that each well log is associated with a specific set of frequencies complicated by the presence of noise. Therefore, successful applications depend on the process of modifying the frequency spectra before correlation. End_of_Article - Last_Page 518------------

Reply by authors to discussion by Douglas J. Guion

The authors’ model studies depended primarily on downward continuation of the magnetic field (p. 884). Satisfactory results were obtained for magnetic models, but certain discrepancies were observed for gravity (p. 887). Mr. Guion’s comments on some differences between the observed and model gravity anomalies are, therefore, well taken. In his view these differences cannot be attributed to the manner in which the regional gradient is removed or to the choice of density contrast used in constructing the model. Our opinion is that he underestimates the importance of both of these parameters.

Geophysical Analysis in Central Indiana using Potential Field Continuation; discussion and reply

I read with interest the article concerning modeling the Hamilton County, Indiana, gravity and magnetic anomaly. The authors’ method for outlining the igneous body by downward continuation aroused my curiosity to the point that I decided to study the results in detail. My investigation revealed that the calculated gravity effect of the model did not satisfy the observed gravity anomaly. In fact, the amount of mismatch is quite serious.