Francis Muir

ROBUST MODELING WITH ERRATIC DATA

An attractive alternative to least‐squares data modeling techniques is the use of absolute value error criteria. Unlike the least‐squares techniques the inclusion of some infinite blunders along with the data will hardly affect the solution to an otherwise well‐posed problem. An example of this great stability is seen when an average is, determined by using the median rather than the arithmetic mean. Algorithms for absolute error minimization are often approximately as costly as least‐squares algorithms; however, unlike least‐squares, they naturally lend themselves to inequality or bounding constraints on models.

Seismic exploration using non-impulsive vibratory sources activated by stationary, Gaussian codes to simulate an impulsive, causal generating, recording and pre-processing system and processing the results into distortion-free final records

The disclosed invention is a method of seismic exploration using non-impulsive vibratory sources activated by filtered stationary, Gaussian codes. The method adds a distortion-free quality to the full-waveform seismic records.

Seismic exploration using non-impulsive vibratory sources activated by stationary, Gaussian codes, detecting vibrations via receivers within a wellbore and processing the results into distortion-free final records

The disclosed invention is a method of seismic exploration using non-impulsive vibratory sources activated by stationary, Gaussian codes in a wellbore environment. The method adds a distortion-free quality to the full-waveform seismic records.

Coupled systems of anisotropic layers: A group formulation

A matrix formalism allows for the simple calculation of the anisotropic, homogeneous medium equivalent to a stationary distribution of thin layers in welded contact. Each layer itself may be an elastic anisotropic medium. The calculated medium is equivalent to the layered medium in the long wavelength limit. The physical properties of any constituent of the heterogeneous system can be shown to be transformable to an element of a commutative group. Adding group elements GA and GB (corresponding to thin layers of constituents A and B, respectively) gives the group element for the homogeneous medium equivalent to the interleaved layers of A and B. The group formulation, which is essentially a statement of conservation laws applicable to layered media, enables us to “decompose” an anisotropic medium into several constituent sets of layers by successive additions of inverse elements, i.e., subtractions. If, after each subtraction, the remaining group element corresponds to a stable anisotropic medium, a valid ...