LEAST-SQUARES SURFACE FITTING WITH DISCONTINUOUS FUNCTIONS.
Abstract
Surfaces with abrupt discontinuities can be described by using discontinuous two dimensional polynomials. Simultaneous least squares solutions can be found which estimate parameters that describe both the discontinuity and the polynomial coefficients. Two models for the common geological example of a faulted structural terrain are treated in detail. In the first the fault plane is vertical, with vertical displacement only. In the second model, both vertical and lateral translation are provided for. The first model is applied to the structural surface of the Dundee Limestone (Devonian) in Central Michigan. Other models for discontinuous surface fitting and other cases in the earth sciences where such models might be useful are briefly mentioned. A computer program for finding the least squares estimates of the fault parameters and the polynomial coefficients is included in an Appendix to this report. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 01, 1968
- Accession Number
- AD0674867
Entities
People
- William R. James
Organizations
- Northwestern University