- Copyright © 2004 Society of Exploration Geophysicists
This is the second of a two-part tutorial (the first part was in October's TLE). It provides a theoretical framework from the field of statistical experimental design (SED, a field of statistics) within which model-based survey and experimental design problems and methods can be understood. Specifically, these tutorials describe methods pertinent to the detection and inference of models of physical properties of rocks in the laboratory, or of the earth. Most of this part can be understood without reading Part 1, but if any discussion is unclear, it is likely that reading Part 1 will help.
The choice of method to use to design experiments depends greatly on how one can measure information about a model that is expected to be gleaned from the data acquisition. This in turn depends principally on whether the relationship between those data and the model parameters of interest is approximately linear, or significantly nonlinear. Consequently, Part 1 of this tutorial dealt with cases where this relationship is approximately linear; Part 2 deals with theory for nonlinear problems.
Since Part 1 and Part 2 are sequential, the equation numbers and figure numbers continue from Part 1. Part 1 had equations 1–8 and, hence, Part 2 starts at equation 9; Part 1 had Figures 1–9 and Part 2 starts at Figure 10.
This part begins with a brief recap of key concepts in linear design theory that were covered in Part 1, including two equations without which Part 2 is incomprehensible. A short section then reviews aspects of probability theory; these …