Optimal experiment design: crossborehole tomographic examples
Abstract
Experiment design optimization requires that the quality of any particular design can be both quantified and then maximized. In this study, experiment quality is defined to measure the constraints on a particular model offered by the anticipated experimental data (that is, it measures anticipated model information postexperiment). Physical and financial constraints define the space of possible experimental designs. The definitions used here require that the relationship between model parameters and data can be linearized without significant loss of information.
Two new measures of model information are introduced and compared to three previously known measures. One of the new measures can be calculated extremely efficiently allowing experiments constraining large model spaces to be designed. This efficiency trades off with a lack of sensitivity to poorly constrained parts of the model. Each measure is used independently to design a crossborehole tomographic survey including surface sources and receivers (henceforth called nodes) which maximally constrains the interborehole velocity structure. The boreholes are vertical and the background velocity is assumed to be approximately constant. Features common to most or all optimal designs form robust design criteria`rules of thumb'which can be applied to design future experiments. These are:
(1) surface nodes significantly improve designs
(2) node density increases steadily down the length of each well
(3) surface node density is increased slightly around the central point between the wells
(4) average node density on the ground surface is lower than that down each well.
Three of these criteria are shown to be intuitively reasonable (the fourth is not), but the current method is quantitative and hence may be applied in situations where intuition breaks down (for example, nonvertical wells with multilateral splays; combining different data types; inversion for anisotropic model parameters). In such cases the optimal design is usually not obvious, but can be found using the quantitative methods introduced and discussed herein.
 Publication:

Geophysical Journal International
 Pub Date:
 March 1999
 DOI:
 10.1046/j.1365246X.1999.00749.x
 Bibcode:
 1999GeoJI.136..637C
 Keywords:

 crossborehole tomography;
 experiment;
 information;
 optimal design;
 survey