Optimal design of focused experiments and surveys

SUMMARY Experiments and surveys are often performed to obtain data that constrain some previously underconstrained model. Often, constraints are most desired in a particular subspace of model space. Experiment design optimization requires that the quality of any particular design can be both quanti¢ed and then maximized.This study shows how the quality can be de¢ned such that it depends on the amount of information that is focused in the particular subspace of interest. In addition, algorithms are presented which allow one particular focused quality measure (from the class of focused measures) to be evaluated e⁄ciently. A subclass of focused quality measures is also related to the standard variance and resolution measures from linearized inverse theory. The theory presented here requires thatthe relationship between model parameters and data can be linearized around a reference model without signi¢cant loss of information. Physical and ¢nancial constraints de¢ne the space of possible experiment designs. Cross-well tomographic examples are presented, plus a strategy for survey design to maximize information about linear combinations of parameters such as bulk modulus, i~jz2k/3.