Derivation and implementation of a nonlinear experimental design criterion and its application to seismic network expansion at Kawerau geothermal field, New Zealand



The accuracy with which geophysical observations are made is inherently determined by the geometry of the observation network, and typically depends on a highly non-linear relationship between data and earth parameters. Statistical experimental design provides a means of optimizing the network geometry to provide maximum information about parameters of interest. Here, we re-derive the nonlinear experimental design DN optimization method, without the need for the usual assumption of a multivariate normal model of data uncertainties. We demonstrate the criterion’s utility by applying it to the problem of seismic network expansion in the active Kawerau geothermal field, Taupo Volcanic Zone, New Zealand. The design calculations maximize the ratio of the hypocentre data generalized variance (attributable to resolvable spatial separation of earthquakes) to the measurement error generalized variance (attributable to observational uncertainties), and incorporate realistic 3-D velocity and attenuation models, surface noise sources, and both P- and S-wave data. In geologically complex areas, statistical experimental design provides a means of objectively deploying finite observational resources to target areas of particular interest while taking into account environmental and logistical factors.