Geodetic network optimization for geophysical parameters

Abstract

The first order design problem in geodesy is generalized here, to seek the network configuration that optimizes the precision of geophysical parameters. An optimal network design that satisfies intuitively appropriate criteria corresponds to minimizing the sum of logarithmic variances of eigenparameters. This is the equivalent to maximizing the determinant of the design matrix, allowing for closed-form analysis. An equivalent expression is also given specifically for square root information filtering, to facilitate numerical solution. Appropriate seeding of numerical solutions can be provided by exact analytical solutions to idealized models. For example, for an ideal transform fault, simultaneous resolution of both the locking depth D and location of the fault is optimized by placing stations at ± D/√3 (∼9 km) from the a priori fault plane. In a two-fault system, the resolution of slip partitioning is optimized by including a station midway between faults; however resolution is fundamentally limited for fault separation <2D (∼30 km).