Geodetic network optimization for geophysical parameters

The first order design problem in geodesy is generalized here, to seek the network configuration that optimizes the precision of geophysical parameter s. An optimal network design that satisfies intuitively appropriate criteri a corresponds to minimizing the sum of logarithmic variances of eigenparame ters. This is 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 numerica l solution. Appropriate seeding of numerical solutions can be provided by e xact analytical solutions to idealized models. For example, for an ideal tr ansform fault, simultaneous resolution of both the locking depth D and loca tion of the fault is optimized by placing stations at +/- D/root3 (similar to9 km) from the a priori fault plane. Tn a two-fault system, the resolutio n of slip partitioning is optimized by including a station midway between f aults; however resolution is fundamentally limited for fault separation <2D (<similar to>30 km).