A LINEAR METHOD FOR ANALYZING LIGHTNING FIELD CHANGES

A constrained, least-squares method for analyzing multiple-station mea surements of lightning field changes (DELTAEs) is introduced. Previous methods have attempted to fit the spatial pattern of lightning DELTAE s using nonlinear models, such as a point charge (Q) or a point dipole (P) model. With the linear method, the DELTAEs are described not by m odels but by a general volume charge distribution that is deposited on a large (40 x 40 x 20 km3) Cartesian grid above the measuring network . A linear system of equations is used to relate the measured DELTAEs to the charges that are deposited at each grid point. With this approa ch, the information content of the measurements can be quantified by a n eigenanalysis of the covariance matrix of the liner system. Constrai nts can be used to reduce the infinity of possible solutions to the li near system and also to reduce systematic biases that can be introduce d by the method of solution. It is shown that a Landweber iterative me thod, derived from the general method of steepest descent, can be used to solve the linear system and that the resulting volume charge distr ibutions are generally consistent with computer-simulated charge sourc es, when these sources are over the measuring network. The Landweber i teration has also provided solutions for natural lightning events that are consistent with Q- and P-model results.