Statistical analysis of geodetic measurements for the investigation of crustal movements

Abstract

(Accepted for publication June 8, 1978) ABSTRACT: Van Mierlo, J. 1979. Statistical analysis of geodetic measurements for the investigation of crustal movements. In: C.A. Whitten, R. Green and B.K. Meade (Editors), Recent Crustal Movements, 1977. Tectonophysics, 52: 457-467. Geodetic networks are designed to obtain data that can be used to monitor crustal movements. The relative position on the earth's surface is determined from these networks by means of coordinates. The coordinates of stations and its variance—covariance matrix are based on the computational model. In spatial networks at least three points, the base points, should be chosen to define the coordinate system “fixed” to the earth. In monitoring crustal movements these base points are considered to be stationary over the time span of the motion involved. A procedure for testing the stability of the base points, together with other stable points, is described. The coordinate differences between two time epochs, t 0 and t 1 , are considered to investigate crustal movements. A statistical test is introduced to determine whether crustal movements have actually occurred. The reliability, i.e., the influence, of nondetected errors in the observations or computations, should be considered. Two types of decisions can be made which may lead to incorrect conclusions. These conclusions are as follows: 1 That no movement has taken place, although a nondetected error leads to the opposite conclusion. 2 That a movement has occurred, although a nondetected error in the observations leads to the opposite conclusion. The chance of arriving at these conclusions can be computed. Boundary values for assumed crustal motion in specified latitudinal and longitudinal directions give a better insight into the desired specifications for geodetic networks. The testing procedure and the above-mentioned method of computing boundary values can be used for all types of networks, e.g., those obtained by conventional triangulation or by a satellite-borne ranging system.