Almost all kinds of observations refering to any geodetic network can be strictly adjusted on the reference ellipsoid by the PAG-U Program. First program was made in 1966 [1]. Computations of crustal strains were added in 1971 [3]. Strains are computed on the local plane-coordinates transformed through a simple formula (1) for individual triangle. If the crust is distorted according to a linear transformation with the lapse of time, relations (2) exist between old and new coordinates of three stations in a triangle, and we can find six strain-constants xo, yo, a, b, c and d for every triangle. In those constants xo and yo refer to parallel movement of the crust alone. All kinds of horizontal crustal strains such as rotation, dilatation, maximum shear, major and minor principal axes of a strain ellipse are computed by using those constants through formulas from (3) to (8) in the previous paper [3]. PAG-U Program has been frequently used to find geodetically crustal deformations in GSI and PASCO. Recently standard deviations have been added to strains in the PAG-U Program in order to estimate rigorously reliabilities of strains. Fig. 1 is flow-chart of revised part in the program. Main part of correction in the program is to insert the computation of (3) in which Ce is a variance-covariance matrix of all strains in a triangle, C is a variance-covariance matrix of unknown column vector X found in old and new geodetic net-adjustments, and T is a coefficient matrix of old and new δλi cos pi and δpi (i=1, 2, 3) in the formulas of all strains. Of course δλi and δpi are small increments to be added to assumed longitude and latitude of st. Pi through net-adjustment. Unknown in longitude is merely not 62 but δλ cos p in PAG-U, because δλ cos p is more convenient than 52 for free-net adjustment. Of course standard deviation of every strain is root of corresponding diagonal element in Ca. The actual computation of T in (3) is not so simple as to be expected from its simplicity, because strains are not directly expressed as functions of longitude and latitude but indirectly as functions of a, b, c and d. There are quaternary propagations in errors between strains and ellipsoidal coordinates. They are propagation relations such as first between strains and (a, b, c, d), second between (a, b, c, d) and plane coordinates of three stations, thirdly between plane coordinates and azimuths (A) and distances (S) of three geodetic lines from local origin to each station, and fourthly between (A, S) and ellipsoidal coordinates. In spite of complexity in propagation of errors, T is accurately found by computing numerically twelve coefficients consisting of old and new (δλicos p i, δpi, i=1, 2, 3) at each steps of the quaternary propagations of errors. An example of actual result of crustal strains with their standard deviations is shown in the Table I.
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