A sparse matrix method is developed for computing variance factors for block-diagonal, bordered systems of equations using MINQUE (Minimum Norm Quadratic Unbiased Estimation). This method greatly reduces the computational effort required to apply MINQUE, thus making it practical to compute variance factors for some very large systems of equations. The computer implementation of the method is described and applied to the computation of variance factors for a combination of 1609 VLBI (Very Long Baseline Interferometry) observing sessions. The purpose of this test was to compute a variance factor for each of the data sets and, perhaps, to obtain more realistic variance estimates to replace those in common use for the analysis of VLBI data. It was found that the method is satisfactory for use with such large problems, and the test served to verify that the variances in current use in VLBI data adjustments are adequate.

We have used Very Long Baseline Interferometry (VLBI) data to compute the site coordinates and constant velocity components for 29 fixed antenna sites and 25 mobile sites. The three singularities which occur in the adjustment with respect to the rotation of the system have been resolved by a constraint holding the net rotation of seven fixed antennas, distributed on the stable portions of four of the geologic plates, to the net rotation for these sites as defined by the NNR-NUVEL1 no net rotation model. In order to achieve a minimally constrained adjustment of this type we have found it necessary to use a new adjustment procedure in which we solve for the coordinates of each site at the weighted mean epoch of all the observations involving that site.

Geodetic very long baseline interferometry measurements have been extended to the southern hemisphere using stations in South Africa, Tasmania, and Chile. These measurements enabled us to add a number of southern hemisphere radio sources to the catalog that defines our celestial reference frame. Positions have been determined for 81 radio sources ranging in declination from 78-degrees-N to 80-degrees-S with formal errors of a few tenths of a millisecond of arc. Numerical experiments to determine the sensitivity of the estimated positions to systematic error sources such as atmospheric refraction variations indicate that they are roughly comparable in magnitude to the formal errors. Preliminary measurements of the total and correlated source flux densities at 2.3 and 8.4 GHz are presented for a subset of the sources in the southern hemisphere.

RADIO observations using very-long-baseline interferometry (VLBI) can measure the deflection of electromagnetic radiation by the Sun's gravitational field with an accuracy of better than 1 milliarcsecond, and can thus be used to test General Relativity. For an object at an angle-alpha from the centre of the Sun, the expected deflection is 1 (1 + gamma) (M(s)/r(e))((1 + cos-alpha)/(1 - cos-alpha)) 1/2, where M(s) is the mass of the Sun in geometrized units 2 (1.477 x 10(5) cm), r(e) is the distance from the Earth to the Sun in cm, and gamma is a parameter whose value is 1 if General Relativity is correct but which takes on different values in other theories of gravity. For gamma = 1, the deflection is 1,750 mas at the Sun's limb, 4 mas at alpha = 90-degrees and 0 at alpha = 180-degrees. Our analysis of ten years of VLBI data, including observations of objects in the range 2.5-degrees < alpha < 178-degrees, yields an estimate gamma = 1.0002 with a formal standard error of 0.00096 and an estimated standard error of 0.002. This determination is comparable in accuracy and in good agreement with the determination from Mars-Viking time-delay measurements 3.

The Managua earthquake occurred at a shallow depth of focus beneath the center of Managua, producing a maximum intensity of MM IX in the center of the city. The epicenter of the main shock is determined to within several kilometers by use of the strong-motion accelerogram recorded at the ESSO refinery. Such accuracy is unprecedented for a large Central American earthquake, and makes the Managua earthquake valuable as a calibration event for minimizing the bias in location of other earthquakes in Nicaragua. The character of the distribution of P-wave residuals and the location of the earthquake well inland from the Benioff zone in Nicaragua suggest that much of the bias in epicenters calculated for earthquakes in the vicinity of Managua is due to station effects rather than source effects. P-wave first-motions are consistent with a left-lateral strike-slip fault as the earthquake source.

Earthquake focal plane solutions are computed using P wave first motion, S wave polarization angles, and combinations of the two. The method used is based on a maximum-likelihood argument implemented by the generation of a score surface on a discrete grid. The combined score is of the form a(P-score)+b(S-score). For the P-solution and S-solution, the computer system also produces contoured fiducial regions about the poles of the focal planes. This permits an evaluation of the quality of the solutions and makes possible the comparison of solutions for different earthquakes. These contoured limits have a probabilistic interpretation as 95 per cent fiducial regions, a term explained by Pope. A new graphical method for P wave solutions makes possible the construction of exact boundaries of the regions. The Aleutian earthquake of 1969 May 14, is analysed, and the solution shows good agreement between the observed P wave first motions and the S polarization angles.