| Abstract: | A variety of geodetic measurements can be combined, in network fashion, to yield adjusted velocities of elevation change. However, it is not always apparent which network junctions have solvable point velocities. When a velocity surface is desired, it is not always apparent how many coefficients should be used. A solvability algorithm, devised to operate on observation equations, answers these questions, and therefore permits the adjustment process to continue with the assurance that the result will be mathematically justified. Using both the hyperboloid and the reciprocal hyperboloid as quadric forms, multiquadric (MQ) analysis has been applied to leveling and tide gauge data in the vicinity of Puget Sound, to obtain heights corresponding to a selected date, and coefficients which collectively define a velocity surface. The solvability algorithm was used to tell which junctions in the level network had solvable point velocities, and consequently where MQ nodal points should be placed for an optimized solution. Networks of simulated data were also used with the solvability algorithm to help determine data requirements for height—velocity adjustments, and to evaluate the ability of MQ analysis to predict velocities. |
