Solvability and multiquadric analysis as applied to investigations of vertical crustal movements

Pattern of recent vertical crustal movements in Canada

“…The method of SPAA avoids many of the limitations associated with traditional approaches of data fitting such as the requirement that the data be of point values, as it is seen in MQ method (Holdahl and Hardy, 1978) and in B-splines (Gregorski et al, 2000;Greiner and Hormann, 1996); or that they should be on grid or at least well distributed (Zhou et al, 1997). SPAA is not restricted to low degree polynomial (as it is seen in Carrera et al, 1991;Vaníček and Nagy, 1981) and the smoothness of the resulting function is guaranteed along the patch boundaries by imposing the continuity and smoothness (zero and first derivative) constraints and the degree of smoothness can be simply controlled by the number and degree of differentiability constraints in the model, which results in a smooth surface.…”

“…Very comprehensive reviews of modeling strategies for vertical crustal deformation are presented by e.g. Vaníček and Christodulids (1974), Holdahl and Hardy (1978), Chrzanowski et al (1986), Vaníček and Sjöberg (1987), Carrera et al (1991), Liu and Parm (1996), and Liu and Chen (1998). All of the models can estimate deformation parameters for multi-epoch observations.…”

Models and Techniques in Geodetic Monitoring of Tectonic Deformations in Greece

“…The simultaneous adjustment of the observations of many epochs was presented by Whitten (1967), where movements are approached by functions of space and time of the above form. Subsequently relevant papers were given by Snay and Gergen (1978), Snay et al (1983), Chrzanowski et al (1986), Welsch (1986) and regarding the determination of the vertical movements by Holdahl (1978), Vanicek (1975, Vanicek et al (1979), Holdahl and Hardy (1979) and Mälzer et al (1979). As in the previous case of dependent movements in time, the following should be noted: -The reference epoch is not necessarily a measuring epoch.…”

Geodetic Monitoring of Tectonic Deformation: Toward a Strategy

“…For describing deformation, we encourage the introduction of more realistic models. Previous data-reduction schemes have concentrated on empirical models, e.g., polynomial or multiquadratic expressions (Vanicek et al, 1979;Snay and Gergen, 1978;Holdahl and Hardy, 1979). Physical models have yet to find widespread applicatio: ► i except perhaps for the dislocation models (Chinnery, 196 1;Savage and Hastie, 1966).…”