Representing distributed deformation by continuous velocity fields

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Haines, A.J.; Jackson, J.A.; Holt, W.E.; Agnew, D.C. 1998 Representing distributed deformation by continuous velocity fields. Lower Hutt: Institute of Geological & Nuclear Sciences. Institute of Geological & Nuclear Sciences science report 98/05 1 v.

Abstract: This report contains the draft of two papers describing techniques for recovering velocity fields representing the long-term deformation of the lithosphere from short-term observations of the strain rate distribution. They are refererred to as Part I, Introducing the new spline method; and Part II, The influence of data uncertainties. In the first paper we explain a new method in which the velocity field is described by a bi-cubic spline expansion fitted to an irregularly-shaped grid. It has considerable advantages of flexibility and resolution over previously-used polynomial expansion, and although we have used it in various studies, it has never been described in sufficient detail for others to use it: that is the purpose of these papers. We illustrate the new method and its application by obtaining velocity fields in the deforming Aegean Sea region of Greece. We compare the spline and polynomial methods, and demonstrate that, by producing diagnostic artifacts when the areas over which the strain rate data are averaged are too small, the improved resolution of the spline method is helpful in determining how large the areas have to be for the seismicity catalogue to be representative of a long-term pattern. In the second paper we discuss problems associated with the data being of short duration, incomplete spatial distribution, limited spatial resolution, limited magnitude range ( in the case of earthquakes), or of mixed type. Most of these problems can be reduced or overcome by treatment of both the data itself (usually involving some smoothing) and its variances and covariances. We discuss the nature of these problems and how to reduce them, focussing especially on aspects related to the data variances and covariances, and then illustrate the application of the methods we advocate to the Aegean Sea region, where it is possible to compare and combine earthquake and geodetic data to estimate where (and how much) strain rates estimated from 82 years of earthquakes are unable to account for the deformation that is occurring. (auth/EB)