<abstract xmlns="http://www.w3.org/1999/xhtml">We present a method of approximation of a deformation field based on the local affine transformations constructed based on <italic>n</italic> nearest neighbors with respect to points of adopted grid. The local affine transformations are weighted by means of inverse distance squared between each grid point and observed points (nearest neighbors). This work uses a deformation gradient, although it is possible to use a displacement gradient instead – the two approaches are equivalent. To decompose the deformation gradient into components related to rigid motions (rotations, translations are excluded from the deformation gradient through differentiation process) and deformations, we used a polar decomposition and decomposition into a sum of symmetric and an anti-symmetric matrices (tensors). We discuss the results from both decompositions. Calibration of a local affine transformations model (i.e., number of nearest neighbors) is performed on observed points and is carried out in a cross-validation procedure. Verification of the method was conducted on simulated data-grids subjected to known (functionally generated) deformations, hence, known in every point of a study area.</abstract>

A method for local approximation of a planar deformation field

<abstract xmlns="http://www.w3.org/1999/xhtml">The study area is focused on the Kuril–Kamchatka Trench, North Pacific Ocean. This region is geologically complex, notable for the lithosphere activity, tectonic plates subduction and active volcanism. The submarine geomorphology is complicated through terraces, slopes, seamounts and erosional processes. Understanding geomorphic features of such a region requires precise modelling and effective visualization of the high-resolution data sets. Therefore, current research presents a Generic Mapping Tools (GMT) based algorithm proposing a solution for effective data processing and precise mapping: iterative module-based scripting for the automated digitizing and modelling. Methodology consists of the following steps: topographic mapping of the raster grids, marine gravity and geoid; semi-automatic digitizing of the orthogonal cross-section profiles; modelling geomorphic trends of the gradient slopes; computing raster surfaces from the xyz data sets by modules nearneighbor and XYZ2grd. Several types of the cartographic projections were used: oblique Mercator, Mercator cylindrical, conic equal-area Albers, conic equidistant. The cross-section geomorphic profiles in a perpendicular direction across the two selected segments of the trench were automatically digitized. Developed algorithm of the semi-automated digitizing of the profiles enabled to visualize gradients of the slope steepness of the trench. The data were then modelled to show gradient variations in its two segments. The results of the comparative geomorphic analysis of northern and southern transects revealed variations in different parts of the trench. Presented research provided more quantitative insights into the structure and settings of the submarine landforms of the hadal trench that still remains a question for the marine geology. The research demonstrated the effectiveness of the GMT: a variety of modules, approaches and tools that can be used to produce high-quality mapping and graphics. The GMT listings are provided for repeatability.</abstract>

Topographic surface modelling using raster grid datasets by GMT: example of the Kuril–Kamchatka Trench, Pacific Ocean

<abstract xmlns="http://www.w3.org/1999/xhtml">The article discusses a method applied for combining the results of Global Navigation Satellite Systems (GNSS) and 75-year old triangulation measurements to estimate the crustal movements in central western Bulgaria region. It was examined for joint analysis based on the results of GNSS with angular measurements of the first order triangulation network in Bulgaria during the period 1923–1930 year. As a result of the processing of GNSS and angular measurements, horizontal velocities of 15 points, strain rates, and rotation rates have been obtained. The results show dominating N–S extension at a rate of 1–2 mm/y and the deformation is not uniformly distributed over the studied area. The obtained results indicate the possibility of using old angular measurement of first-order triangulation points, together with GNSS data, to obtain estimates of the horizontal crustal movements.</abstract>

Deformation analysis in central west Bulgaria using triangulation and GPS data

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Reports on Geodesy and Geoinformatics

Volume 108 (2019): Issue 1 (December 2019)

Original Article

A method for local approximation of a planar deformation field

Topographic surface modelling using raster grid datasets by GMT: example of the Kuril–Kamchatka Trench, Pacific Ocean

Deformation analysis in central west Bulgaria using triangulation and GPS data

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