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Fig. 1 | Earth, Planets and Space

Fig. 1

From: High-fidelity elastic Green’s functions for subduction zone models consistent with the global standard geodetic reference system

Fig. 1

Schematics of the coordinate transformation. For simplicity, 1/8 portion of the GRS80 reference ellipsoid is visualized. a Transformation of the coordinate of P from the geographical coordinate system to the ECEF system. Notably, P is located at the ellipsoidal height h. Because the region for the input data is defined in a rectangle area in the geographical coordinate system, it appears to be distorted in the ECEF system, as shown by the area surrounded by the dotted-dashed lines. b Transformation of the coordinate of P from the ECEF system to a local Cartesian coordinate system in which the origin is located at \(P_\text{c}\). Assuming \(h_\text{c}=0\), \(P_\text{c}\) is located on the surface of the GRS80 reference ellipsoid. c Generation of new data points denoted by the black circles that were aligned in an equally spaced structured grid in the xy plane in the local Cartesian coordinate system. White circles are the data points in the original DEM data that are not aligned in an equally spaced structured grid in the local Cartesian system. The z components in the points of the black circles are interpolated from those of the white circles by using the near-neighbor algorithm, as denoted by arrows

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