Globe-module

Modeling horizontal movements and computing parameters of deformations over regular grid on globe. Interpolations are computed by method of inverse distance.
No graphical output.

RELATED ITEMS

It is possible to use two kind of coordinates:

id, Lamda, Fi a dLambda, dFi (their increments).
id, XYZ and their changes (1 _ + _ 3 _ + _ 3 columns)

INPUT DATA FORMAT (without header)

p.n. Lambda Fi delta-La delta-Fi

---------------------------------------------

72 42.47215 49.89760 -0.01 0.03

73 59.14953 35.05893 -0.37 -1.53

p.n. X Y Z dX dY dZ

-----------------------------------------------------------------------------

14 4581691.012 556114.680 4389360.696 -0.0131 0.0189 0.0101

15 4461400.895 919593.423 4449504.682 -0.0187 0.0200 0.0086

Following modification of coordinates performed by module:

coordinates Lamda, Fi are directly used.
coordinates XYZ are transformed Lamdda, Fi (ellipsoid GRS80 is used).

In all following computation simplification is used – Lambda, Fi are supposed to be globe coordinates.

Interpolations by method of inverse distance

GRID COMPUTATION

Main input information is size of grid cell given in degrees (0-360°). (Value suggested in form is 1/10 of maximum latitude).

From (max-min)/2 middle coordinate is computed and by subtracting of grid cell minimal φ is computed. Using then the regular grid from south to north is computed until value exceeds maximal a minimal value (extrapolation is 1 grid cell). For each latitude is computed:

[1]

Using those we get all necessary grid points.

Coordinates of grid are written to text protocol with matrix indexes.

INTERPOLATION PARAMETERS

interpolation parameter – give a number to multiple cell grid to get maximum length in degrees. Only given points closer than this distance will be used for interpolation as confidential.
interpolation parameter – number of points in this distance for interpolated value to be finally signed as confidential (+).

Example:

given points:

Lambda Fi

72 49.89760 42.47215 0.01 -0.03

73 35.05893 59.14953 0.37 -1.83

106 57.74075 44.10062 1.59 -1.53

80 44.67548 41.77455 2.46 -2.41

81 15.93475 32.27514 1.67 -1.40

82 50.79597 36.54120 0.13 -0.16

83 58.22966 58.90978 6.56 -3.29

84 27.39723 68.96487 9.42 -2.78

85 33.96653 29.05811 6.30 -5.19

79 19.53515 31.42702 4.20 -5.08

402 51.49218 26.49980 0.04 -0.44

grid cell: 4

parameter 1: 2

parameter 2: 1

RELIABILITY MATRIX OF INTERPOLATED VALUES

grid cell: 4

parameter 1: 5

parameter 2: 2

RELIABILITY MATRIX OF INTERPOLATED VALUES

INTERPOLATION(INVERSE DISTANCE METHOD)

For each grid point ( i ) its distance (see [3]) to all given points (j) is computed. If the distance is smaller then given maximal distance the value is signed as confidential. If there is requested number of such values, resulting value will be signed as confidential („+“ in reliability matrix).

In case point is not confidential interpolation is computed by same way but distances from ALL given points are used. Resulting value ii signed ( - ) in reliability matrix.

Formula to interpolate value:

[2] , where

where

is resulting interpolated value in given grid point.

are values of displacement at given points

weigh

distances between grid point and given points

COMPUTING DISTANCE BETWEEN GIVEN POINT AND GRID POINT

[3]

RESULTS

TEXT FILE IS GIVEN TO BASIC PROGRAM FOR COMPUTATION OF DEFORMATION PARAMETERS
TEXT PROTOCOL WITH:

user ID
grid cell size and interpolation parameters
number of columns and rows in grid¨
number of given points
reliability matrix of interpolated values for both component of displacement vector.
Grid coordinates Lambda, Fi with matrix indexes