94 lines
3.9 KiB
C
94 lines
3.9 KiB
C
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/*
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Functions that calculate the gravitational potential and its first and second
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derivatives for the MAG_tesseroid.
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The gravity gradients can be calculated using the general formula of
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Grombein et al. (2010).
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The integrals are solved using the Gauss-Legendre Quadrature rule
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(Asgharzadeh et al., 2007).
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The derivatives of the potential are made with respect to the local coordinate
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system x->North, y->East, z->Up (away from center of the Earth).
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To maintain the standard convention, only for component gz the z axis is
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inverted, so a positive density results in positive gz.
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Example
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-------
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To calculate the gzz component due to a MAG_tesseroid on a regular grid:
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#include <stdio.h>
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#include "glq.h"r
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#include "constants.h"
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#include "grav_tess.h"
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int main()
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{
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MAG_TESSEROID tess = {1000, 44, 46, -1, 1, MEAN_EARTH_RADIUS - 100000,
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MEAN_EARTH_RADIUS};
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GLQ *glqlon, *glqlat, *glqr;
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double lon, lat, r = MEAN_EARTH_RADIUS + 1500000, res;
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int order = 8;
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glqlon = glq_new(order, tess.w, tess.e);
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glqlat = glq_new(order, tess.s, tess.n);
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glqr = glq_new(order, tess.r1, tess.r2);
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for(lat = 20; lat <= 70; lat += 0.5)
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{
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for(lon = -25; lon <= 25; lon += 0.5)
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{
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res = tess_gzz(tess, lon, lat, r, *glqlon, *glqlat, *glqr);
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printf("%g %g %g\n", lon, lat, res);
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}
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}
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glq_free(glqlon);
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glq_free(glqlat);
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glq_free(glqr);
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return 0;
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}
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References
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----------
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Asgharzadeh, M.F., von Frese, R.R.B., Kim, H.R., Leftwich, T.E. & Kim, J.W.
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(2007): Spherical prism gravity effects by Gauss-Legendre quadrature integration.
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Geophysical Journal International, 169, 1-11.
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Grombein, T.; Seitz, K.; Heck, B. (2010): Untersuchungen zur effizienten
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Berechnung topographischer Effekte auf den Gradiententensor am Fallbeispiel der
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Satellitengradiometriemission GOCE.
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KIT Scientific Reports 7547, ISBN 978-3-86644-510-9, KIT Scientific Publishing,
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Karlsruhe, Germany.
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*/
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#ifndef _MAG_TESSEROIDS_GRAV_TESS_H_
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#define _MAG_TESSEROIDS_GRAV_TESS_H_
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/* Needed for definition of MAG_TESSEROID */
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#include "geometry.h"
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/* Needed for definition of GLQ */
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#include "glq.h"
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double calc_tess_model(MAG_TESSEROID *model, int size, double lonp, double latp, double rp, GLQ *glq_lon, GLQ *glq_lat, GLQ *glq_r, double (*field)(MAG_TESSEROID, double, double, double, GLQ, GLQ, GLQ));
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void calc_tess_model_triple(MAG_TESSEROID *model, int size, double lonp, double latp, double rp, GLQ *glq_lon, GLQ *glq_lat, GLQ *glq_r,
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void (*field_triple)(MAG_TESSEROID, double, double, double, GLQ, GLQ, GLQ, double*), double *res);
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double calc_tess_model_adapt(MAG_TESSEROID *model, int size, double lonp, double latp, double rp, GLQ *glq_lon, GLQ *glq_lat, GLQ *glq_r, double (*field)(MAG_TESSEROID, double, double, double, GLQ, GLQ, GLQ), double ratio);
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double tess_gxx(MAG_TESSEROID tess, double lonp, double latp, double rp, GLQ glq_lon, GLQ glq_lat, GLQ glq_r);
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double tess_gxy(MAG_TESSEROID tess, double lonp, double latp, double rp, GLQ glq_lon, GLQ glq_lat, GLQ glq_r);
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double tess_gxz(MAG_TESSEROID tess, double lonp, double latp, double rp, GLQ glq_lon, GLQ glq_lat, GLQ glq_r);
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double tess_gyy(MAG_TESSEROID tess, double lonp, double latp, double rp, GLQ glq_lon, GLQ glq_lat, GLQ glq_r);
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double tess_gyz(MAG_TESSEROID tess, double lonp, double latp, double rp, GLQ glq_lon, GLQ glq_lat, GLQ glq_r);
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double tess_gzz(MAG_TESSEROID tess, double lonp, double latp, double rp, GLQ glq_lon, GLQ glq_lat, GLQ glq_r);
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void tess_gxz_gyz_gzz(MAG_TESSEROID tess, double lonp, double latp, double rp, GLQ glq_lon, GLQ glq_lat, GLQ glq_r, double *res);
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void tess_gxx_gxy_gxz(MAG_TESSEROID tess, double lonp, double latp, double rp, GLQ glq_lon, GLQ glq_lat, GLQ glq_r, double *res);
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void tess_gxy_gyy_gyz(MAG_TESSEROID tess, double lonp, double latp, double rp, GLQ glq_lon, GLQ glq_lat, GLQ glq_r, double *res);
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#endif
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