initial upload

lib/grav_tess.h

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