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/***********************************************/
/**
* @file kernelGeoid.cpp
*
* @brief Integral kernel of geoid computation.
* (= Poisson Kern * gamma).
* @see Kernel
*
* @author Torsten Mayer-Guerr
* @date 2003-09-20
*
*/
/***********************************************/
#include "base/import.h"
#include "base/planets.h"
#include "classes/gravityfield/gravityfield.h"
#include "classes/kernel/kernel.h"
#include "classes/kernel/kernelGeoid.h"
/***********************************************/
Vector KernelGeoid::coefficients(Vector3d const &q, UInt degree) const
{
try
{
if(degree==INFINITYDEGREE)
throw(Exception("INFINITYDEGREE requested"));
Vector k(degree+1);
Double *kn = k.field();
Double gamma = Planets::normalGravity(q);
for(UInt n=0; n<=degree; n++)
*kn++ = gamma;
return k;
}
catch(std::exception &e)
{
GROOPS_RETHROW(e)
}
}
/***********************************************/
Vector KernelGeoid::inverseCoefficients(Vector3d const &p, UInt degree, Bool /*interior*/) const
{
try
{
if(degree==INFINITYDEGREE)
throw(Exception("INFINITYDEGREE requested"));
Vector k(degree+1);
Double *kn = k.field();
Double gamma = Planets::normalGravity(p);
for(UInt n=0; n<=degree; n++)
*kn++ = 1./gamma;
return k;
}
catch(std::exception &e)
{
GROOPS_RETHROW(e)
}
}
/***********************************************/
Double KernelGeoid::kernel(Vector3d const &p, Vector3d const &q) const
{
Vector3d diff = p-q;
Double r = p.r();
Double R = q.r();
Double l = diff.r();
return Planets::normalGravity(q) * R*(r*r-R*R)/(l*l*l);
}
/***********************************************/
Double KernelGeoid::radialDerivative(Vector3d const &p, Vector3d const &q) const
{
Vector3d diff = p-q;
Double r = p.r();
Double R = q.r();
Double l = diff.r();
Double cos_psi = (R*R+r*r-l*l)/(2*R*r);
Double dl_dr = (r-R*cos_psi)/l;
return Planets::normalGravity(q) * R*(2*r*l-(r*r-R*R)*3*dl_dr)/(l*l*l*l);
}
/***********************************************/
Vector3d KernelGeoid::gradient(Vector3d const &p, Vector3d const &q) const
{
Vector3d diff = p-q;
Double r = p.r();
Double l = diff.r();
Double R = q.r();
return Planets::normalGravity(q) * (2/(l*l*l)*p - 3*(r*r-R*R)/(l*l*l*l*l)*diff);
}
/***********************************************/
Tensor3d KernelGeoid::gradientGradient(const Vector3d &p, const Vector3d &q) const
{
Tensor3d tns;
Vector3d diff = p-q;
Double r = p.r();
Double R = q.r();
Double l = diff.r();
Double l2 = l*l;
Double l3 = l2*l;
Double l5 = l3*l2;
Double l7 = l5*l2;
Double term = r*r-R*R;
tns.xx() = 2.0/l3 - 12.0*p.x()*diff.x()/l5 + 15*term*diff.x()*diff.x()/l7 - 3.0*term/l5;
tns.yy() = 2.0/l3 - 12.0*p.y()*diff.y()/l5 + 15*term*diff.y()*diff.y()/l7 - 3.0*term/l5;
tns.zz() = 2.0/l3 - 12.0*p.z()*diff.z()/l5 + 15*term*diff.z()*diff.z()/l7 - 3.0*term/l5;
tns.xy() = -6.0*(p.x()*diff.y()+p.y()*diff.x())/l5 + 15.0*term*diff.x()*diff.y()/l7;
tns.xz() = -6.0*(p.x()*diff.z()+p.z()*diff.x())/l5 + 15.0*term*diff.x()*diff.z()/l7;
tns.yz() = -6.0*(p.y()*diff.z()+p.z()*diff.y())/l5 + 15.0*term*diff.y()*diff.z()/l7;
return Planets::normalGravity(q) * tns;
}
/***********************************************/
Double KernelGeoid::inverseKernel(Vector3d const &p, Vector3d const &q, const Kernel &kernel) const
{
// geoid = potential/gamma
return (1./Planets::normalGravity(p)) * kernel.kernel(p, q);
}
/***********************************************/
Double KernelGeoid::inverseKernel(const Time &time, const Vector3d &p, const GravityfieldBase &field) const
{
// geoid = potential/gamma
return (1./Planets::normalGravity(p)) * field.potential(time, p);
}
/***********************************************/
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