/// <summary>
/// Evaluate the components of the gravity anomaly vector using the spherical approximation.
/// </summary>
/// <param name="lat">the geographic latitude (degrees).</param>
/// <param name="lon">the geographic longitude (degrees).</param>
/// <param name="h">the height above the ellipsoid (meters).</param>
/// <returns>
/// <list type="bullet">
/// <item><i>Dg01</i>, the gravity anomaly (m s^−2).</item>
/// <item><i>xi</i>, the northerly component of the deflection of the vertical (degrees).</item>
/// <item><i>eta</i>, the easterly component of the deflection of the vertical (degrees).</item>
/// </list>
/// </returns>
/// <remarks>
/// The spherical approximation (see Heiskanen and Moritz, Sec 2-14) is used so that the results of
/// the NGA codes are reproduced accurately. approximations used here.
/// Details are given in
/// <a href="https://geographiclib.sourceforge.io/html/gravity.html#gravitygeoid">Details of the geoid height and anomaly calculations</a>.
/// </remarks>
public (double Dg01, double xi, double eta) SphericalAnomaly(double lat, double lon, double h)
{
Span <double> M = stackalloc double[Geocentric.dim2_];
var(X, Y, Z) = _earth.Earth.IntForward(lat, lon, h, M);
double
T = InternalT(X, Y, Z, out var deltax, out var deltay, out var deltaz, true, false),
clam = M[3], slam = -M[0],
P = Hypot(X, Y),
R = Hypot(P, Z),
// psi is geocentric latitude
cpsi = R != 0 ? P / R : M[7],
spsi = R != 0 ? Z / R : M[8];
// Rotate cartesian into spherical coordinates
Span <double> MC = stackalloc double[Geocentric.dim2_];
Geocentric.Rotation(spsi, cpsi, slam, clam, MC);
Geocentric.Unrotate(MC, deltax, deltay, deltaz, out deltax, out deltay, out deltaz);
// H+M, Eq 2-151c
var Dg01 = -deltaz - 2 * T / R;
var(_, gammaX, gammaY, gammaZ) = _earth.U(X, Y, Z);
var gamma = Hypot(Hypot(gammaX, gammaY), gammaZ);
var xi = -(deltay / gamma) / Degree;
var eta = -(deltax / gamma) / Degree;
return(Dg01, xi, eta);
}
/// <summary>
/// Evaluate the gravity at an arbitrary point above (or below) the ellipsoid.
/// </summary>
/// <param name="lat">the geographic latitude (degrees).</param>
/// <param name="lon">the geographic longitude (degrees).</param>
/// <param name="h">the height above the ellipsoid (meters).</param>
/// <returns>
/// <list type="bullet">
/// <item><i>W</i>, the sum of the gravitational and centrifugal potentials (m^2 s^−2).</item>
/// <item><i>gx</i>, the easterly component of the acceleration (m s^−2).</item>
/// <item><i>gy</i>, the northerly component of the acceleration (m s^−2).</item>
/// <item><i>gz</i>, the upward component of the acceleration (m s^−2); this is usually negative.</item>
/// </list>
/// </returns>
/// <remarks>
/// The function includes the effects of the earth's rotation.
/// </remarks>
public (double W, double gx, double gy, double gz) Gravity(double lat, double lon, double h)
{
Span <double> M = stackalloc double[Geocentric.dim2_];
var(X, Y, Z) = _earth.Earth.IntForward(lat, lon, h, M);
var(Wres, gx, gy, gz) = W(X, Y, Z);
Geocentric.Unrotate(M, gx, gy, gz, out gx, out gy, out gz);
return(Wres, gx, gy, gz);
}
/// <summary>
/// Evaluate the gravity disturbance vector at an arbitrary point above (or below) the ellipsoid.
/// </summary>
/// <param name="lat">the geographic latitude (degrees).</param>
/// <param name="lon">the geographic longitude (degrees).</param>
/// <param name="h">the height above the ellipsoid (meters).</param>
/// <returns>
/// <list type="bullet">
/// <item><i>T</i>, the corresponding disturbing potential (m2 s−2).</item>
/// <item><i>deltax</i>, the easterly component of the disturbance vector (m s^−2).</item>
/// <item><i>deltay</i>, the northerly component of the disturbance vector (m s^−2).</item>
/// <item><i>deltaz</i>, the upward component of the disturbance vector (m s^−2).</item>
/// </list>
/// </returns>
public (double T, double deltax, double deltay, double deltaz) Disturbance(double lat, double lon, double h)
{
Span <double> M = stackalloc double[Geocentric.dim2_];
var(X, Y, Z) = _earth.Earth.IntForward(lat, lon, h, M);
var Tres = InternalT(X, Y, Z, out var deltax, out var deltay, out var deltaz, true, true);
Geocentric.Unrotate(M, deltax, deltay, deltaz, out deltax, out deltay, out deltaz);
return(Tres, deltax, deltay, deltaz);
}
/// <summary>
/// Evaluate the gravity.
/// </summary>
/// <param name="lon">the geographic longitude (degrees).</param>
/// <returns>
/// <list type="bullet">
/// <item><i>W</i>, the sum of the gravitational and centrifugal potentials (m^2 s^−2).</item>
/// <item><i>gx</i>, the easterly component of the acceleration (m s^−2).</item>
/// <item><i>gy</i>, the northerly component of the acceleration (m s^−2).</item>
/// <item><i>gz</i>, the upward component of the acceleration (m s^−2); this is usually negative.</item>
/// </list>
/// </returns>
/// <remarks>The function includes the effects of the earth's rotation.</remarks>
public (double W, double gx, double gy, double gz) Gravity(double lon)
{
Span <double> M = stackalloc double[Geocentric.dim2_];
SinCosd(lon, out var slam, out var clam);
var(Wres, gx, gy, gz) = W(slam, clam);
Geocentric.Rotation(_sphi, _cphi, slam, clam, M);
Geocentric.Unrotate(M, gx, gy, gz, out gx, out gy, out gz);
return(Wres, gx, gy, gz);
}
/// <summary>
/// Evaluate the gravity disturbance vector.
/// </summary>
/// <param name="lon">the geographic longitude (degrees).</param>
/// <returns>
/// <list type="bullet">
/// <item><i>T</i>, the corresponding disturbing potential (m2 s−2).</item>
/// <item><i>deltax</i>, the easterly component of the disturbance vector (m s^−2).</item>
/// <item><i>deltay</i>, the northerly component of the disturbance vector (m s^−2).</item>
/// <item><i>deltaz</i>, the upward component of the disturbance vector (m s^−2).</item>
/// </list>
/// </returns>
public (double T, double deltax, double deltay, double deltaz) Disturbance(double lon)
{
Span <double> M = stackalloc double[Geocentric.dim2_];
SinCosd(lon, out var slam, out var clam);
var Tres = InternalT(slam, clam, out var deltax, out var deltay, out var deltaz, true, true);
Geocentric.Rotation(_sphi, _cphi, slam, clam, M);
Geocentric.Unrotate(M, deltax, deltay, deltaz, out deltax, out deltay, out deltaz);
return(Tres, deltax, deltay, deltaz);
}
private (double Bx, double By, double Bz) Field(double t, double lat, double lon, double h, bool diffp,
out double Bxt, out double Byt, out double Bzt)
{
Bxt = Byt = Bzt = default;
Span <double> M = stackalloc double[Geocentric.dim2_];
var(X, Y, Z) = _earth.IntForward(lat, lon, h, M);
// Components in geocentric basis
// initial values to suppress warning
var(BX, BY, BZ) = FieldGeocentric(t, X, Y, Z, out var BXt, out var BYt, out var BZt);
if (diffp)
{
Geocentric.Unrotate(M, BXt, BYt, BZt, out Bxt, out Byt, out Bzt);
}
Geocentric.Unrotate(M, BX, BY, BZ, out var Bx, out var By, out var Bz);
return(Bx, By, Bz);
}
private (double Bx, double By, double Bz) Field(double lon, bool diffp,
out double Bxt, out double Byt, out double Bzt)
{
Bxt = Byt = Bzt = default;
SinCosd(lon, out var slam, out var clam);
Span <double> M = stackalloc double[Geocentric.dim2_];
Geocentric.Rotation(_sphi, _cphi, slam, clam, M);
var(BX, BY, BZ) = FieldGeocentric(slam, clam, out var BXt, out var BYt, out var BZt);
if (diffp)
{
Geocentric.Unrotate(M, BXt, BYt, BZt, out Bxt, out Byt, out Bzt);
}
Geocentric.Unrotate(M, BX, BY, BZ, out var Bx, out var By, out var Bz);
return(Bx, By, Bz);
}
/// <summary>
/// Evaluate the components of the gravity anomaly vector using the spherical approximation.
/// </summary>
/// <param name="lon">the geographic longitude (degrees).</param> w
/// <returns>
/// <list type="bullet">
/// <item><i>Dg01</i>, the gravity anomaly (m s^−2).</item>
/// <item><i>xi</i>, the northerly component of the deflection of the vertical (degrees).</item>
/// <item><i>eta</i>, the easterly component of the deflection of the vertical (degrees).</item>
/// </list>
/// </returns>
/// <remarks>
/// The spherical approximation (see Heiskanen and Moritz, Sec 2-14) is used so that the results of the NGA codes are
/// reproduced accurately. approximations used here.
/// Details are given in
/// <a href="https://geographiclib.sourceforge.io/html/gravity.html#gravitygeoid">Details of the geoid height and anomaly calculations</a>.
/// </remarks>
public (double Dg01, double xi, double eta) SphericalAnomaly(double lon)
{
if (_caps.HasFlag(GravityFlags.SphericalAnomaly))
{
return(double.NaN, double.NaN, double.NaN);
}
SinCosd(lon, out var slam, out var clam);
double
deltax, deltay, deltaz,
T = InternalT(slam, clam, out deltax, out deltay, out deltaz, true, false);
// Rotate cartesian into spherical coordinates
Span <double> MC = stackalloc double[Geocentric.dim2_];
Geocentric.Rotation(_spsi, _cpsi, slam, clam, MC);
Geocentric.Unrotate(MC, deltax, deltay, deltaz, out deltax, out deltay, out deltaz);
// H+M, Eq 2-151c
var Dg01 = -deltaz - 2 * T * _invR;
var xi = -(deltay / _gamma) / Degree;
var eta = -(deltax / _gamma) / Degree;
return(Dg01, xi, eta);
}
