Gravityfield

This class computes functionals of the time depending gravity field, e.g potential, gravity anomalies or gravity gradients.

If several instances of the class are given the results are summed up. Before summation every single result is multiplicated by a factor. To subtract a normal field like GRS80 from a potential to get the disturbance potential you must choose one factor by 1 and the other by -1. To get the mean of two fields just set each factor to 0.5.

Some of the instances gives also information about the accuracy. The variance of the result (sum) is computed by means of variance propagation.

PotentialCoefficients

Reads coefficients of a spherical harmonics expansion from file. The potential is given by \[ V(\lambda,\vartheta,r) = \frac{GM}{R}\sum_{n=0}^\infty \sum_{m=0}^n \left(\frac{R}{r}\right)^{n+1} \left(c_{nm} C_{nm}(\lambda,\vartheta) + s_{nm} S_{nm}(\lambda,\vartheta)\right). \]If set the expansion is limited in the range between minDegree and maxDegree inclusivly. The computed result is multiplied with factor. If setSigmasToZero is true the variances are set to zero. This option is only important for variance propagation and does not change the result of the gravity field functionals.

Name	Type	Annotation
inputfilePotentialCoefficients	filename
minDegree	uint
maxDegree	uint
factor	double	the result is multiplied by this factor, set -1 to subtract the field
setSigmasToZero	boolean	set variances to zero, should be used by adding back reference fields

PotentialCoefficientsInterior

Reads coefficients of a spherical harmonics expansion (for inner space) from file. If set the expansion is limited in the range between minDegree and maxDegree inclusivly. The computed result is multiplied with factor. If setSigmasToZero is true the variances are set to zero. This option is only important for error propagation and does not change the result of the gravity field functionals.

Name	Type	Annotation
inputfilePotentialCoefficients	filename
minDegree	uint
maxDegree	uint
factor	double	the result is multiplied by this factor, set -1 to subtract the field
setSigmasToZero	boolean	set variances to zero, should be used by adding back reference fields

FromParametrization

Reads a solution vector from file inputfileSolution which may be computed by a least squares adjustment (e.g. by NormalsSolverVCE). The coefficients of the vector are interpreted from position indexStart (counting from zero) with help of parametrizationGravity. If the solution file contains solution of several right hand sides you can choose one with number rightSide (counting from zero). You can also read a vector from file inputfileSigmax containing the accuracies of the coefficients.

The computed result is multiplied with factor.

Name	Type	Annotation
parametrization	parametrizationGravity
inputfileSolution	filename	solution vector
inputfileSigmax	filename	standards deviations or covariance matrix of the solution
indexStart	uint	position in the solution vector
rightSide	uint	if solution contains several right hand sides, select one
factor	double	the result is multiplied by this factor, set -1 to subtract the field

TimeSplines

Read a time variable gravity field from file inputfileTimeSplinesGravityfield represented by a spherical harmonics expansion in the spatial domain and spline functions in the time domain. If set the expansion is limited in the range between minDegree and maxDegree inclusivly.

This file can be created for example by Gravityfield2TimeSplines or PotentialCoefficients2BlockMeanTimeSplines.

The computed result is multiplied with factor.

Name	Type	Annotation
inputfileTimeSplinesGravityfield	filename
inputfileTimeSplinesCovariance	filename
minDegree	uint
maxDegree	uint
factor	double	the result is multiplied by this factor, set -1 to subtract the field

Trend

The given gravityfield is interpreted as trend function and the result is computed at time $t$ as follows \[ V(\M x,t) = \frac{t-t_0}{\Delta t}V(\M x), \]with $t_0$ is timeStart and $\Delta t$ is timeStep.

Name	Type	Annotation
gravityfield	gravityfield	this field is multiplicated by (time-time0)/timeStep
timeStart	time	reference time
timeStep	time

Oscillation

The given gravityfield is interpreted as oscillation function and the result is computed at time $t$ as follows \[ V(\M x,t) = \cos(\omega)V_{cos}(\M x)+\sin(\omega)V_{sin}(\M x), \]with $\omega=\frac{2\pi}{T}(t-t_0)$.

Name	Type	Annotation
gravityfieldCos	gravityfield	multiplicated by cos(2pi/T(time-time0))
gravityfieldSin	gravityfield	multiplicated by sin(2pi/T(time-time0))
time0	time	reference time
period	time	[day]

InInterval

A gravityfield is only evaluated in the interval between timeStart inclusively and timeEnd exclusively. Outside the interval the result is zero.

This class is useful to get a time series of monthly mean GRACE gravity field solutions. In each month another file of potentialCoefficients is valid. This can easily be created with loop.

Name	Type	Annotation
gravityfield	gravityfield
timeStart	time	first point in time
timeEnd	time	last point in time will be less or equal timeEnd

Tides

Treat tides as gravitational forces. The tides need a realization of earthRotation to transform between the CRF and TRF and to compute rotational deformation from polar motion. It also needs ephemerides from Sun, moon, and planets.

Name	Type	Annotation
tides	tides
earthRotation	earthRotation
ephemerides	ephemerides

Topography

The gravity is integrated from a topographic mass distribution. For each grid point in inputfileGridRectangular a prisma with density is assumed. The horizontal extension is computed from the grid spacing and the vertical extension is given by radialLowerBound and radialUpperBound above ellipsoid. All values are expressions and computed for each point with given data in the grid file. The standard variables for grids are available, see dataVariables.

Example: The grid file contains the orthometric height of the topography in the first column, the geoid height in the second and the mean density of each prism in the third column. In this case the following settings should be used:

• radialUpperBound = data0+data1,
• radialLowerBound = data1,
• density = data2.

As the prim computation is time consuming a maximum distance around the evaluation point can defined with distancePrism. Afterwards a simplified radial line (the prism mass is concentrated to a line in the center) is used up to a distance of distanceLine. At last the prim is approximated by a point mass in the center up to a distance distanceMax (if set). Prisms nearby the evaluation point can be excluded with distanceMin.

Name	Type	Annotation
inputfileGridRectangular	filename	Digital Terrain Model
density	expression	expression [kg/m**3]
radialUpperBound	expression	expression (variables 'height', 'data', 'L', 'B' and, 'area' are taken from the gridded data
radialLowerBound	expression	expression (variables 'height', 'data', 'L', 'B' and, 'area' are taken from the gridded data
distanceMin	double	[km] min. influence distance (ignore near zone)
distancePrism	double	[km] max. distance for prism formular
distanceLine	double	[km] max. distance for radial integration
distanceMax	double	[km] max. influence distance (ignore far zone)
factor	double	the result is multiplied by this factor, set -1 to subtract the field

EarthquakeOscillation

The given gravityfield is interpreted as an oscillation function in the gravitational potential field, caused by large earthquakes. The result is computed at time $t$ as follows: \[ C_{lm}(\M t) = \sum_{n=0}^NC_{nlm}(1-\cos(\omega)\exp(\frac{-\omega}{2Q_{nlm}})), \]with $\omega=\frac{2\pi}{T_{nlm}}(t-t_0)$. In this equation, $Q_{nlm}$ is the attenuation factor, $n$ is the overtone factor, $m$ is degree, $l$ is order, and $t$ is time in second. $T_{nlm}$ and $Q_{nlm}$ are computed with the elastic Earth model or observed from the long period record of superconducting gravimeter measurements after the earthquakes.

Name	Type	Annotation
inputCoefficientMatrix	filename	oscillation model parameters
time0	time	the time earthquake happened
minDegree	uint
maxDegree	uint
GM	double	Geocentric gravitational constant
R	double	reference radius

Filter

Convert gravityfield to spherical harmonics and filter the coefficients.

Name	Type	Annotation
gravityfield	gravityfield
filter	sphericalHarmonicsFilter

Group

Groups a set of gravityfield and has no further effect itself.

Name	Type	Annotation
gravityfield	gravityfield
factor	double	the result is multiplied by this factor, set -1 to subtract the field