Developed by Xiao-Le Deng in cooperation with Wen-Bin Shen.

Based on the Tesseroids software, We offer the codes for modeling Gravitational Curvatures (GC) of tesseroids, which are third-order derivatives of the gravitational potential (GP).

Tesseroids is a collection of command-line tools for modeling the gravitational potential, acceleration, and gradient (Marussi) tensor. See details at Leouieda's Github: tesseroids.

SConstruct and src are the codes for modeling the gravitational curvatures of tesseroids, in corporation with the Tesseroids software.

Experiments is used to reproduce the results presented in Deng and Shen (2019).

The codes are used for calculating the gravitational curvatures of a tesseroid under the terms of the BSD 3-clause license. See LICENSE.

If you use these codes in your research, please cite the papers in your publications:

Uieda, L., V. Barbosa, and C. Braitenberg (2016), Tesseroids: Forward-modeling gravitational fields in spherical coordinates, GEOPHYSICS, F41-F48, doi:10.1190/geo2015-0204.1.

Deng, X.L., Shen, W.B (2019), Topographic effects up to Gravitational Curvatures of tesseroids: A case study in China, Studia Geophysica et Geodaetica, 63(3), 345-366, doi:10.1007/s11200-018-0772-4.

Installing these codes on Ubuntu, please see Ubuntu installs Tesseroid1.2.1 and Gravitational Curvatures of Tesseroids.

1. Install the Tesseroids software. see help at leouieda/tesseroids: Forward modeling of gravity fields in spherical coordinates;

2. Download the codes at xiaoledeng/Gravitational_Curvatures_of_Tesseroids;

3. Replace the SConstruct and put the codes in src file at right place, and compile with

    $ scons -c
    $ scons
   

4. Test the success of installing by using:

    $ tessgzzz -h
   
    Usage: tessgzzz MODELFILE [OPTIONS]
   
    Calculate the gzzz component due to a tesseroid model on
    specified observation points.
   
    Values are calculated in the local coordinate system of the
    observation point: x-> North  y-> East  z-> Up (away from the
    center of the Earth).
    In order to maintain mainstream convention, component gz is
    calculated with z-> Down.
   
    All units either SI or degrees!
   
    The computation of the gravitational effect of the tesseroids
    is done using the Gauss-Legendre Quadrature (GLQ) numerical
    integration method.
   
    WARNING: Avoid computing directly on top or inside the
     tesseroids! This will break the GLQ and the formulas!
   
    Input:
    	Computation points passed through standard input (stdin).
    	Reads 3 or more values per line and inteprets the first 3 as:
    	longitude, latitude and height
    	of a computation points. Height should be in meters.
    	Othervalues in the line are ignored.
    	Lines that start with # are ignored as comments.
    	Lines should be no longer than 10000 (ten thousand) characters.
   
    Output:
    	Printed to standard output (stdout) in the form:
    	lon lat height ... result
    	... represents any values that were read from input and
    	ignored. In other words, the result is appended to the last
    	column of the input. Use this to pipe tessg* programs
    	together.
   
    	* Comments about the provenance of the data are inserted into
   
    	the top of the output
   
    MODELFILE: File containing the tesseroid model
    	* Each tesseroid is specified by the values of its borders
   
    		and density
    	* The file should contain one tesseroid per line
    	* Each line should have the following column format:
   
    		West East South North Top Bottom Density
    	* Top and Bottom should be read as 'height to top' and
   
    		'height to bottom' from the mean Earth radius. Use negative
    		values if bellow the surface, for example when modeling
    		deep structures, and positive if above the surface, for
    		example when modeling topography.
    * If a line starts with # it will be considered a comment and
   
    		will be ignored.
   
    Options:
    	-a             Disable the automatic subdividing of
             			tesseroids. Subdividing is done to ensure the
             			GLQ gives accurate results. ONLY USE THIS
             			OPTION IF YOU KNOW WHAT YOU ARE DOING!
    	-tRATIO        Use a custom distance-size ratio for the
             			automatic subdivision of tesseroids. ONLY USE
             			THIS OPTION IF YOU KNOW WHAT YOU ARE DOING!
    	-oOLON/OLAT/OR GLQ order to use in the longitudinal,
             			latitudinal and radial integrations,
             			respectively. Defaults to 2/2/2.
             			Subdividing of tesseroids works best with the
             			default order.
    	-h             Print instructions.
    	--version      Print version and license information.
    	-v             Enable verbose printing to stderr.
    	-lFILENAME     Print log messages to file FILENAME.
   
    	Part of the Tesseroids package (v2017).
   
    	Project site: <http:https://www.leouieda.com/tesseroids/>
    	Report bugs at: <https://github.com/leouieda/tesseroids/issues>
   
    	Copyright (C) 2011-2017, Leonardo Uieda.
    	This software is distributed under the terms of the BSD License:
    	<http:https://tesseroids.readthedocs.org/en/latest/license.html>
    	This is free software: you are free to change and redistribute it.
    	There is NO WARRANTY, to the extent permitted by law.