- Email: [email protected]
Graphical interactive generation of gravity and magnetic fields
Computers & Geosciences 37 (2011) 567–572
Contents lists available at ScienceDirect
Computers & Geosciences journal homepage: www.elsevier.com/locate/cageo
Graphical interactive generation of gravity and magnetic fields$ A. Pignatelli a,, I. Nicolosi a,1, R. Carluccio a,2, M. Chiappini a,2, R. von Frese b,3 a b
Istituto Nazionale di Geofisica e Vulcanologia, via di Vigna Murata 605, 00143 Roma, Italy School of Earth Sciences, The Ohio State University, Columbus, 43210 OH, USA
a r t i c l e in f o
abstract
Article history: Received 10 August 2009 Received in revised form 6 October 2010 Accepted 8 October 2010 Available online 25 November 2010
This paper presents a MATLABs - based geopotential field generator called GamField that constructs and visualizes subsurface sources in 3-D space and computes their gravity and magnetic effects. GamField also computes anomaly gradients and remanent magnetization effects. The user inputs Cartesian prisms along with their physical properties to fabricate subsurface sources. Examples illustrating the utility of GamField for synthetic anomaly generation of gravity and magnetic fields are shown. ftp://ftp.ingv.it/pub/ alessandro.pignatelli/Pignatelli & 2010 Elsevier Ltd. All rights reserved.
Keywords: Gravity anomaly computation Magnetic anomaly computation MATLABs
1. Introduction Gravity and magnetic observation surveys aimed to the exploration of Earth subsurface are nowadays increasingly growing, due to their superior cost-effectiveness. They can be applied to a great variety of applications, ranging in scale from archaeological and engineering site investigations up to regional and global crust studies of Earth, Moon and even solar system planets (von Frese et al., 1981). In potential fields analysis, many algorithms, designed to extract quantitative subsurface information, do exist (Last and Kubic, 1983; Guillen and Menichetti, 1984; Li and Oldenburg, 1996; Fedi and Rapolla, 1999; Pignatelli et al., 2007). Before using these methods on real data and in order to verify their effectiveness, they are usually tested on synthetic data. However, due to synthetic calculation complexity, magnetic and gravimetric sources are often replaced with simple geometrical primitives (spheres, cylinders or prisms) very far from being representative of real geological sources. In this paper, a suite of MATLABs procedures called GamField is presented that greatly simplifies the graphical windowsinteractive construction of complex 3-D distributions of Cartesian prisms for gravity and magnetic anomaly modeling. The package has been already used to compute a large variety of synthetic fields aimed at testing the quality of several interpretation techniques (Pignatelli et al., 2007; Nicolosi et al., 2006; Ravat et al., 2007). $
Code available from: ftp://ftp.ingv.it/pub/alessandro.pignatelli/Pignatelli.
Corresponding author. Tel.: +39 06 36915605; fax: + 39 06 36915617.
E-mail addresses: [email protected] (A. Pignatelli), [email protected] (I. Nicolosi), [email protected] (R. Carluccio), [email protected] (M. Chiappini), [email protected] (R. von Frese). 1 Tel.: +39 06 36915633; fax: +39 06 36915617. 2 Tel.: +39 06 51860313; fax: + 39 06 36915617. 3 Tel.: +01 614 292 5635; fax: + 01 614 292 7688. 0098-3004/$ - see front matter & 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.cageo.2010.10.003
GamField includes three different graphical user interfaces (GUIs) for:
interactive environment for 3-D construction and visualization of source distributions of cartesian prisms;
definition of coordinates for the calculated data; calculation and visualization of source generated gravity and magnetic effects. Unlike already published PC-based codes, that compute either a magnetic (Mendel et al., 2005; Cooper, 1997) or gravity (Pinto and Casas, 1996; Rama Rao et al., 1999; Chakravarthi et al., 2002) field, GamField permits the combined calculation of both fields, their gradients and the magnetic vector components, through a graphical interactive 3-D approach in the construction of generic sources. GamField is maintained by the Italian National Institute of Geophysics and Volcanology (INGV) and can be freely downloaded (together with the examples presented in this paper) from the INGV website ftp://ftp.ingv.it/pub/alessandro.pignatelli/Pignatelli.
2. GamField anomaly computations GamField calculates in Cartesian coordinates the magnetic and gravity effects of sources that are represented by distributions of rectangular prisms. The generalized magnetic effect Bm of the prism with volume v and the uniform magnetization vector Js with intensity Js, inclination Is, and declination Ds, is (von Frese et al., 1981; Blakely, 1995) ZZZ 1 Bm ðrÞ ¼ Js r0 us rs dv ð1Þ r
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A. Pignatelli et al. / Computers & Geosciences 37 (2011) 567–572
Here, r is the vector connecting source and observation point coordinates, (xs, ys, zs) and (x0, y0, z0), respectively; rs and r0 are the respective source and observation point gradient operators, and us is the unit magnetization vector such that Js ¼ Jsus. The above volume integral evaluated for the gradient operators in the x-, y-, and z-directions give the respective vector components Bmx, Bmy, and Bmz of Bm. Furthermore, to obtain the scalar total magnetic field anomaly TBm , we simply take the dot product u0 Bm ðrÞ ¼ TBm , where u0 is the unit vector of the Earth’s main field F0 at the observation point with inclination I0 and declination D0, so that F0 ¼ F0 u0 . A straightforward simplification of the above volume integral allows the computation of the prism’s gravity anomaly Bg as the vertical component of its gravity field from ZZZ @ 1 @r Bg ¼ G s dv ð2Þ @r r @z where s is the uniform density of the prism and G is the gravitational constant. GamField uses the detailed expressions of Sharma (1986) programmed in MATLABs to calculate the magnetic (Bm, Bmx, Bmy, Bmz, TBm) and gravity (Bg) effects of the prism. GamField also computes numerical first vertical derivatives of these effects with the formula: BðP þhi ÞBðPÞ ð3Þ BiuðPÞ ¼ hi i where P is the space point where the derivative is computed, hi is the step increment along the required direction i A fx,y,zg, and B is the magnetic or gravimetric field computed with the Sharma formula and hi is a variable parameter to be chosen in an input requester according to the survey scale. Note that for any derivative direction i the software calculates only the homonym component Bi. 3. GamField implementation The basic idea behind GamField is to use Eqs. (1) and (2) to compute fields generated by complex volumetric structures (sources) approximated by an ensemble of identical rectangular prisms. Due to the magnetic and gravimetric field linearities, the field at a particular point in space is computed by summing all the contributions from each prism. Positive tests have been conducted on an uniformly magnetized rectangular prism whose fields are well known and reported by Sharma (1986). The main feature of the software is the ability to build up a complex ensemble of prisms in a simple and interactive way. An ‘editable’ volume must first be defined that is divided in equal rectangular prisms to form what will be called from now on the source grid. For each cell of the source grid, the magnetization direction and intensities
for the magnetic field, and densities for gravimetric field can be set. The program computes the effect of the sources on a rectangular regular grid lying on an horizontal ‘survey plane’ called the observation grid. A schematic representation of source and survey grids is visible in Fig. 1. Alternatively the fields can be computed on an irregular grid imported from a plain text file of three columns containing the easting, northing and altitude coordinates. Further details for the use of GamField are given in the next section, where its installation and functions are outlined. This section is followed with illustrations of the use of GamField in some gravity and magnetic modeling examples.
4. GamField operations 4.1. Installation GamField is a suite of three separate interacting modules: a main field computation module (GamField) complete with the observation and source grid parameters input GUI, a source builder (ModelBuilder), and a results viewer module (FieldViewer). The archive containing all the files needed to install the program can be downloaded from: ftp://ftp.ingv.it/pub/alessandro.pigna telli/Pignatelli. The archive GamField.zip must be extracted into a single folder (preferably using a path containing no spaces). Upon extracting the archive the user can proceed with the installation of the package. Detailed instructions are included in the documentation. Note also that the Matlab runtimes need to be installed prior to running GamField for the first time. 4.2. Initial settings From the GamField module window, the user first specifies the boundaries for the source and observation grids. These parameters include the north, south, east and west boundary coordinates for both grids, the top and bottom bounds of the source grid, and the altitude for observation grid (see Fig. 1). The interval spacing in each of the three axes of the source grid as well as the two axes of the observation grid also must be set. All of these parameters are defined in meters. In addition, altitudes above and below sea level are input as negative and positive values, respectively. For total magnetic field (TBm) calculations, the mean inclination and declination in degrees of the Earth’s main field over the observation grid are also input (Fig. 2). Upon setting the observation grid parameters, the user must check for the integrity and completeness of the data inputs by clicking on the Confirm Parameters button. All parameters can be saved either in a separate or in a single file. Previously constructed source models can be loaded from the File menu. Otherwise, models can be built from the ModelBuilder module. 4.3. Model building
Fig. 1. Source and survey grids.
To build a model, the user follows the File x Model x BuildModel option from the File menu in the GamField window. This option activates the module window shown in Fig. 3. The checker board layers give a stylized 3-D view of the gridded source space, where the layers are separated vertically at intervals of the prism thickness. Each prism has its top on a plane and extends horizontally at the north interval- and the east interval-values that were input as source grid parameters. The initial model starts with all the physical parameters (density and magnetization inclination, declination and intensity) set to zero or the off-state. When the magnetization or density parameters of a cell are different from zero, the cell is set to the on-state and its contribution is added to the field computation. ModelBuilder allows the user to construct a
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Fig. 2. Screen grab of survey (left) and source (right) grid GUIs for GamField.
Fig. 3. Screen plots of the ModelBuilder GUI for constructing 3-D gravity and magnetic anomaly sources in GamField.
complex source distribution of prisms by using mouse clicks to interactively toggle the cell states on and off. The user chooses a layer to assign prisms with physical properties that are input in the boxes as density in g/cm3 for gravity modeling, and magnetization (intensity) in A/m, and inclination and declination in degrees for magnetic modeling. Highlighting next the layer’s depth in the top right Depth field brings up the Layer Editor window as shown in Fig. 4. From this window, the mouse is used to move the cross-hairs over the cells and click them on and off. Pressing ENTER closes the edit session and confirms the cell selection and assigned physical property values. To assign cells with different physical properties to the same depth plane requires that the Layer Editor be called up again for each different set of the physical property values. The ModelBuilder module provides additional tools to facilitate the source modeling efforts. For example, clicking on the Polygon
option in the Selection Mode field allows the user to draw a polygon onto the layer with mouse clicks to switch on or off all the cells covered or partially covered by the polygon. The Multiple Layer Copy button in the ModelBuilder window provides another option that allows the user to copy the cells of a layer to other layers. The copying is done by clicking on the button and following the program requests. Note that the button is not present if the source grid is empty. The Show 3-D Model button in the ModelBuilder window allows the user to view the model in 3-D from different perspectives as shown by the example in Fig. 5. Two formats are available for saving the volumetric distribution of prisms. Firstly, during the construction of a complicated source distribution, the intermediate model files can be saved in the binary .mat format using the Save Builder Model button in the ModelBuilder window. In this binary format, the model can be loaded directly by the ModelBuilder module using the Load Builder Model button.
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Secondly, for processing by the GamField main module, the model must be saved as a plain text .txt export file. This option can be done by the Save Model For GamField button in the ModelBuilder window. However, the model also can be immediately submitted to the GamField main module using the Send Model To GamField button in the ModelBuilder window. 4.4. Field calculations Once the model is available in the GamField module, it can be examined with the menu View x Built Model. A 3-D representation
Fig. 4. Layer Editor window: Mouse click activates the prism beneath the cross-hairs with the selected physical properties. Clicking on an activated prism deactivates it. In polygon mode clicks define a polygon inside which cells are updated.
of the source is shown. The user can change the point of view interactively, see Fig. 5. If everything is ok, the field computation can be started. To compute the magnetic or gravity effects of the input model, the user selects the Magnetic Field or Gravity Field options, respectively, from the Compute menu. In addition, the gradient calculations are enabled by checking the Compute Gradients tab, otherwise this option is disabled to minimize computing time. MULTILEVEL MAGNETIC FIELD and MULTILEVEL GRAVIMETRIC FIELD generate anomaly fields over a range of altitudes at the user-specified interval. In addition, profiles across the computed anomaly maps may be selected and displayed using the menu COMPUTE x PROFILE ON MAP. This opens the anomaly map and the starting and ending points of the profile can be interactively specified together with the profile step. Just before the anomaly computation starts, GamField asks if the user wants to upload a list of survey points rather than use the survey grid. In this case, the survey points list should be an ascii file of three columns containing the easting, northing and altitude coordinates. A second display of the computed anomaly field is also produced. Activating the BUILT MODEL and COMPLETE MODEL EFFECTS options from the View menu gives additional plots of the model and the various components for the selected anomaly field, respectively. Under the TOPOGRAPHY menu, GamField loads a digital elevation model (DEM) and computes, displays, and saves its magnetic or gravity effects. The DEM should be a plain text file organized in seven columns (easting, northing, top, bottom, magnetization intensity, magnetization inclination and magnetization declination). The first two columns must represent a regular grid sorted by northing coordinate first (see the example files). From this file GamField builds up a source made of uniformly magnetized rectangular prisms ranging each from bottom to top and with horizontal dimensions automatically computed from the grid step. Files with less columns can also be loaded provided they are of 3,4,5 or 7 columns according to Table 1, which describes the program’s assumptions for these cases. GamField evaluates these topographic effects over the observation grid or on a survey point list, as described before. To facilitate the management of the models, the CLEAR ALL MODELS button 2 is provided that cleans the memory of all the built and loaded models. 4.5. Output graphics the field viewer module can be started by the menu commands View x Complete Model Effects and View x Complete DEM Effects option of the GamField window. In this module, it is possible to display each field component or derivative of the last computed fields by means of a combo box. It is also possible to view some statistical parameters of the calculated field.
5. GamField examples
Fig. 5. GamField 3-D viewer tool. The point of view can be interactively changed.
In this section the interactive anomaly modeling and graphics capabilities of GamField are illustrated with the aid of two examples. Example #1 models the magnetic and gravity effects
Table 1 Topographic file model loading rules. Col. #
Easting, northing
Top
3 4 5 7
From From From From
From From From From
file file file file
file file file file
Bottom
Magnetization
Incl., decl
Minimum of top From file From file From file
Asked Asked From file From file
From From From From
grid source grid source grid source file
A. Pignatelli et al. / Computers & Geosciences 37 (2011) 567–572
of a simple distribution of prisms and Example #2 evaluates a synthetic terrain effect of a DEM of Tenerife Island (Canarian Archipelago). Users can replicate these examples using the files described in Table 2 that are included with every release of GamField. To calculate the magnetic effects in Example #1, the file Ex1m_parameters.txt of observation and source grid parameters
Table 2 List of files used for the examples in this study. Magnetics
Gravity
Example #1
Ex1m_parameters.txt Ex1m_model.txt
Ex1g_parameters.txt Ex1g_model.txt
Example #2
Ex2_Tenerife_OBS.txt Ex2m_Tenerife_DEM.txt Ex2_T_survey_pars.txt
Ex2_Tenerife_OBS.txt Ex2g_Tenerife_DEM.txt Ex2_T_survey_pars.txt
Fig. 6. Source model (a), magnetic (b) and gravimetric (c) fields of example #1.
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is loaded from the menu File x Total Parameters x Load. The observation grid parameters include calculating the anomaly values at the altitude and station interval of 0 and 1000 m, respectively. For calculating the magnetic effects, the model parameter file, Ex1m_model.txt, is loaded by the menu command File x Model x Load Model. Each row of the model file describes a prism in nine columns that include its east coordinate, north coordinate, top, magnetization intensity, easting width, northing width, thickness, and magnetization inclination and declination. For the gravity effects of the simple prism distribution in Example #1, the files Ex1g_parameters.txt and Ex1g_model.txt are loaded. These files are formatted like the magnetic files, but the gravity calculations ignore the inclination and declination columns and read the source magnetization intensity column for the density value. Fig. 6 shows the loaded model together with results of fields computations. They are also stored in the Ex1m_fields.txt and Ex1g_fields.txt files that were created using the Save Field option of the File menu. Example #2 illustrates the use of GamField for calculating the synthetic magnetic and gravity effects of the loaded DEM. Here, the menu Topography x Load Topographic Model is used to load the Ex2m_Tenerife_DEM.txt and Ex2g_Tenerife_DEM.txt files to compute the respective magnetic and gravity effects. The Observation Grid parameters can be loaded from the file Ex2_T_survey_pars.txt. Again Fig. 7 shows the results of fields computation. For this example the file Ex2_Tenerife_OBS.txt is also provided in order to perform the fields calculation on an irregular grid. This is done by selecting ‘yes’ to the request of loading the stations file that appears before the computation.
Fig. 7. Tenerife magnetic (a) and gravimetric (b) fields of example #2.
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6. Conclusions GamField is a valuable geophysical resource for interactive 3-D modeling of realistic geological sources and calculation of their gravity and magnetic anomalies. GamField can be freely downloaded from ftp://ftp.ingv.it/pub/alessandro.pignatelli/Pignatelli. The INGV operates this site as a public service from which updates of GamField also will be periodically distributed. In addition, the site entertains questions and recommendations from the user community for, respectively, implementing and improving GamField.
Acknowledgments We thank the President of INGV, Prof. E. Boschi, for his encouragement and support in developing this geophysical resource. We also thank Dr. M.M. Lizzano for helping in designing the layout of the GUIs. We acknowledge the valuable support of Dr. S. Chiappini for his technical advice in computer science related subjects. References Blakely, R., 1995. Potential Theory in Gravity and Magnetic Applications. Cambridge University Press, New York.
Chakravarthi, V., Raghuram, H., Singh, S., 2002. 3-D forward gravity modeling above which the density contrast varies continuously with depth. Computers & Geosciences 22, 53–57. Cooper, G., 1997. Forward modeling of magnetic data. Computers & Geosciences 23, 1125–1129. Fedi, M., Rapolla, A., 1999. 3D inversion of gravity and magnetic data with depth resolution. Geophysics 64, 452–460. Guillen, A., Menichetti, V., 1984. Gravity and magnetic inversion with minimization of a specific functional. Geophysics 49, 1354–1360. Last, B., Kubic, K., 1983. Compact gravity inversion. Geophysics 48, 713–721. Li, Y., Oldenburg, D., 1996. 3-D inversion of magnetic data. Geophysics 61, 394–407. Mendel, V., Munschy, M., Sauter, D., 2005. Modmag, a matlab program to model marine magnetic anomalies. Computers & Geosciences 31, 589–597. Nicolosi, I., Blanco-Montenegro, I., Pignatelli, A., Chiappini, M., 2006. Estimating the magnetization direction of crustal structures by means of an equivalent source algorithm. Physics of the Earth and Planetary Interiors 155, 163–169. Pignatelli, A., Nicolosi, I., Chiappini, M., 2007. An alternative 3-D source inversion of magnetic anomalies method with depth resolution. Annales of Geophysics 169, 1021–1027. Pinto, V., Casas, A., 1996. An interactive 2D and 3D gravity modeling program for IBM-compatible personal computers. Computers & Geosciences 22, 535–546. Rama Rao, P., Swamy, K., Murthy, I.R., 1999. Inversion of gravity anomalies of threedimensional density interfaces. Computers & Geosciences 25, 887–896. Ravat, D., Pignatelli, A., Nicolosi, I., Chiappini, M., 2007. A study of spectral methods of estimating the depth to the bottom of magnetic sources from near-surface magnetic anomaly data. Geophysical Journal International 169, 421–434. Sharma, P., 1986. Geophysical Methods in Geology, second ed. Elsevier, Amsterdam. von Frese, R., Hinze, W., Braile, L., 1981. Spherical earth gravity and magnetic anomaly analysis by equivalent point source inversion. Earth and Planetary Science Letters 53, 69–83.
Contents lists available at ScienceDirect
Computers & Geosciences journal homepage: www.elsevier.com/locate/cageo
Graphical interactive generation of gravity and magnetic fields$ A. Pignatelli a,, I. Nicolosi a,1, R. Carluccio a,2, M. Chiappini a,2, R. von Frese b,3 a b
Istituto Nazionale di Geofisica e Vulcanologia, via di Vigna Murata 605, 00143 Roma, Italy School of Earth Sciences, The Ohio State University, Columbus, 43210 OH, USA
a r t i c l e in f o
abstract
Article history: Received 10 August 2009 Received in revised form 6 October 2010 Accepted 8 October 2010 Available online 25 November 2010
This paper presents a MATLABs - based geopotential field generator called GamField that constructs and visualizes subsurface sources in 3-D space and computes their gravity and magnetic effects. GamField also computes anomaly gradients and remanent magnetization effects. The user inputs Cartesian prisms along with their physical properties to fabricate subsurface sources. Examples illustrating the utility of GamField for synthetic anomaly generation of gravity and magnetic fields are shown. ftp://ftp.ingv.it/pub/ alessandro.pignatelli/Pignatelli & 2010 Elsevier Ltd. All rights reserved.
Keywords: Gravity anomaly computation Magnetic anomaly computation MATLABs
1. Introduction Gravity and magnetic observation surveys aimed to the exploration of Earth subsurface are nowadays increasingly growing, due to their superior cost-effectiveness. They can be applied to a great variety of applications, ranging in scale from archaeological and engineering site investigations up to regional and global crust studies of Earth, Moon and even solar system planets (von Frese et al., 1981). In potential fields analysis, many algorithms, designed to extract quantitative subsurface information, do exist (Last and Kubic, 1983; Guillen and Menichetti, 1984; Li and Oldenburg, 1996; Fedi and Rapolla, 1999; Pignatelli et al., 2007). Before using these methods on real data and in order to verify their effectiveness, they are usually tested on synthetic data. However, due to synthetic calculation complexity, magnetic and gravimetric sources are often replaced with simple geometrical primitives (spheres, cylinders or prisms) very far from being representative of real geological sources. In this paper, a suite of MATLABs procedures called GamField is presented that greatly simplifies the graphical windowsinteractive construction of complex 3-D distributions of Cartesian prisms for gravity and magnetic anomaly modeling. The package has been already used to compute a large variety of synthetic fields aimed at testing the quality of several interpretation techniques (Pignatelli et al., 2007; Nicolosi et al., 2006; Ravat et al., 2007). $
Code available from: ftp://ftp.ingv.it/pub/alessandro.pignatelli/Pignatelli.
Corresponding author. Tel.: +39 06 36915605; fax: + 39 06 36915617.
E-mail addresses: [email protected] (A. Pignatelli), [email protected] (I. Nicolosi), [email protected] (R. Carluccio), [email protected] (M. Chiappini), [email protected] (R. von Frese). 1 Tel.: +39 06 36915633; fax: +39 06 36915617. 2 Tel.: +39 06 51860313; fax: + 39 06 36915617. 3 Tel.: +01 614 292 5635; fax: + 01 614 292 7688. 0098-3004/$ - see front matter & 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.cageo.2010.10.003
GamField includes three different graphical user interfaces (GUIs) for:
interactive environment for 3-D construction and visualization of source distributions of cartesian prisms;
definition of coordinates for the calculated data; calculation and visualization of source generated gravity and magnetic effects. Unlike already published PC-based codes, that compute either a magnetic (Mendel et al., 2005; Cooper, 1997) or gravity (Pinto and Casas, 1996; Rama Rao et al., 1999; Chakravarthi et al., 2002) field, GamField permits the combined calculation of both fields, their gradients and the magnetic vector components, through a graphical interactive 3-D approach in the construction of generic sources. GamField is maintained by the Italian National Institute of Geophysics and Volcanology (INGV) and can be freely downloaded (together with the examples presented in this paper) from the INGV website ftp://ftp.ingv.it/pub/alessandro.pignatelli/Pignatelli.
2. GamField anomaly computations GamField calculates in Cartesian coordinates the magnetic and gravity effects of sources that are represented by distributions of rectangular prisms. The generalized magnetic effect Bm of the prism with volume v and the uniform magnetization vector Js with intensity Js, inclination Is, and declination Ds, is (von Frese et al., 1981; Blakely, 1995) ZZZ 1 Bm ðrÞ ¼ Js r0 us rs dv ð1Þ r
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A. Pignatelli et al. / Computers & Geosciences 37 (2011) 567–572
Here, r is the vector connecting source and observation point coordinates, (xs, ys, zs) and (x0, y0, z0), respectively; rs and r0 are the respective source and observation point gradient operators, and us is the unit magnetization vector such that Js ¼ Jsus. The above volume integral evaluated for the gradient operators in the x-, y-, and z-directions give the respective vector components Bmx, Bmy, and Bmz of Bm. Furthermore, to obtain the scalar total magnetic field anomaly TBm , we simply take the dot product u0 Bm ðrÞ ¼ TBm , where u0 is the unit vector of the Earth’s main field F0 at the observation point with inclination I0 and declination D0, so that F0 ¼ F0 u0 . A straightforward simplification of the above volume integral allows the computation of the prism’s gravity anomaly Bg as the vertical component of its gravity field from ZZZ @ 1 @r Bg ¼ G s dv ð2Þ @r r @z where s is the uniform density of the prism and G is the gravitational constant. GamField uses the detailed expressions of Sharma (1986) programmed in MATLABs to calculate the magnetic (Bm, Bmx, Bmy, Bmz, TBm) and gravity (Bg) effects of the prism. GamField also computes numerical first vertical derivatives of these effects with the formula: BðP þhi ÞBðPÞ ð3Þ BiuðPÞ ¼ hi i where P is the space point where the derivative is computed, hi is the step increment along the required direction i A fx,y,zg, and B is the magnetic or gravimetric field computed with the Sharma formula and hi is a variable parameter to be chosen in an input requester according to the survey scale. Note that for any derivative direction i the software calculates only the homonym component Bi. 3. GamField implementation The basic idea behind GamField is to use Eqs. (1) and (2) to compute fields generated by complex volumetric structures (sources) approximated by an ensemble of identical rectangular prisms. Due to the magnetic and gravimetric field linearities, the field at a particular point in space is computed by summing all the contributions from each prism. Positive tests have been conducted on an uniformly magnetized rectangular prism whose fields are well known and reported by Sharma (1986). The main feature of the software is the ability to build up a complex ensemble of prisms in a simple and interactive way. An ‘editable’ volume must first be defined that is divided in equal rectangular prisms to form what will be called from now on the source grid. For each cell of the source grid, the magnetization direction and intensities
for the magnetic field, and densities for gravimetric field can be set. The program computes the effect of the sources on a rectangular regular grid lying on an horizontal ‘survey plane’ called the observation grid. A schematic representation of source and survey grids is visible in Fig. 1. Alternatively the fields can be computed on an irregular grid imported from a plain text file of three columns containing the easting, northing and altitude coordinates. Further details for the use of GamField are given in the next section, where its installation and functions are outlined. This section is followed with illustrations of the use of GamField in some gravity and magnetic modeling examples.
4. GamField operations 4.1. Installation GamField is a suite of three separate interacting modules: a main field computation module (GamField) complete with the observation and source grid parameters input GUI, a source builder (ModelBuilder), and a results viewer module (FieldViewer). The archive containing all the files needed to install the program can be downloaded from: ftp://ftp.ingv.it/pub/alessandro.pigna telli/Pignatelli. The archive GamField.zip must be extracted into a single folder (preferably using a path containing no spaces). Upon extracting the archive the user can proceed with the installation of the package. Detailed instructions are included in the documentation. Note also that the Matlab runtimes need to be installed prior to running GamField for the first time. 4.2. Initial settings From the GamField module window, the user first specifies the boundaries for the source and observation grids. These parameters include the north, south, east and west boundary coordinates for both grids, the top and bottom bounds of the source grid, and the altitude for observation grid (see Fig. 1). The interval spacing in each of the three axes of the source grid as well as the two axes of the observation grid also must be set. All of these parameters are defined in meters. In addition, altitudes above and below sea level are input as negative and positive values, respectively. For total magnetic field (TBm) calculations, the mean inclination and declination in degrees of the Earth’s main field over the observation grid are also input (Fig. 2). Upon setting the observation grid parameters, the user must check for the integrity and completeness of the data inputs by clicking on the Confirm Parameters button. All parameters can be saved either in a separate or in a single file. Previously constructed source models can be loaded from the File menu. Otherwise, models can be built from the ModelBuilder module. 4.3. Model building
Fig. 1. Source and survey grids.
To build a model, the user follows the File x Model x BuildModel option from the File menu in the GamField window. This option activates the module window shown in Fig. 3. The checker board layers give a stylized 3-D view of the gridded source space, where the layers are separated vertically at intervals of the prism thickness. Each prism has its top on a plane and extends horizontally at the north interval- and the east interval-values that were input as source grid parameters. The initial model starts with all the physical parameters (density and magnetization inclination, declination and intensity) set to zero or the off-state. When the magnetization or density parameters of a cell are different from zero, the cell is set to the on-state and its contribution is added to the field computation. ModelBuilder allows the user to construct a
A. Pignatelli et al. / Computers & Geosciences 37 (2011) 567–572
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Fig. 2. Screen grab of survey (left) and source (right) grid GUIs for GamField.
Fig. 3. Screen plots of the ModelBuilder GUI for constructing 3-D gravity and magnetic anomaly sources in GamField.
complex source distribution of prisms by using mouse clicks to interactively toggle the cell states on and off. The user chooses a layer to assign prisms with physical properties that are input in the boxes as density in g/cm3 for gravity modeling, and magnetization (intensity) in A/m, and inclination and declination in degrees for magnetic modeling. Highlighting next the layer’s depth in the top right Depth field brings up the Layer Editor window as shown in Fig. 4. From this window, the mouse is used to move the cross-hairs over the cells and click them on and off. Pressing ENTER closes the edit session and confirms the cell selection and assigned physical property values. To assign cells with different physical properties to the same depth plane requires that the Layer Editor be called up again for each different set of the physical property values. The ModelBuilder module provides additional tools to facilitate the source modeling efforts. For example, clicking on the Polygon
option in the Selection Mode field allows the user to draw a polygon onto the layer with mouse clicks to switch on or off all the cells covered or partially covered by the polygon. The Multiple Layer Copy button in the ModelBuilder window provides another option that allows the user to copy the cells of a layer to other layers. The copying is done by clicking on the button and following the program requests. Note that the button is not present if the source grid is empty. The Show 3-D Model button in the ModelBuilder window allows the user to view the model in 3-D from different perspectives as shown by the example in Fig. 5. Two formats are available for saving the volumetric distribution of prisms. Firstly, during the construction of a complicated source distribution, the intermediate model files can be saved in the binary .mat format using the Save Builder Model button in the ModelBuilder window. In this binary format, the model can be loaded directly by the ModelBuilder module using the Load Builder Model button.
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Secondly, for processing by the GamField main module, the model must be saved as a plain text .txt export file. This option can be done by the Save Model For GamField button in the ModelBuilder window. However, the model also can be immediately submitted to the GamField main module using the Send Model To GamField button in the ModelBuilder window. 4.4. Field calculations Once the model is available in the GamField module, it can be examined with the menu View x Built Model. A 3-D representation
Fig. 4. Layer Editor window: Mouse click activates the prism beneath the cross-hairs with the selected physical properties. Clicking on an activated prism deactivates it. In polygon mode clicks define a polygon inside which cells are updated.
of the source is shown. The user can change the point of view interactively, see Fig. 5. If everything is ok, the field computation can be started. To compute the magnetic or gravity effects of the input model, the user selects the Magnetic Field or Gravity Field options, respectively, from the Compute menu. In addition, the gradient calculations are enabled by checking the Compute Gradients tab, otherwise this option is disabled to minimize computing time. MULTILEVEL MAGNETIC FIELD and MULTILEVEL GRAVIMETRIC FIELD generate anomaly fields over a range of altitudes at the user-specified interval. In addition, profiles across the computed anomaly maps may be selected and displayed using the menu COMPUTE x PROFILE ON MAP. This opens the anomaly map and the starting and ending points of the profile can be interactively specified together with the profile step. Just before the anomaly computation starts, GamField asks if the user wants to upload a list of survey points rather than use the survey grid. In this case, the survey points list should be an ascii file of three columns containing the easting, northing and altitude coordinates. A second display of the computed anomaly field is also produced. Activating the BUILT MODEL and COMPLETE MODEL EFFECTS options from the View menu gives additional plots of the model and the various components for the selected anomaly field, respectively. Under the TOPOGRAPHY menu, GamField loads a digital elevation model (DEM) and computes, displays, and saves its magnetic or gravity effects. The DEM should be a plain text file organized in seven columns (easting, northing, top, bottom, magnetization intensity, magnetization inclination and magnetization declination). The first two columns must represent a regular grid sorted by northing coordinate first (see the example files). From this file GamField builds up a source made of uniformly magnetized rectangular prisms ranging each from bottom to top and with horizontal dimensions automatically computed from the grid step. Files with less columns can also be loaded provided they are of 3,4,5 or 7 columns according to Table 1, which describes the program’s assumptions for these cases. GamField evaluates these topographic effects over the observation grid or on a survey point list, as described before. To facilitate the management of the models, the CLEAR ALL MODELS button 2 is provided that cleans the memory of all the built and loaded models. 4.5. Output graphics the field viewer module can be started by the menu commands View x Complete Model Effects and View x Complete DEM Effects option of the GamField window. In this module, it is possible to display each field component or derivative of the last computed fields by means of a combo box. It is also possible to view some statistical parameters of the calculated field.
5. GamField examples
Fig. 5. GamField 3-D viewer tool. The point of view can be interactively changed.
In this section the interactive anomaly modeling and graphics capabilities of GamField are illustrated with the aid of two examples. Example #1 models the magnetic and gravity effects
Table 1 Topographic file model loading rules. Col. #
Easting, northing
Top
3 4 5 7
From From From From
From From From From
file file file file
file file file file
Bottom
Magnetization
Incl., decl
Minimum of top From file From file From file
Asked Asked From file From file
From From From From
grid source grid source grid source file
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of a simple distribution of prisms and Example #2 evaluates a synthetic terrain effect of a DEM of Tenerife Island (Canarian Archipelago). Users can replicate these examples using the files described in Table 2 that are included with every release of GamField. To calculate the magnetic effects in Example #1, the file Ex1m_parameters.txt of observation and source grid parameters
Table 2 List of files used for the examples in this study. Magnetics
Gravity
Example #1
Ex1m_parameters.txt Ex1m_model.txt
Ex1g_parameters.txt Ex1g_model.txt
Example #2
Ex2_Tenerife_OBS.txt Ex2m_Tenerife_DEM.txt Ex2_T_survey_pars.txt
Ex2_Tenerife_OBS.txt Ex2g_Tenerife_DEM.txt Ex2_T_survey_pars.txt
Fig. 6. Source model (a), magnetic (b) and gravimetric (c) fields of example #1.
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is loaded from the menu File x Total Parameters x Load. The observation grid parameters include calculating the anomaly values at the altitude and station interval of 0 and 1000 m, respectively. For calculating the magnetic effects, the model parameter file, Ex1m_model.txt, is loaded by the menu command File x Model x Load Model. Each row of the model file describes a prism in nine columns that include its east coordinate, north coordinate, top, magnetization intensity, easting width, northing width, thickness, and magnetization inclination and declination. For the gravity effects of the simple prism distribution in Example #1, the files Ex1g_parameters.txt and Ex1g_model.txt are loaded. These files are formatted like the magnetic files, but the gravity calculations ignore the inclination and declination columns and read the source magnetization intensity column for the density value. Fig. 6 shows the loaded model together with results of fields computations. They are also stored in the Ex1m_fields.txt and Ex1g_fields.txt files that were created using the Save Field option of the File menu. Example #2 illustrates the use of GamField for calculating the synthetic magnetic and gravity effects of the loaded DEM. Here, the menu Topography x Load Topographic Model is used to load the Ex2m_Tenerife_DEM.txt and Ex2g_Tenerife_DEM.txt files to compute the respective magnetic and gravity effects. The Observation Grid parameters can be loaded from the file Ex2_T_survey_pars.txt. Again Fig. 7 shows the results of fields computation. For this example the file Ex2_Tenerife_OBS.txt is also provided in order to perform the fields calculation on an irregular grid. This is done by selecting ‘yes’ to the request of loading the stations file that appears before the computation.
Fig. 7. Tenerife magnetic (a) and gravimetric (b) fields of example #2.
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6. Conclusions GamField is a valuable geophysical resource for interactive 3-D modeling of realistic geological sources and calculation of their gravity and magnetic anomalies. GamField can be freely downloaded from ftp://ftp.ingv.it/pub/alessandro.pignatelli/Pignatelli. The INGV operates this site as a public service from which updates of GamField also will be periodically distributed. In addition, the site entertains questions and recommendations from the user community for, respectively, implementing and improving GamField.
Acknowledgments We thank the President of INGV, Prof. E. Boschi, for his encouragement and support in developing this geophysical resource. We also thank Dr. M.M. Lizzano for helping in designing the layout of the GUIs. We acknowledge the valuable support of Dr. S. Chiappini for his technical advice in computer science related subjects. References Blakely, R., 1995. Potential Theory in Gravity and Magnetic Applications. Cambridge University Press, New York.
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