Arabian Journal of Geosciences (2021) 14:268 https://doi.org/10.1007/s12517-021-06656-9 ORIGINAL PAPER GravPack: a MATLAB-based gravity data processing package Nedim Gökhan Aydın & Turgay İşseven Received: 21 May 2019 / Accepted: 29 January 2021 # Saudi Society for Geosciences 2021 Abstract GravPack is a gravity data processing package developed utilizing MATLAB The package is aimed at providing a standalone and processing environment for Bouguer gravity data by putting various modules (such as spectral analysis, filtering, boundary analyses, and modelling) together It is designed to be user-friendly, which results in an easy-to-use graphical user interface (GUI) consisting of a single window with separate tabs for each processing step Aside from Bouguer gravity data processing, GravPack includes other useful features such as coordinate conversion, cropping, gridding, re-formatting data files, and displaying data in various ways, all of which can be used on various datasets other than gravity data In this paper, the theoretical background for gravity data processing and interpretation is summarized Then, GravPack and its capability of applying these processing steps are introduced using Bouguer gravity data of Konya-Çumra area (Western Anatolia) And finally, current capabilities and superiorities of GravPack are discussed Keywords Gravity Anomaly Bouguer Data processing MATLAB Toolbox Introduction Gravity field is affected by variations in geometry and density of subsurface Measured data includes all the masses’ effects, some of which are undesired in the case of layered earth model studies, so some corrections are needed These corrections are latitude correction (Blakely 1995), free air correction (Faye 1895), Bouguer correction (Bouguer 1749), and terrain correction (Hammer 1939) After applying the corrections to the measured data, resulting gravity data is called Bouguer gravity anomalies, which should reflect gravity data of layered earth The gravitational acceleration equation derived from Newton’s law states that the larger and closer the mass is, the larger the gravitational acceleration will be However, a body at a distance with a large density is possible to result in Responsible Editor: Narasimman Sundararajan * Nedim Gökhan Aydın aydinn@itu.edu.tr Turgay İşseven isseven@itu.edu.tr Department of Geophysics, Faculty of Mines, Istanbul Technical University, 34469, Maslak, Istanbul, Turkey the same gravity anomaly as another body that is closer with much smaller density This dilemma brings out the requirement of certain constraints in the interpretation of gravity data and the importance of analyzing and processing the gravity data to extract the desired anomalies from it There is a relation between potential anomalies and depth of the sources, so the depth of the sources may be estimated from potential anomalies (Spector and Grant 1970) To establish such a relation, one has to take Fourier transform of the potential data and analyze the data in wavenumber domain Power spectrum should be radially averaged to estimate the “mean” depth of interfaces, regardless of their exact position and geometry (Mugglestone and Renshaw 1998; Spector and Grant 1970) Shallow structures mainly affect higher wavenumber parts of power spectrum, while the deep sources affect lower wavenumber parts (Maus and Dimri 1996) The depth of a source body/interface can be estimated by splitting the spectrum into linear segments Each segment should represent the average depth of the sources, which can be estimated using Eq (1) e −ln E e1 ln E hẳ 1ị 4k k ị where h represents the depth of the source, k1 and k2 represent wave numbers, and Ẽ1 and Ẽ2 represent power values 268 Page of Arab J Geosci Since each slope represents a particular part of the sources, the gravity anomaly of those sources can be obtained by filtering gravity data Cut-off wave numbers should be obtained from the lineaments of the spectrum mentioned above Filtering is done in Fourier domain using Eq (2) È À ÁÉ g F x; yị ẳ F F fgx; yịgS k x ; k y ð2Þ where F , F −1 denotes Fourier and inverse Fourier transforms; g F filtered gravity data; S filter function; x, y Cartesian coordinates; and kx, ky wavenumber components in these Cartesian coordinates In order to estimate filter S(kx, ky), the radial distances of the two cut-off wavenumbers (k1 and k2) should be determined Then, sinusoidal tapers should be defined centering the cut-off wavenumbers The filter should be as in Eq (3) qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi > 1; k þ ε < k 2x þ k 2y < k ỵ > > > q > < sine taper; k < k ỵ k < k ỵ 1 x y S k x; k y ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi > > 2 > cosine taper; k −ε < k x ỵ k y < k ỵ > > : 0; else ð3Þ where ε is the half width of taper windows Another processing step is (upward and downward) analytical continuation (Bracewell 1965), which is applied by multiplying the anomalies with an exponential expression in Fourier domain as in Eq (4) & p ' z k 2x ỵk 2y gzị x; yị ẳ F F ẵg x; yÞ ð4Þ e where z represents continuation amount in kilometers Analytical continuation process simulates vertical shifting of measurement planes, thus enhancing or damping anomalies by virtually carrying measurement points closer or further to the sources Upward analytical continuation exaggerates deep sources’ contribution into the gravity anomaly while diminishing shallow sources’ contribution Downward analytical continuation is the opposite of upward analytical (2021) 14:268 continuation There are several methods that are aimed at detecting edges of buried sources by processing gravity data These methods are called boundary analyses, most of which use derivatives of gravity anomalies Analytical signal (AS), tilt angle (TA), and theta map (TM) are most commonly used derivative methods (Eqs 5, 6, and 7) sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 2 g g g AS ẳ 5ị ỵ ỵ ∂x ∂y ∂z ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi s 2 2ffi g g g A = TA ẳ tan1 @ 6ị þ ∂z ∂x ∂y 0sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1 0sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1 2 2 2 2 2 ∂g ∂g A @ g g g A = TM ẳ @ ỵ ỵ þ ∂x ∂y ∂x ∂y ∂z Blakely and Simpson (1986) approached boundary analysis in a simpler way by numerically comparing each value with adjacent eight grid point values to get a boundary estimation These adjacent points are checked in four directions using the disequilibria given in the Blakely and Simpson method; maximum points are calculated and plotted If the density of a structure is known, then it is possible to estimate its geometry For three-dimensional modelling, generally an initial model is estimated; then, the model is refined with iterations and inverse solution methods Cordell and Henderson (1968) used vertical prisms in a grid with different depths/heights (vertical prism method (VPM)) The initial estimate of the depth to the bottom of the prisms is calculated using Eq (8): ∂g p ¼ 2πGρ∂zi ð8Þ where δgp represents gravity anomaly, G universal gravity constant, ρ density contrast, and δzi approximate depth For any given point, gravity anomaly of vertical prisms is calculated using Eq (9) (Cordell and Henderson 1968) qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 13 3 222 0 0 0 xx0 ị2 ỵ yy0 ị2 ỵ z0ị2 A5 x2 y2 z2 g x ; y ; ¼ −GΔρ  444 x−x ln yy ỵ R ỵ yy ln xx þ R þ zarctan@z  ðx−x0 Þðy−y0 Þ x1 y1 z1 where Δg(x′,y′,0) is gravity anomaly of a prism at measurement point at (x′,y′,0) coordinate; Δρ is density contrast of the prism; x1, x2, y1, y2, z1, and z2 are coordinates of the corners of the prisms; and R is the distance between the corners of the prism and the measurement point Using the differences ð7Þ ð9Þ between calculated and measured gravity values, the model is regenerated This process is repeated until an acceptable solution The processing methods applied to gravity data are very similar to the processing methods applied to other potential Arab J Geosci (2021) 14:268 Page of 268 Fig Flowchart displaying GravPack’s processing cycles field data, especially magnetic data For example, Generic Mapping Tools (Wessel and Smith 1991) are able to apply gridding, cropping, filtering, and spectral analysis to both gravity and magnetic data without an interface The commercial software packages such as Geosoft Oasis Montaj, Fig GravPack GUI displaying data initialization phase ModelVision, and Intrepid handle most potential data processing steps There are also several data management tools that organize gravity data points, calculate Bouguer anomalies, and grid the data, including pyGrav (Hector and Hinderer 2016) and GravProcess (Cattin et al 2015) There 268 Page of are various data displaying tools exist in literature; the most commonly used one is Surfer (Golden Software 2014), which also can handle various gridding and filtering processes Two-dimensional modelling softwares such as FastGrav (Price 2017) and Potential-Field (Phillips 1997) are present For 3D modelling, there is a MATLAB package called Potensoft (Arısoy and Dikmen 2011) which handles spatial/frequency domain filtering, boundary analyses, and manual voxel modelling for gravity data Recently, there was another gravity modelling program published by Pham and Öksüm (2018), called GHC_gravinv which is a MATLAB-based modelling application specifically designed for sedimentary basin interpretation It is clear to see that there is not a program available that can carry out preparing, processing, and interpreting steps of gravity data all together GravPack is a MATLAB program that puts various gravity data processing steps together It has a simple graphical interface stacked into a single window, separating the steps with tabs and panels In order to make the user even more comfortable, the GUI itself has been built to be modifiable; i.e., it is possible to translate the program into another language via translating an external spreadsheet file or change the colors and color maps used throughout Aside from processes mentioned in the previous paragraphs, GravPack also contains various useful modules such as coordinate conversions, gridding, and filtering that can be applied on datasets other than gravity data Consequently, GravPack is a package that eases gravity data processing with its capabilities and interface Fig Bouguer gravity anomalies of Konya-Çumra area (Aydın and İşseven 2018) Dotted pattern, sediments; vertical-lined pattern, marbles; horizontalbricked pattern, limestone; curvelined pattern, ophiolites Arab J Geosci (2021) 14:268 GravPack’s features and highlights GravPack is an all-in-one gravity data processing package capable of applying all the aforementioned processing steps from within a single window with a user-friendly graphical interface GravPack can grid, analyze, filter, and model gravity data and export into different file formats (Fig 1) The aim of GravPack is to provide the user a single and simple application that does not require any other external software The functions built into GravPack can also be used on non-gravity data for conversions, gridding, filtering, boundary analyses, and displaying The package is developed using MATLAB on Windows operating system, but also can be used on any operating system that can run MATLAB The GUI has a resolution of 800 × 600 pixels Operations are packed into different tabs Although the texts used in tabs are in English, they can be converted to any languages after filling appropriate sections in spreadsheet file supplied with the package GravPack uses ASCII text files with *.DAT extension as data sources, in which columns are separated with space The data file has to have at least three columns: latitude, longitude, and gravity value The gravity data are expected to be Bouguer anomalies to further analyze and process the data; however, GravPack is able to convert raw gravity data into Bouguer anomalies by applying necessary corrections and reductions If the Bouguer gravity data are to be calculated, tide-corrected gravity data, topographic data, and terrain correction data are required along with the coordinates within the data file The content of the selected file is displayed upon Arab J Geosci (2021) 14:268 Page of 268 Fig a Gridding scattered Bouguer anomalies b Depth estimations using interactive power spectrum plot loading (Fig 2) There are no specific column order requirements for data files since it is possible to define each column within the GUI The coordinates can be in Cartesian coordinates (in meters) or geographic coordinates (in decimal degrees) The package includes a coordinate conversion module to convert decimal degrees to Universal Transverse Mercator (UTM) coordinates by selecting desired datum and UTM zone, of which central meridian is used as central meridian of TM The data can be visualized and cropped by defining desired area after reading and converting input The area of interest can be determined by mouse clicks or by manually defining coordinates In order to make any processing, the data should be gridded into the regular spacing GravPack calculates and displays radially averaged power spectrum of the gridded data Each linear segment is identified by the user either using mouse as an input or manually giving the wavenumbers There are maximum four linear segments that can be created by GravPack In the estimation of the average depth of the sources, each segment is used separately GravPack will automatically estimate average depth to the sources Gravity anomalies due to the sources represented by each segment can be calculated by using upper and lower cut-off wave numbers in the filtering process Upper and lower cutoff wave numbers can be imported into the filtering process Upward and downward analytical continuation of gravity anomalies can be calculated using the MATLAB functions 268 Page of Arab J Geosci (2021) 14:268 Fig a Input Bouguer anomalies b Sample band-pass filter result of a for 0.1336–0.2212 cut-off wavenumbers c One-kilometer downward analytical continuation of a (d) Total horizontal derivative of a e Theta map result of a (f) Canny edge detection method result of a written by Oruỗ (2012) Continuation distance should be input in kilometer The sign of the distance parameter defines whether upward (negative distance) or downward (positive distance) continuation will be calculated GravPack has an internal module operating a compilation of boundary analysis functions It is possible to calculate first and second horizontal and vertical derivatives Analytical signal, tilt angle, tilt derivative, and theta map are produced by the methods defined by Miller and Singh (1994), Nabighian (1972), and Wijns et al (2005) The Blakely and Simpson (1986) method has also been implemented We found that Canny (Canny 1986) and Laplacian of Gaussian (Marr and Hildreth 1980) methods provide effective results on gravity data, despite both being originally designed to be applied on images to enhance edges These methods can Fig a GUI during modelling process b Calculated Bouguer anomalies c Calculated depth model Arab J Geosci (2021) 14:268 be used in GravPack providing Image Processing Toolbox which is installed GravPack can calculate three-dimensional earth model from Bouguer gravity anomalies by using the VPM (Cordell and Henderson 1968) Modelling interface accepts inputs for mean depth, density contrast, and input data for one layer GravPack calculates gravity anomalies of a given model and corrects the model differences between calculated and measured gravity data The iteration can be controlled by either defining a root mean square (RMS) threshold or maximum iteration number Iterations are displayed on the console of GravPack All the parameters in this process are stored and displayed to the user after the process ends GravPack is able to export 3-column XYZ and gridded data in text formats (*.DAT or *.TXT), MATLAB data file (*.MAT), and Surfer grid file (*.GRD) GravPack allows multiple selection of datasets in export process There is also a function to clear all temporary data since a user may need to clear temporary data to avoid RAM clogging when working with large data Application on gravity data In this paper, GravPack software is used on gravity anomaly data from Konya-Çumra (Aydın and İşseven 2018) The data covers an area of 110 × 132 km2 (Fig 3) The data show relatively high Bouguer gravity anomalies where there are only young sediments visible on the surface and interpreted to be related to a buried ophiolite body (Aydın and İşseven 2018) The data file is loaded into GravPack as explained in GravPack’s Features and Highlights section The coordinates are in decimal degrees, so the coordinates are converted into WGS84 datum UTM format in 36S zone The scattered Bouguer data is then gridded with 1000-m sampling interval and plotted in contour format (Fig 4a) Power spectrum of the gridded Bouguer anomalies are calculated and depth estimations are made using interactive plot (Fig 4b) Using the wave numbers from spectral analysis, four different filters have been designed and produced filtered datasets Original data is given in Fig 5a and a sample filtered map in Fig 5b One-kilometer downward analytical continuation of the same data is given in Fig 5c Total horizontal derivative, theta map analysis, and Canny image edge detection results are given in Fig 5d, e, and f, respectively For VPM, the data is first filtered to represent the deepest layer To improve the computation time, the data is resampled into higher gridding interval The density contrast is taken as 0.25 g/cm3 and iterations are controlled with RMS error threshold RMS value of mGal is achieved after 10 iterations Modelling process and the results are shown in Fig Page of 268 All these conversions and calculations are done within GravPack without using any other software other than MATLAB All the processes took less than 10 min, which proves GravPack’s superiority in capability and effectiveness in gravity data processing Conclusions In this paper, we briefly summarize processing steps applied on gravity data and introduce GravPack, the MATLAB-based gravity data processing package The capabilities of GravPack are displayed through the Bouguer gravity data from KonyaÇumra area It is obvious that gravity data require many corrections and processes before reaching a final conclusion Whether the conclusion is a depth estimation, a boundary analysis, or a model, most of the software involved in gravity data processing does not include the processing steps we have described so far, all together Therefore, researchers are forced to use more than one software which is time-consuming and sometimes frustrating GravPack hopefully fulfills the need of a software that is a compilation of preparing, processing, and displaying methods in gravity data with a simple graphical user interface With coordinate conversion, Bouguer anomaly calculation from raw gravity data, gridding, and cropping features, GravPack covers the data processing required during the preparation part The software is able to apply spectral analysis, filtering, and analytical continuation processes from a single GUI window and display the results in various ways With the boundary analysis and modelling functions, GravPack becomes an all-in-one gravity data processing software in MATLAB, operating independently from other programs Finally, GravPack is an open-source MATLAB application, meaning that it can be improved and changed depending on the user’s needs unless proper credits are given Supplementary Information The online version contains supplementary material available at https://doi.org/10.1007/s12517-021-06656-9 Acknowledgements The authors would like to thank Mr H Tuğrul GENÇ and Prof Dr Bülent ORUÇ for their extensive supports during the development of GravPack Code availability Gravity data processing package, GravPack, consists of a single MATLAB file (gravpack.m) and two folders called lang and sys in the same directory The package is developed by Nedim Gökhan Aydın (aydinn@itu.edu.tr, +90 538 716 6286) at Istanbul Technical University (34469, Maslak, Istanbul, Turkey) The package is available since summer of 2018 and can be run on all devices with MATLAB 2015 or its newer versions Only two of the boundary analysis methods require Image Processing Toolbox installed The package’s size is about 380 kb in zipped form and can be downloaded from Mendeley database (10.17632/br8rkv76x5.1) 268 Page of Funding This study is resulted from the MSc Thesis of Nedim Gökhan AYDIN and is supported with the research funds of Istanbul Technical University Scientific Research Projects (ITU-BAP, Project ID 40703) Declarations The authors declare that they have no conflict of interest This paper does not contain any studies with human participants and animals performed by any of the authors Consequently, there were no requirement for the obtainment of the informed consent References Arısoy MÖ, Dikmen Ü (2011) Potensoft: MATLAB-based software for potential field data processing, modeling and mapping Comput Geosci 37:935–942 https://doi.org/10.1016/j.cageo.2011.02.008 Aydın NG, İşseven T (2018) What is the reason for the high Bouguer gravity anomaly at Çumra, Konya (Central Anatolia)? Tur J Earth Sci 27:318–328 https://doi.org/10.3906/yer-1801-17 Blakely RJ (1995) Potential theory in gravity and magnetic applications Camb Univ Press Blakely RJ, Simpson RW (1986) Approximating edges of source bodies from magnetic or gravity anomalies Geophysics 51:1494–1498 Bouguer P (1749) La Figure de la Terre Aca R Sci Paris Bracewell R (1965) Fourier transform and its applications New York Canny J (1986) A computational approach to edge detection Pattern Analysis and Machine Intelligence, IEEE Tran 679-698 Cattin R, Mazzotti S, Baratin LM (2015) GravProcess: an easy-to-use MATLAB software to process campaign gravity data and evaluate the associated uncertainties Comput Geosci 81:20–27 https://doi org/10.1016/j.cageo.2015.04.005 Cordell L, Henderson RG (1968) Iterative three dimensional solution of gravity anomaly data using a digital computer Geophysics 33:596–601 Arab J Geosci (2021) 14:268 Faye H (1895) Réduction au niveau de la mer de la pesanteur observée la surface de la Terre Comp Ren Séan l’Acad Sci 120:1081–1086 Hammer S (1939) Terrain corrections for gravimeter stations Geophysics 4:184–194 Hector B, Hinderer J (2016) PyGrav, a Python-based program for handling and processing relative gravity data Comput Geosci 91:90– 97 https://doi.org/10.1016/j.cageo.2016.03.010 Marr D, Hildreth E (1980) Theory of edge detection Proc R Soc Lon 207: 187–217 https://doi.org/10.1098/rspb.1980.0020 Maus S, Dimri V (1996) Depth estimation from the scaling power spectrum of potential fields? Geop J Int 124:113–120 Miller HG, Singh V (1994) Potential-field tilt - a new concept for location of potential-field sources J of App Geop 32:213–217 Mugglestone MA, Renshaw E (1998) Detection of geological lineations on aerial photographs using two-dimensional spectral analysis Comp Geos 24:771–784 Nabighian MN (1972) The analytical signal of two-dimensional magnetic bodies with polygonal cross-section: its properties and use for automated interpretation Geophysics 37:507517 Oruỗ B (2012) Dorusal Olmayan Ters Çưzüm Teori ve Ưrneklerle Jeofizikte Modelleme 232-263 Umuttepe Yayınları, Kocaeli Pham LT, Öksüm E (2018) GCH_gravinv: a MATLAB-based program for inverting gravity anomalies over sedimentary basin Comput Geosci 120:40–47 Phillips JD (1997) Potential-field geophysical software for the PC, version 2.2 US Geol Sur 10.3133/ofr97725 Price A (2017) FastGrav: Quick, simple gravity modelling software for Mac and Pc Software G (2014) Surfer.:14 Spector A, Grant FS (1970) Statistical models for interpreting aeromagnetic data Geophysics 35:293–302 Wessel P, Smith WHF (1991) Free software helps map and display data Ear Spa Sci News:441–446 Wijns C, Perez C, Kowalczyk P (2005) Theta map: edge detection in magnetic data Geophysics 70:39–43 ... the MATLAB-based gravity data processing package The capabilities of GravPack are displayed through the Bouguer gravity data from KonyaÇumra area It is obvious that gravity data require many... clear temporary data to avoid RAM clogging when working with large data Application on gravity data In this paper, GravPack software is used on gravity anomaly data from Konya-Çumra (Aydın and... as coordinate conversions, gridding, and filtering that can be applied on datasets other than gravity data Consequently, GravPack is a package that eases gravity data processing with its capabilities