# GRASS GIS for topographic and geophysical mapping of the Peru-Chile Trench

Polina Lemenkova

► To cite this version:

Polina Lemenkova. GRASS GIS for topographic and geophysical mapping of the Peru-Chile Trench. Forum Geografic. Geographical studies and environment protection research, 2020, 19 (2), pp.143-157. 10.5775/fg.2020.009.d. hal-03155346

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# GRASS GIS for topographic and geophysical mapping of the Peru-Chile Trench

Polina LEMENKOVA<fnref n="1" />,*

Received on 03-05-2020, reviewed on 25-08-2020, accepted on 15-09-2020

## Abstract

The study area is located along the western continental margins of South America, Peru-Chile Trench south-east Pacific Ocean, geographically encompasses 90° to 60°W longitude and 55°S to 0° latitude. The study aims to perform a spatial analysis using GRASS GIS approach applied for processing and visualizing topographic and geophysical data on the study area. Data include following raster grids: topographic SRTM_15PLUS raster grid with 15 arc-second resolution, geoid model (EGM96), geophysical fields and gravity maps (marine free-air gravity and vertically corrected free-air gravity). The thematic grids were mapped by GRASS GIS modules and visualized for comparative analysis. Spatial analysis included plotting slope aspect, profile curvature, terrain elevation and modeled topographic classes based on the neighborhood analysis. The results include visualized geophysical and topographic maps of the study area showing correlation between the geophysical fields and topographic elevation. The variety of forms of the submarine relief of the Pacific Ocean seafloor was formed as a result of complex factors: tectonic movements, dislocations, active volcanism, geologic variations in rock density, which is reflected in visualized gravity and geoid maps. The actuality of the study is explained by high potential commercial interests in deep-water mineral resource deposits, oil and gas, which make ocean seafloor studies one of the most promising topics in geoscience. At the same time, the need for programming applications for big data analysis in geosciences requires testing advanced scripting approaches in cartography. Therefore, the current paper presents a multi-disciplinary approach combining geological analysis with technical cartographic aspects of data analysis and visualization.

**Keywords:** South America, GRASS GIS, cartography, gravity, geoid, topography

## Rezumat. Grass-GIS pentru cartarea topografică și geofizică a Gropii Peru-Chile

Zona de studiu este localizată în marjele continentale vestice ale Americii de Sud, Groapa Peru-Chile în sud-estul Oceanului Pacific, cuprinde geografic 90° - 60° V longitudine și 55° S până la 0° latitudine. Scopul studiului este realizarea unei analize spațiale folosind abordarea GRASS GIS aplicată pentru prelucrarea și vizualizarea datelor topografice și geofizice din zona de studiu. Datele includ următoarele griduri raster: raster SRTM_15PLUS topografic cu rezoluție de 15 secunde în arc, model geoid (EGM96), câmpuri geofizice și hărți gravitaționale (gravitație aer liberă marină și gravitație aer liberă corectată vertical). Rețelele tematice au fost reprezentate cu GRASS GIS și vizualizate pentru analiză comparativă. Analiza spațială a inclus aspectul de pantă, curbura profilului, altitudinea terenului și clase topografice modelate pe baza analizei de vecinătate. Rezultatele includ hărți geofizice și topografice ale zonei de studiu care prezintă corelația între câmpurile geofizice și creșterea topografică. Varietatea formelor reliefului submarin al oceanului Pacific a fost configurată ca urmare a unor factori complexi: mișcări tectonice, discolații, vulcanism activ, variații geologice ale densității rocilor, care se reflectă în hărțile vizualizate ale gravitației și geoidelor. Actualitatea studiului este explicată de interesele comerciale potențiale ridicate în depozitele de la adâncime, petrol și gaze, ceea ce face ca studiile de pe malul oceanului să fie unul dintre cele mai promitătoare în direcțiile de geostiință. În același timp, nevoia de programare a aplicațiilor pentru analiza datelor în geostiințe necesită testarea abordărilor avansate de script în cartografie. Prin urmare, lucrarea actuală prezintă o abordare multidisciplinară, combinând analiza geologică cu aspecte cartografice tehnice ale analizei și vizualizării datelor.

**Cuvinte-cheie:** America de Sud, GRASS GIS, cartografie, gravitație, geoid, topografie

## Introduction

The study of the bathymetry of the ocean seafloor and its structure is one of the most important means for understanding the principles of the geological structure and development of the oceanic crust. Modeling seafloor and development of the GIS based methods for its visualization facilitates ocean exploration and assists in prognosis of the vast mineral resources hidden in the ocean: petroleum and gas, raw materials, sand and gravel, phosphorite, corals, biogenic carbonates, heavy metal ores

(Seibold & Berger, 1993). The ocean seafloor has continuously been an object of the geomorphological, geological and geophysical research (Suetova et al. 2005; Kuhn et al. 2006; Gauger et al. 2007; Schenke & Lemenkova, 2008; Jamieson et al. 2010; Contreras-Reyes & Carrizo, 2011; Hu et al. 2016; Stewart & Jamieson, 2018; Lemenkova, 2019a, 2019b; 2019c; 2020e; Jamieson & Stewart, 2020).

The analysis of the correlation between the seafloor topography, deep geologic structure of the oceanic seafloor rocks and anomalies in geophysical fields reveals the role of various factors in its formation. Furthermore, it helps understanding the origin and evolution of the morphostructure of the

<footnote n="1">¹ Schmidt Institute of Physics of the Earth, Russian Academy of Sciences. Laboratory of Regional Geophysics and Natural Disasters (Nr. 303), Department of Natural Disasters, Anthropogenic Hazards and Seismicity of the Earth. Bolshaya Gruzinskaya Str. 10, Bld. 1, Moscow, 123995, Russia. https://orcid.org/0000-0002-5759-1089</footnote>

<footnote>* Corresponding author: pauline.lemenkova@gmail.com</footnote>
ocean seafloor in the view of plates tectonics. The morphostructure of the ocean seafloor reflects the geological structure and tectonics of the oceanic crust in the submarine topography of the seafloor. The morphostructure of the submarine relief of deep-sea trenches mirrors the geologic development and tectonic movements, volcanism and the geological structure of the ocean floor in the specific area of plate subduction that causes formation of the oceanic trenches. However, the advanced mapping and visualization of such structure as oceanic seafloor is only possible by means of advanced technical mapping, remote sensing and GIS.

Gravimetric studies and visualization are of great importance and stand apart in the complex of geological and geophysical studies focused on the World Ocean, since gravimetric modeling enables to detect density variations at different depths of the Earth (Chambat & Valette, 2005; Claessens, & Hirt, 2013), detect isostatic areas (Gvirtzman et al. 2016). Detailed studies enable to detect crust strength, asthenosphere viscosity in the upper mantle, create thermochemical convection models based on the analysis of basalt content, showing the influence of viscosity of mantle on the evolution and distribution of Earth's mantle heterogeneity (Yan et al. 2020), detect impact factors that affect isostasy instability, to mention some. Moreover, the study of the gravitational field of the oceans is crucial for correct modelling of the Earth's shape, for navigation purposes, for calculation of the orbits of the artificial Earth satellites and trajectories of the space research vehicles.

Along with collecting gravimetric data on the World Ocean, a mapping of the free-air gravity anomalies has been continuously improved and updated with the beginning of the history of gravimetric measurements in early 20th century. Thus, the first gravity observations and regular mapping has been performed by Dutch scientist Vening-Meinesz in 1929 for the region of Indonesia where he measured horizontal and vertical accelerations, angular movements of the pendulum apparatus and created a formule for the correction for deviations of gravity and initiated gravity observations. The first map of the free-air gravity anomalies in Bouguer correction for the Pacific Ocean was created in the U.S. using both pendulum and marine gravity observations. Gravity measurements were then continuously performed using methods of the advanced data analysis (Drinkwater et al. 2003; Knudsen et al. 2011; Eshagh, 2013; Godah et al. 2018).

## Study Objectives

This study contributes to the investigations of the oceanic seafloor with a case study of the South

America region and specifically, Peru-Chile trench bordering the continent on the west in the south-east Pacific Ocean. The objectives of this work included:

1. visualizing the relationships between the morphostructure forms of the submarine relief, the structure of the oceanic seafloor;

2. mapping anomalies in geophysical fields and gravity in south-east Pacific Ocean;

3. cartographic modelling of the variations in the and the geoid model in the study area;

4. literature based analysis of the geological structure in the Peru-Chile Trench, South America;

5. technical testing of GRASS GIS scripting functionality and use of its various modules;

6. spatial analysis of the topographic patterns: slope, aspect, elevations and curvature distribution and their relationship with the main topographic structure of the ocean seafloor in the region of the Chile-Peruvian Trench, the features of their geomorphic structure and dissection;

7. textual based analysis of the role of the tectonic movements, faults, volcanism, and sedimentation in the formation of the ocean floor based on the extensive literature review;

8. visualization of the bathymetry of the submarine relief and morphostructure of the seafloor in western part of South America.

## Study Area

The study area is located in the western continental margins of South America in the Peru-Chile Trench, which stretches as a narrow strip along its coast, and geographically lies between 90° to 60°W longitude and 55°S to 0° latitude. (Fig. 1). The Peru-Chile Trench is formed along the continental margin slope of South America in the subduction zone of Nazca and Antarctic plates of the Pacific Ocean under the South American Plate. The forearc region of the South American Plate margin (northern Chile) is notable for subduction erosion and regional uplift (Adam & Reuther, 2000). Since oceanic plates are more dense than continental plate, their structure is processed and modified as a result of physicochemical processes in the collision zone. As a result, a new continental crust is formed, which builds up the edges of the continental plates and Peru-Chile Trench.

The region of South America along the Pacific margin has a complex tectonic setting which should be briefly described. Detailed studies shown that geometry, geospatial trending in orientation, kinematics and time of deformation differ in the Atacama fault system, northern Chile (Ruthven et al. 2020). The continental margins were formed along the eastern periphery of the Pacific Ocean, with changing zones of the accumulation and subduction of the tectonic plates. This was caused by the partial
overlapping of the axis of extension of the mid-ocean
ridge by the continent. Besides, various exogenous
factors affect the formation of the deep-sea trenches:
sediment accumulation, erosion and deposition and
movement of sediments, causing significant
geomorphological changes in the relief on the
continental slopes of the Pacific Ocean (Lemenkova,
2018a; 2018b). The Nazca and Antarctic plates move
eastwards and subduct under the Peru-Chile trench.
Located to the norther, Panama and adjacent minor
tectonic plates move eastward and north-eastward
and also experience subduction at the junction with
the Middle America (Guatemala) Trench (Lemenkova,
2019f).

<figure><img src="image_2.png" /><figcaption>Fig. 1: Topographic map of the Peru-Chile Trench and western segment of South America, Pacific Ocean. Cartographic mapping: GRASS GIS. Raster grid: SRTM_15PLUS</figcaption></figure>

The southern part of the Peru-Chile Trench is
notable for transform fault off the coast of Chile which
is formed in the boundary of the tectonic plates
sliding past one another. Bending of the tectonic
plates prior to subduction is caused by the negative
buoyancy of the sinking plate, that is, a slab pull
(Contreras-Reyes & Osses, 2010).

The region of the Peru-Chile Trench is notable for
high seismicity and repetitive earthquakes (Das et al.
2020). Thus, the seismic belt in the east of the Pacific
Ocean extends along the active continental margins
of South America, including Peru-Chile Trench and
continuous sequence of mountain ranges of Andes
and Cordillera. This makes the region of South
America along the Peru-Chile Trench notable for a
large number of catastrophic earthquakes with
magnitudes of 7.0–8.5. Many shallow earthquakes are
also located along the Peru-Chile Trench and
neighboring coastal land areas. The fault plane here
is vague and tilted at a slight angle (20–25°) reaching
depths of 200–250 km. Focal hypocenters are in
depths at 250-500 km are almost not detected, but at
a depth of 500-700 km there is another zone of
earthquake foci on a steeper falling focal plane, which
indicates a fracture of the oceanic plate moving under
the continent.

The Nazca Plate plays important role in the
formation of the Peru-Chile Trench (Yáñez et al.
2002). At its eastern border it adjoins the Pacific Plate
along the East Pacific Rise and borders the Antarctic
Plate along the Chile Rise. The eastern edge of the
Chile Rise subducts beneath the South American plate
at the Chile Triple Junction., which is formed in the
place of collision of three tectonic plates (Antarctic,
South America and Nazca) causing huge stress on
sides of the fault, break of rocks and earthquakes
along the South America slope (Espurt et al. 2008).

The eastern part of the Nazca Plate is sinking
along the Peru-Chile Trench, which causes the
formation of Andes. As a consequence, the Cordillera
of the Andes as an orogenic belt was built up by
thickening of South American plate crust (Faccenna
et al. 2017). Such complex movements of three
tectonic plates result in numerous earthquakes along
the Peru-Chile Trench with the largest earthquake
ever recorded (magnitude 9.5) in 1960 (Lara et al.
2004; Cisternas et al. 2017).

During the Oligocene and Miocene periods, the
Chile rift zone was stretching along the modern South
Galapagos and Chile uplifts to the north, merging with
the rift zone of the East Pacific Rise, until the
California Gulf rift through a transform fault. After the
Mesozoic period, the southern segment of the Pacific
Ocean seafloor around the South America, rift zone
and South Pacific Rise did not undergo significant
tectonic rearrangements and continued to actively
developing up to the present time. This caused
gradual separation of the Pacific and Antarctic
tectonic plates which affected actual geomorphic
structure of the seafloor. Further extensive studies on
South America tectonics and the geology of the Peru-
Chile Trench region can be found in relevant
publications (Bourgois et al. 2000; Alvarado et al.,
2007; Cobbold et al. 2007; Scherwath et al. 2009;
Geersen et al., 2011).
## Methods

There is a vast variety of spatially distributed geophysical and geological datasets, both in raster and vector formats. The problem of its interpretation, analysis and visualization is important and requires an integrated systematic approach with correctly chosen GIS software.

For instance, statistical modeling of spatial phenomena and geological variables enables to sort, plot and analyze measurements as a datasets and obtain a model of the data distribution in space (Pyrcz & Deutsch, 2014; Klaučo et al. 2013a; 2013b; Webster & Oliver, 2007; Lemenkova, 2019e, 2020f; Kurowicka & Cooke, 2006; Reynard et al. 2010). Statistical data analysis often includes various types of geological modeling applied for tabular datasets aimed at data inventory, following the conceptual geological modeling, mathematical simulations, plotting and approximations for the assessment of physical properties of rock and soil types (Lindh, 2003; Lindh & Winter, 2003).

In contrast with the statistical approach, cartographic data analysis requires strong mapping techniques, since data analysis by GIS reveals hidden information and correlation through visualization which is the key concept in cartography. There are many and various GIS software that can be used for data processing and cartographic visualization, and the choice of GIS is often a challenge. This is the case of ArcGIS, a commercial desktop GIS developed by ESRI, often used in geospatial research due to its functionality and structural architecture as a modular system (ArcMap, ArcCatalog, ArcToolbox, ArcScene, ArcGlobe) and a variety of functions for data processing (Klaučo et al., 2014; 2017). One of the advantages of ArcGIS is its compatibility with Python which is powerful for geographic data analysis and interpretation (Lemenkova, 2019h; 2019i).

The Generic Mapping Tools (GMT) is another cartographic program which, in contrast to GIS, is a scripting toolset run from the console. GMT is a powerful mapping instrument often used for geophysical data analysis, effective visualization and interpretation (Lemenkova, 2019d; 2020a; 2020b, 2020c, 2020f). Other examples of geodata analysis include application of remote sensing data analysis in environmental, spatial, marine biological or oceanographocal studies (Jamieson, 2018; Stewart & Jamieson, 2019; Lemenkova, 2019g; Abdel-Mageed et al. 2020; Jamieson et al. 2020).

The GRASS GIS (Geographic Resources Analysis Support System) was selected for this research as an excellent multi-functional free GIS (Neteler & Mitasova, 2004). GRASS GIS is an open source free software with many applications (Neteler, 2001; 2005; Mitasova et al., 2005). The main reason for the GRASS GIS consists in its combination of scripting

console-based approach with powerful functionality in geomorphometric analysis: topographic analysis of tangential and profile curvature, slope, aspect and visualization of raster and vector datasets via the command line.

## Geoid modelling

The geoid dataset was visualized using Earth Gravitational Model (Pavlis et al., 2012; Lemoine et al., 1998), geopotential models of the Earth EGM96, a version from 1996, as the geoid reference of the World Geodetic System. Worldwide, the geoid undulations range from -107 m to 85 m relative to the WGS 84 ellipsoid. In geodesy, the free-air reduction condensed the topographic shape, so the station is projected onto the geoid, while geoid is a surface of the terrestrial masses, and gravity is measured on the geoid. Current advances in physical geodesy present technologies of optical frequency references using lazer spectroscopy utilized in global satellite navigation systems and satellite geodesy (Giorgi et al. 2019). The derivation of the geoid from gravity after estimating gravity measurements is based on the assumption of the geoid as hypothetical spherically symmetric, rotating Earth, as described in geodetic studies (Vaniček et al. 2001; Steinberger et al. 2010).

<figure><img src="image_3.png" /><figcaption>Fig. 2: Geoid model of the Peru-Chile Trench and western segment of South America, Pacific Ocean. Raster grid: EGM96 (geoid.egm96.grd). Cartographic mapping: GRASS GIS</figcaption></figure>
The geoid was visualized using modules of GRASS GIS and GDAL library for raster import:

#!/bin/sh

1. r.in.gdal -o pct_geoid.nc out=pct_geoid

2. g.list rast

3. d.mon wx0

4. d.erase

5. g.region res=0.001

6. g.region raster=pct_geoid -p -w -m nsres=0.0001 ewres=0.0001 res=0.0001

7. rcolors pct_geoid col=roygbiv

8. d.rast pct_geoid

9. d.redraw

10. d.grid size=5 color=white border_color=yellow width=0.1 fontsize=8 text_color=red

11. r.info pct_geoid

12. d.legend raster=pct_geoid range=-12,53 title=Geoid,mGal titleFontsize=8 font=Helvetica fontsize=8 -t -b bcolor=white labelStep=5 border_color=gray thin=8

13. d.text text="Geoid: EGM96 grid" color=yellow size=1.0 font="Times New Roman" linespacing=0.7

## Topographic mapping

The topographic DEM data is based on the SRTM15_PLUS raster grids of the seafloor global fabric (Becker et al., 2009; Olson et al., 2016). The SRTM15_PLUS presents a grid at 15 arc-second resolution (ca. 500 m). Terrain elevations of the SRTM15_PLUS are based on the data from the SRTM and ASTER DEMs while ocean bathymetry is based on bathymetric predictions from the global gravity model from CryoSat-2 and Jason-1 with depth soundings at 15 arc-second resolution. The mapping was done using a sequence of 19 GRASS GIS modules in a shell script:

#!/bin/sh

1. g.list rast

2. r.info pct_relief

3. d.mon wx0

4. g.region raster=pct_relief -p

5. v.in.region output=pct_bbox

6. g.list vect

7. v.info map=pct_bbox

8. rcolors pct_relief col=srtm_PLUS

9. d.rast pct_relief

10. r.contour pct_relief out=TopoPCT step=2500

11. d.vect TopoPCT color='100:93:134' width=0

12. d.grid size=5 color='172:219:250' border_color=yellow width=0.1 fontsize=8 text_color=red

13. d.vect pct_bbox color=red width=3 fill_color="none"

14. r.info pct_relief

15. d.legend raster=pct_relief range=-8100,6600 title=Topography,m titleFontsize=8 font= Arial fontsize=8 -t -b bcolor=white labelStep=500 border_color=gray thin=8

16. d.text text="Topography" color='0:0:51' size=1.5 font= Arial

17. d.text text="SRTM15_PLUS" color='0:0:51' size=1.5 font= Arial

18. d.text text="Peru-Chile region" color='0:0:51' size=1.5 font= Arial

19. d.text text="South America" color='0:0:51' size=1.5 font= Arial

Spatial analysis is particularly problematic in submarine geomorphology, where the bathymetry as inferred from the remote-sensing data such as Digital Elevation Models (DEMs) and computer-based modelling is the only observable data. Therefore, high-resolution DEM of Earth SRTM 15_PLUS was used to map terrain elevation and topographic derivatives evaluating slope features.

## Free-air gravity mapping

Free-air gravity data were taken from the satellite altimetry-derived gravity grid of Sandwell and Smith (2009). The geoid undulations, marine free-air gravity and vertical gravity anomalies, as well as gravity gradient changes reflect the density variations of the Earth which is caused by different density in geochemical content of rocks. The difference between the geophysical and geodetic concepts of gravity mirrors the difference between the ellipsoid and the geoid. The gravity anomaly is explained by the gravitational effect of the seafloor topography and crust-mantle rock density contrast, reflected in geopotential models of the Earth, e. g. EGM-2008 (Hirt et al. 2016). The compiled free-air and vertical gravity anomaly maps were plotted around the Peru-Chile Trench region to visualize the variation in the processes in the oceanic seafloor surrounding the South America region.

Gravitational anomalies have sharp gradients along the active continental margins of the eastern Pacific Ocean, which is caused by the contrasting geomorphology: coastal mountainous land areas on the one hand and deep-sea trenches along the foot of the continental slope on the other. Besides, the gravitational values are affected by the variations in density of the oceanic lithosphere, isostatically compensated by ocean deepening, which is reflected in the ocean-floor structure (Tenzer et al. 2015). Faye anomalies vary from the strongly positives over Andes to strongly negative values (100-200 mGal) over the deep-sea Peru-Chile Trench. Other studies present gravity models that reveal crustal thickening of the Andes Cordillera and show that dip and depth of the oceanic subduction varies in its different segments (Tamay et al. 2018). The Bouguer anomalies,
representing the variations in the gravity corrected for height at the Earth's surface (Meurers, 2017) increase sharply from the strongly negative above the coastal mountain up to +300 mGal above the adjacent ocean seafloor. The free-air gravity anomalies (Fig. 3) show gravity with height correction.

<figure><img src="image_4.png" /><figcaption>Fig. 3: Marine free-air gravity model of the Peru-Chile Trench and western segment of South America, Pacific Ocean. Raster grid: grav_27.1.img (Scripps Institution of Oceanography). Cartographic mapping: GRASS GIS</figcaption></figure>

## DEM spatial analysis

The spatial analysis based on the Digital Elevation Models (DEM) is performed using various raster datasets visualizing topography of the study area and its derivatives. Using `r.slope aspect` GRASS module, four topographic derivatives were modeled: slope, aspect, tangential and profile curvatures of the slope. Hence, the topographic analysis has been performed using GRASS GIS module using scripting sequence of commands as follows:

```bash
#!/bin/sh
```

1. `r.slope aspect` elevation=pct_relief slope=PCTslope aspect=PCTaspect pcurvature=PCTpcurv tcurvature=PCTtcurv.

2. `d.mon wx0`

3. `r colours map=PCTaspect color=aspectcolr`

4. `d.rast PCTaspect`

5. `d.grid size=5 color='252:242:180' border_color=blue width=0.1fontsize=8 text_color=blue`

6. `d.legend raster=PCTaspect title=Aspect,grad titlesize=8 font= Arial fontsize=8 -t -b bgcolor=white label step=30 border color=gray thin=8`

7. `d.text text="Aspect map" color=blue size=1.0 font=" Arial" linespacing=0.7`

The given above example is a script visualizing the aspect map (Fig. 5). Other topographic maps of the Peru-Chile Trench (PCT) have been plotted using this script as a template with inserted target layouts (PCTslope, PCTtcurv, PCTtcurv), respectively.

Spatial analysis using neighborhood analysis approach and cross-category statistics was performed using 'r.neighbors' GRASS GIS module by shell script in 20 steps:

```bash
#!/bin/sh
```

1. `d.mon wx0`

2. `g.region raster=pct_relief -p`

3. `r colours pct_relief col=elevation`

4. `r.info pct_relief`

5. `d.rast pct_relief`

6. `d.mon wx1`

7. `r neighbors pct_relief out=pct_reliefSmooth7 method=diversity size=7`

8. `r colours pct_reliefSmooth7 col=elevation`

9. `d.rast pct_reliefSmooth7`

10. `r.info pct_reliefSmooth7`

11. `d.vect pct_bbox color=red width=3 fill_color="none"`

12. `r.contour pct_relief out=TopoPCT step=2500 --overwrite`

13. `d.vect TopoPCT color='100:93:134' width=0`

14. `d.grid size=5 color=grey border_color=yellow width=0.1fontsize=8 text_color=red`

15. `d.legend raster=pct_reliefSmooth7 range=1,49 title=SmoothTopo title fontsiz=8 font= Arial fontsize=8 bgcolor=white label step=10 border color=grey thin=8 units=m -v -t -b`

16. `d.text text="Topography" color='0:0:51' size=1.5 font= Arial`

17. `d.text text="SRTM15_PLUS" color='0:0:51' size=1.5 font= Arial`

18. `d.text text="Spatial analysis" color='0:0:51' size=1.5 font= Arial`

19. `d.text text="Neighborhood" color='0:0:51' size=1.5 font= Arial`

20. `d.text text="Method diversity" color='0:0:51' size=1.5 font= Arial`

The presented map (Fig. 8) shows the topographic surface recalculated by method of neighborhood diversity. This approach is based on the GRASS GIS 'neighborhood' operator (Neteler & Mitasova, 2008)
which re-calculates a new value for each cell as a function of the values in its neighboring cells. Hence, the cells in a raster grid become new center cells of a neighborhood. The algorithm of the neighborhood approach consists in the window which moves throughout the map capturing and recalculating cells. In this research, the 'diversity' approach was applied. It computes the number of cell values within the neighborhood with the defined size of 7.

## Results

The Peru-Chile Trench is the most extended continuous submarine morphostructure in the World ocean (total length is m). The geomorphology of its southern segment is characterized by valley-block dissection with a minor trench where depths <4500 m. Northern segment of the Peru-Chile Trench is presented by the continental slope with simpler structure, a convex cross-section profile with steepness gradually increasing downward. The seafloor shape is narrow and mostly flat. The bathymetry varies for both trenches with maximum depths of 8069 m in its Chilean segment and 6601 m in the Peruvian segment.

<figure><img src="image_5.png" /><figcaption>Fig. 4: Vertical free-air gravity model of the Peru-Chile Trench and western segment of South America, Pacific Ocean. Raster grid: curv_27.1.img (Scripps Institution of Oceanography). Cartographic mapping: GRASS GIS</figcaption></figure>

The seafloor geodynamics of the Pacific Ocean is determined by the lateral movements of several large tectonic plates: Pacific, North American, Antarctic, Peruvian-Chilean, and microplates: Panama, Guatemala, and Tehuantepek. The speed of the expansion (opening) of the rift and, accordingly, tectonic plate movement in the South and East Pacific rises, is 2.0-4.0 and 4.2-6.0 cm/year, respectively. Current fault activity in the coastline of northern Chile is presented by two large features (Coastal Scarp and the Atacama Fault) having active deformation since Quaternary.

The zones of junction of the oceanic and continental lithosphere on the tectonic plate gradually become tectonically passive regions and the main leading process affecting the topography of the trench becomes the immersion of the marginal parts of the continents and formation of a sedimentary rock cover. This briefly describes the formation of the Peru-Chile Trench morphostructure, the shelf, submarine fans and sediment deposits at the foot of the continental slope of South America.

Among other basins of the Pacific Ocean, the Peru and Chilean basins, together with Caroline, Melanesian, are characterized by slightly positive values of the Faye gravity anomaly (Fig. 3), while Northwest, Northeast, East Mariana Basin and Central Pacific Basin have slightly negative Faye gravity anomalies.

<figure><img src="image_6.png" /><figcaption>Fig. 5: Topographic aspect map: Peru-Chile Trench and western segment of South America, Pacific Ocean. Model based on processing raster SRTM_15PLUS grid. Cartography: GRASS GIS</figcaption></figure>
The free-air gravity anomalies reflect topographic structure of the region (compare Fig. 1 and Fig. 2). Gravity field of the Peru-Chile Trench (Fig. 3) is depicted as narrow strip (purple colored). The free-air gravity reach slightly positive values (2-7 mGal, cyan color) above the topographic elevations, negative values (0 to -10 mGal, dark blue color) on the most area of basins; 20-25 mGal (red color) can be seen on the Andes ares and above the ridges (Copiapó Ridge, Taltal Ridge and Iquique Ridge, Nazca Ridge in the coastal shelf zone). The values above 55 mGal are notable in the high mountains of Andes with selected anomalies (dark purple color, below -45 mGal) in the depressions. Thus, the distribution of the gravity field mirrors geological properties of rocks and their distribution over the study area, since density in the rocks affect gravity values.

<figure><img src="image_7.png" /><figcaption>**Fig. 6: Topographic profile curvature map:**
Peru-Chile Trench and western segment of South America, Pacific Ocean. Model based on raster SRTM_15PLUS grid. Cartography: GRASS GIS</figcaption></figure>

Vertical free-air gravity raster shows vertical gradient of actual gravity (Fig. 4) which, compared with elevation map (Fig. 7) presents correlation between the gravity anomaly and topographic patterns. From the Poincare-Pray gradient Vanicek et al. (2001) define that larger local density results in smaller vertical gradient in absolute values, and

proves existing approximately linear relation between the density and the vertical gradient of the gravity. Thus, the difference between mean vertical gradient of gravity on the Earth surface and the geoid shape can be obtained from mathematical computations and is visualized on Fig. 3 and 4.

The aspect map (Fig. 5) shows visualized geomorphic slope orientation, direction of gradient, steepest slope and flow direction in degrees. As can be seen (Fig. 5), the majority of degrees in orientation is presented by 45°-100° (bright green color) dominating the scene, followed by 250°-290° (red color) which follows the faults lines on the seafloor and 330°-360° (yellow), mostly for the terrestrial areas in the Andes. The Andes slope close to the Chile Trench (southern segment of the study area) has predominantly 160°-200° oriented slopes (cyan color).

The quantitative land-surface analysis such as topographic aspect of slope curvature enables to describe the topography of the surface and geomorphological processes at various spatial and temporal scales. Practical values of aspect maps in special-temporal analysis for instance, visualize changes in the geomorphic types using slope curvature or aspect categories which can be translated into geomorphological landforms which has been a study object for many papers continuously during recent decades (Stevenson et al., 2010; Sofia et al., 2013).

<figure><img src="image_8.png" /><figcaption>**Fig. 7: Terrain elevation map based on raster SRTM_15PLUS grid: South America. Cartographic mapping: GRASS GIS**</figcaption></figure>

The topographic analysis was computed as a set of parameters (slope aspect and curvature) that indicates geometrical properties of the Earth's surface. These parameters describe surface
mathematics at a cell point and in its immediate
surroundings (neighbor cells) which is computed by
GRASS GIS embedded functions using differential
geometry by partial derivatives of the function
mathematically approximating the surface.

The inclined plains of the accumulative sediment
plumes formed along the foot of the continental
slope, overlapping continental or marginal troughs.
However, in the zones of active sediment absorption,
the rate of sedimentation was insufficient to
compensate for the deflections. As a result, the deep-
sea Peru-Chile Trench continued to develop in such
areas as the most typical example of the zone
stretching along the coast of South America.

The geomorphology of the western slope of South
America is presented by the marine terrace resulted
from a complex processes of tectonic erosion, which
is also pointed by Clift et al. (2003). The marine
terrace continuing as a continental slope into the
western slope of the Andes mountain range. The
surface of the shelf in the coastal zone is hilly, in the
outer part of the shelf – more leveled. The depths of
the outer shelf edge are mostly 50-80 m, reaching on
the submerged steps up to 150-200 m.

Among the important features in the geological
structure of the Peru-Chile Trench there are the
following ones: 1) the placement of undeformed flat-
lying sediments against the 45° steep eastern wall of
the trench which is a unique process, since such
sediments are usually swallowed up in the subduction
zone; and 2) the grabben geomorphic structure of the
trench.

The continental slope of the Peru-Chile Trench is
formed by a stepped ledge with slope steepness and
curvature varying along the coast of South America
(Lemenkova, 2019). The curvature map indicates
concave and convex areas related to the convergence
and divergence curvatures of the geomorphic slopes.
Negative and positive values on the grid indicate
geomorphic variations: negative values show a
concave surface on a grid while positive values
indicate convex, respectively.

Therefore, the curvature map (Fig. 6) shows that
the most dissected convex-shaped slopes (positive
curvature values) are located in the terrestrial regions
of the Andes (pink to purple colored areas) indicating
that surface in the mountainous areas is upwardly
convex at the computed cells. On the contrary,
negative curvature values (bluish colored)
demonstrate concave, that is, the surface is directed
concave at that cell. Following this logic, values close
to zero indicate flat or almost-flat surface (greenish
colors on the map, Fig. 6).

The elevation map (Fig. 7) shows a visualized DEM
based on the SRTM15_PLUS raster grid with a spatial
analysis based on the neighborhood approach (Fig.
8). Along the continental margin of northern Peru
exist mass rock wasting caused by the avalanche

morphology, which covers the lower slope and trench
axis seaward. Slope failures and landslides are a
source of destructive events and cause both
geographic and economic losses, which is also
discussed in the published works on landslide
geomorphology (Mergili et al. 2018; Lemenkova et al.
2012).

The variety of forms of the submarine relief of the
Pacific Ocean seafloor was formed by the end of the
Pliocene as a result of complex factors: horizontal and
vertical tectonic movements, dislocations, active
volcanism as well as various exogenous factors, e.g.
sedimentation as the most important ones. During
the Pleistocene, there were no significant
rearrangements in the morphostructure of the Pacific
seafloor with the exception of the formation of the
new oceanic crust in the rift zones, volcanic island
arcs and continental margins.

<figure><img src="image_9.png" /><figcaption>Fig. 8: Spatial analysis of raster DEM SRTM15_PLUS Method: Neighborhood analysis and cross-category statistics. Mapping: GRASS GIS</figcaption></figure>

One of the most interesting geological phenomena
of the Peru-Chile Trench consists in the formation of
the Chile Triple Junction along the western coast of
Chile. The Chile Triple Junction is formed in the place
where three tectonic plates (Nazca, Antarctic and
South America) intersect in a unique unprecedented
way: an actively spreading mid-ocean ridge is being
subducted beneath a continental South America
Plate, which is further discussed by Lim et al. (2018).

The Bouguer gravity anomaly is corrected for the
height at which it is measured and the attraction of
terrain. Specifically, for the Pacific Ocean, the average
level of the Bouguer anomalies varies in the basins of
the Pacific Ocean. Thus, the Northeast Basin is
notable by the lower positive Bouguer anomalies (250
to 350 mGal), increasing in its western part to 400
mGal. The relatively low values of Bouguer anomalies
(280-300 mGal) are noted in the Guatemala, Peru and
Chile basins.

Such variations in gravity indicate differences in
the subsurface rock density. Thus, higher gravity
values are notable over the denser rocks, and vice
versa, lower gravity values over the less dense rocks
of the seafloor. In the Peru Basin along the South
Galapagos Rise, slightly elevated anomalies from 5 to
18 are observed, mostly oriented in the sub-
meridional direction, at some angle to the system of
the anomalies of the East Pacific Rise.

Deep correlation between the geophysical settings and height elevation as effects of topography and geoid on gravity anomalies are reported recently by Pivetta & Braitenberg, (2020). Furthermore, García et al. (2018) report example for the mountainous areas of Central Andes with rugged topography of the relief and show correlation between the geoid undulations, orogenic deformation and lower crust high-gravity anomaly, as well as the elastic thickness and heat flow, proving interplay between the geophysical and topographic settings.

Discussions

Practical values of the performed
geomorphometric analysis consists in the need of
comprehensive, geomorphic models describing
continental and seafloor tectonics, bedrock geological
evolution, slope curvature and erosion
mathematically. This can be performed by the
geomorphometric surface based analysis combining
data on surface topography, geophysics, gravity fields
analysis, coastal bathymetry, surface roughness and
slope curvature, geologic dynamics and elevation
mapping. The particular problem of the ocean studies
is that in contrast to the terrestrial geoscience, there
are fewer and more costly instrumented observations
as well as restrained access to the study object
(Mitchell, 2012). This necessarily makes a need for
advanced methods of data analysis, GIS and remote
sensing as key tool for correct spatial analysis.

As a recommendation for future studies, thematic
datasets could be included in the research for more
comprehensive analysis: e.g. marine biological data,
sediments (transport, direction and volumes),
earthquakes and volcanic activities affecting the

shape of the seafloor. Testing various GRASS GIS
modules for geophysical and tectonic mapping
through overlay of data layers and accurate modelling
is useful for study of the sediment transport and
deposition, erosion and marine habitat modelling
along the South American coasts. The bathymetric
and geophysical data are useful for verification of
modelling.

The actuality of the study is explained by high
interests in deep-water mineral resource deposits,
which make ocean seafloor studies one of the most
promising in geoscience for investigations of the
seafloor geophysics. Rapid development of the
programming applications in geosciences creates a
need for testing advanced scripting based GIS.
Therefore, the paper contributed to the studies of
topographic and geophysical analysis through
technical approach of the open source GRASS GIS for
advanced spatial analysis. This work presents a
combination of various thematic data (tectonics,
gravity, geoid, topography) to better understand the
principles of the morphostructure and development of
the ocean seafloor topography.

Conclusion

The methodological basis of the work is based on
the morphostructure analysis of the seafloor relief in
the Peru-Chile Trench, along the South America. The
methodology includes GRASS GIS based spatial
analysis, literature review, mapping and
interpretation of the multi-source data, sequential
geomorphological analysis developed to
automatically obtain data on the slope steepness,
aspect, elevation, geophysical anomalies, slope
curvature, model of the smoothed topography using
neighborhood diversity.

The comparative analysis of the
geomorphological, geophysical, and geological
datasets aimed to identify the correlation between
settings of the submarine topography (elevations,
slope, aspect, geophysical fields, curvature) with
geologic processes and deep geomorphic structures.

Future research can include other areas of the
Pacific deep-sea trenches using the proposed
methodology of the GRASS GIS and application of the
presented scripts. Nowadays, geophysical and
geomorphological mapping is significantly improved
with rapidly developed technical tools and
instruments for measurements and GIS mapping. The
mathematical improvements and corrections of
gravity results in reduced influence of the random
errors in the observation datasets, decreased the
impact of surface relief and local variations in density
of the Earth's crust. For instance, the Bouguer
corrections errors caused by the seafloor roughness
do not exceed 10-15 mGal.
The difficulties encountered in this research included two major points: 1) technical processes of data analysis: shell scripting, syntax of GRASS GIS; 2) data capture from the open sources (raster grids). A theoretical basis of the present work is the concept of the plate tectonics which explains factors in the relief formation. The extended functionality of GRASS GIS enables to arrange multi-source data in a project, process datasets, visualize correlations in maps through cartographic overlays.

The importance of this research consists in the actuality of geophysical, geomorphological and topographic studies for our understanding of the ocean seafloor. As a result of numerous international expeditions, there is now a big datasets available for mapping and modelling various parameters of the World Ocean with particular focus on the ocean seafloor geomorphology, tectonics, magnetic and gravity anomalies, heat flow. Processing of such massive data for modelling of the oceanic seafloor, prognosis of mineral resources and thematic mapping requires the use of the advanced tools for big data analysis. This paper was a contribution towards testings of such methods using functionality of GRASS GIS for scripting cartography.

## Acknowledgements

I thank two anonymous reviewers whose comments and suggestions helped improve and clarify this manuscript. This research was implemented in the framework of the Project No. 0144-2019-0011, Schmidt Institute of Physics of the Earth, Russian Academy of Sciences.

## Author contribution

The author of this paper (P. Lemenkova) performed all research steps: formulation of the problem and study goal, data collection (SRTM15_PLUS, EGM96), importing and converting via GDAL library, GRASS GIS shell scripting, cartographic mapping, literature review, geologic analysis, preparing, structuring and writing the manuscript.

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