# GEBCO and ETOPO1 gridded datasets for GMT based cartographic mapping of Hikurangi, Puysegur and Hjort Trenches, New Zealand

Polina Lemenkova

► To cite this version:

Polina Lemenkova. GEBCO and ETOPO1 gridded datasets for GMT based cartographic mapping of Hikurangi, Puysegur and Hjort Trenches, New Zealand. Acta Universitatis Lodziensis. Folia Geographica Physica, 2020, 19, pp.7 - 18. 10.18778/1427-9711.19.01. hal-03122231

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Submitted on 10 Feb 2021

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Polina Lemenkova

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Schmidt Institute of Physics of the Earth of the Russian Academy of Sciences, Department of Natural Disasters, Anthropogenic Hazards and Seismicity of the Earth, Laboratory of Regional Geophysics and Natural Disasters

E-mail: pauline.lemenkova@gmail.com

# GEBCO and ETOPO1 gridded datasets for GMT based cartographic Mapping of Hikurangi, Puysegur and Hjort Trenches, New Zealand

# Rastrowe zestawy danych GEBCO i ETOPO1 dla kartowania opartego na GMT Kartowanie rowów Hikurangi, Puysegur i Hjort, Nowa Zelandia

**Abstract**

The study focused on the comparative analysis of the submarine geomorphology of three oceanic trenches: Hikurangi Trench (HkT), Puysegur Trench (PT) and Hjort Trench (HjT), New Zealand region, Pacific Ocean. HjT is characterized by an oblique subduction zone. Unique regional tectonic setting consist in two subduction zones: northern (Hikurangi margin) and southern (Puysegur margin), connected by oblique continental collision along the Alpine Fault, South Island. This cause variations in the geomorphic structure of the trenches. PT/HjT subduction is highly oblique (dextral) and directed southwards. Hikurangi subduction is directed northwestwards. South Island is caught in between by the "subduction scissor". Methodology is based on GMT (The Generic Mapping Tools) for mapping, plotting and modelling. Mapping includes visualized geophysical, tectonic and geological settings of the trenches, based on sequential use of GMT modules. Data include GEBCO, ETOPO1, EGM96. Comparative histogram equalization of topographic grids (equalized, normalized, quadratic) was done by module 'grdhisteq', automated cross-sectioning – by 'grdtrack'.

Results shown that HjT has a symmetric shape form with comparative gradients on both western and eastern slopes. HkT has a trough-like flat wide bottom, steeper gradient slope on the North Island flank. PT has an asymmetric V-form with steep gradient on the eastern slopes and gentler western slope corresponding to the relatively gentle slope of a subducting plate and steeper slope of an upper one. HkT has shallower depths <2,500 m, PT is <-6,000 m. The deepest values >6,000 m for HjT. The surrounding relief of the HjT presents the most uneven terrain with gentle slope oceanward, and a steep slope on the eastern flank for PT, surrounded by complex submarine relief along the Macquarie Arc. Data distribution for the HkT demonstrates almost equal pattern for the depths from -600 m to -2,600 m. PT has a bimodal data distribution with 2 peaks: 1) -4,250 to -4,500 m (18%); 2) -2,250 to -3,000 m, <7,5%. The second peak corresponds to the Macquarie Arc. Data distribution for HjT is classic bell-shaped with a clear peak at -3,250 to -3,500 m. The asymmetry of the trenches resulted in geomorphic shape of HkT, PT and HjT affected by geologic processes.

**Keywords**

GMT, Hikurangi Trench, Puysegur Trench, Hjort Trench, geomorphic modelling, cartography, visualization, data analysis, bathymetry, Pacific Ocean.

**Zarys treści**

Studium poświęcone jest analizie porównawczej rzeźby dna trzech rowów oceanicznych: Hikurangi (HkT), Puysegur (PT) i Hjort (HjT), położonych w pobliżu Nowej Zelandii na południowym Pacyfiku. HjT charakteryzuje się skośną strefą subdukcji. Unikalna sytuacja geotektoniczna regionu polega na rozdzieleniu dwóch stref subdukcji: północnej (Hikurangi) i południowej (Puysegur), strefą kolizji kontynentalnej wzdłuż uskoku Alpine Fault na Wyspie Południowej. Subdukcja na południe od Wyspy Południowej zachodzi pod dużym kątem w kierunku południowo-wschodnim (PT i HjT), podczas gdy w strefie północnej (Hikurangi) odbywa się na północny zachód. W konsekwencji Wyspa Południowa jest ujęta w swego rodzaju „nożycy subdukcyjne”. Metodologia oparta na GMT (The Generic Mapping Tools) posłużyła do skartowania, wykreślenia i modelowania obszaru. Kartowanie obejmuje wizualizację danych geofizycznych oraz pozycji tektonicznej i geologicznej rowów, opartą na sekwencyjnym użyciu modułów GMT. Dane obejmują GEBCO, ETOPO1, EGM96. Porównawcza korekcja histogramu siatek topograficznych (wyrównana, znormalizeda, kwadratowa) została wykonana przez moduł „grdhisteq”, zaś zautomatyzowane przekroje – przez moduł „grdtrack”.

Analiza wykazała, że rów Hjort ma symetryczną formę z porównywalnymi nachyeniami zarówno na zachodnich, jak i wschodnich zboczach. Rów Hikurangi ma podobne do koryta płaskie szerokie dno, a stok od strony zachodniej (przylegający do Wyspy Północnej) jest nachylony pod większym kątem od stoku wschodniego. Rów Puysegur ma asymetryczną V-kształtną formę ze stromo nachylonym zboczem wschodnim i łagodniejszym zachodnim. Rów HkT jest relatywnie płytki <2500 m, PT osiąga głębokość <-6000 m. Największą głębokość (>6000 m) stwierdzono dla rowu Hjort. Rzeźba dna w otoczeniu HjT jest najbardziej zróżnicowana. a w przypadku położonego bardziej na północ PT zaznacza się wyraźna dysproporcja pomiędzy łagodnym oceanicznym zboczem na zachodzie i stromym zboczem grzbietu Puysegur (północny odcinek Łuku Macquarie) na wschodniej flance rowu. Rozkład danych z 2 pikami: 1) 4250 do 4500 m (18%); 2) 2250 do 3000 m, <7,5%. Druga koncentracja danych odpowiada łukowi Macquarie. Rozkład danych dla HjT ma klasyczny kształt dzwonu z wyraźnym ekstremum odpowiadającym głębokościom 3250 do 3500 m. Asymetria zaprezentowanych rowów oceanicznych jest uwarunkowana przez procesy geotektoniczne.

**Słowa kluczowe**

GMT, rów Hikurangi, rów Puysegur, rów Hjort, modelowanie geomorfologiczne, kartografia, wizualizacja, analiza danych, batymetria, Ocean Spokojny.
# 1. Introduction

Worldwide, deep-sea ocean trenches are mostly formed in the locations of the subduction zones of plate, along which lithospheric tectonic plates subduct one under another. Morphologically presented as long, narrow, steep-sided depressions in the ocean bottom, hadal trenches typically occur in the maximum oceanic depths, ca 7,300 up to >11,000 m (e.g. Mariana Trench). The geomorphic appearance of hadal trenches is their cross-sections is highly variable (V-shaped, U-shaped, elongated to upside-down-ridge-like, circular-like, arcuate, symmetric of irregular: left- or right-sided), which is often related to the prevailing tectonic plate movements, geologic regime and substrate, contributing to the geomorphic shape of the trenches.

The focus of this study is set on the comparative analysis of the three oceanic trenches: Hikurangi, Puysegur and Hjort, located near New Zealand, southwest Pacific Ocean (Fig. 1). Unique tectonic setting of the region consist in the connection of two subduction zones in the north (Hikurangi margin) and in the south (Puysegur margin), connected by an oblique continental collision along the Alpine Fault located in the South Island of New Zealand.

This cause variations in the submarine geomorphic structure of the trenches which is also referred as "subduction scissor" (Pysklywec et al. 2010).

The Puysegur/Hjort subduction is highly oblique (dextral) and directed southeastwards. The Hikurangi subduction is directed northwestwards. Hence, the South Island is caught in between by the "subduction scissor". In the absence of available high-resolution information and detailed mapping on the seabed geomorphology of the Hikurangi, Puysegur and Hjort trenches, a GMT approach to map their seafloor on a local scale were undertaken. Since seafloor of the deep-sea trench represents an integrated response to a complex range of factors, such as oceanographic, geological and tectonic conditions which eventually define the present shape of the seabed landforms, an integrated approach was used to visualize, model and map three trenches on the New Zealand margin.

In this study, following key questions were addressed: the most repetitive depths of the seafloor of the trenches, and analysis of variations in the trench geomorphology. The cross-section modelling was performed via GMT modules 'psxy' and 'grdtrack'.

<figure><img src="image_5.png" /><figcaption>**Fig. 1.** GEBCO based topographic map of the New Zealand, Hikurangi, Puysegur and Hjort Trenches (ed. by author)</figcaption></figure>

<caption>**Ryc. 1.** Mapa topograficzna Nowej Zelandii i rowów oceanicznych Hikurangi, Puysegur i Hjort w oparciu o GEBCO (oprac. autorki)</caption>
## 2. Study area

### 2.1. Hikurangi Trench

The Hikurangi Trench (sometimes also referred as trough) is located on the Hikurangi margin which is 500 km long by 480 km wide (Nicol, Wallace 2007), located northeast from the North Island. The toponymy of the Hikurangi Trench vary in the existing literature due to its specific geomorphology: in some works it is referred as 'trench' (e.g. Reyes et al. 2010; Reyners et al. 2011; Clark et al. 2019), in other works – as 'trough' (e.g. Barnes et al. 2010; Greinert et al. 2010; Jiao et al. 2015; Jiao et al. 2017).

The tectonic location of the Hikurangi is at the southern end of the 1000 km long Tonga-Kermadec-Hikurangi subduction systems, where Pacific Plate subducts obliquely northwestwards beneath the Indo-Australian Plate (Barnes, Mercier de Lepinay 1997) and Indo-Australian Plate has a strike-slip motion at 4 cm/yr. Comparing to the Kermadec trench reaching up to 9000 m, Hikurangi trench is shallow (ca. 3000 m). Pacific Plate dips at Hikurangi trench at a gentle angle of about 3° for at least 100 km beneath the trench and then further steepens beneath the North Island (Barker et al. 2009). The Alpine Fault stretches sub-parallel to the western edge of the Hikurangi Trench (Fig. 2). The speed of subduction on the Hikurangi Margin varies with a general trend of increase northwards: 34 mm/yr in the south (westward off Bounty Trough), 38 mm/yr in its central part (North Island) and 47 mm/yr in the North Island (Reyners 2013).

The Hikurangi north-west dipping subduction zone is old (started ca. 20 Ma). The subducted slab has a well defined Wadati-Benioff zone and steepens from shallow angles near the surface to near-vertical at depths > 100 km (Ballance 1976).

The geophysical, topographic and geological settings of the Hikurangi margin vary along the trench from south to north (Wallace et al. 2009), comparing Figure 2, 3, 4 and 5. Thus, interseismic coupling is strong and deep in the south, then gradually shallows northwards and becomes shallow and weak in the north. Southern region is characterized by accretionary wedge and tectonic contraction in the forearc. Northern region is characterized by frontal subduction erosion, numerous seamounts, and a slightly extensional upper plate. Kinematics of the Hikurangi Margin studied by GPS measurements of the horizontal velocity fields (Nicol, Wallace 2007) shown changes in faulting along the margin and clockwise tectonic block rotations caused by collision of the Hikurangi Plateau and Chatham Rise with Hikurangi Trench and subduction of oceanic crust northeast of the North Island.

Hikurangi Plateau initially formed a part and now separated from the largest oceanic plateau on Earth, the Ontong Java Plateau, located in the southwestern Pacific Ocean (Neal et al. 1997). Hikurangi Margin and continental shelf of the North Island of the New Zealand

<figure><img src="image_6.png" /><figcaption>**Fig. 2.** Tectonic and geological settings of the study area, New Zealand region. The Pacific Plate subducts beneath the Indo-Australian Plate at the Hikurangi Trench; Indo-Australian Plate subducts beneath the Pacific Plate at the Puysegur and Hjort Trenches. Two subduction margins joined by dextral transform Alpine Fault, New Zealand (ed. by author)</figcaption></figure>

<caption>**Ryc. 2.** Pozycja geotektoniczna badanego obszaru w regionie Nowej Zelandii. Płyta pacyficzna ulega subdukcji pod płytę indo-australijską wzdłuż rowu oceanicznego Hikurangi; w rowach oceanicznych Puysegur i Hjort subdukcja zachodzi w przeciwnym kierunku. Obydwie strefy subdukcji rozdziela prawoprzesuwczy uskok transformacyjny Alpine Fault, Nowa Zelandia (oprac. autorki)</caption>

is well studied through various geologic investigations, more specifically: bathymetric, hydro-acoustic investigations (Barnes et al. 2010), active tectonics. Palaeogeographic reconstruction of the evolution of topography/bathymetry in the region of Hikurangi (Jiao et al. 2015) uses advanced methods of the thermochronology. Further findings in exploration geology in the Hikurangi Trench with a special focus on methane seepage and gas hydrates in the underlying sediments are relatively well studied (e.g. Klaucke et al. 2010; Krabbenhoeft et al. 2010, 2013; Martin et al. 2010; Pecher et al. 2010; Wang et al. 2017) studies on subduction earthquakes in Holocene, coseismic coastal deformation and tsunamis (Berryman et al. 2011; Clark et al. 2019) which later on largely affected submarine geomorphology of the Hikurangi margin forming submerged terraces (Berryman 1993).
## 2.2. Puysegur Trench

Puysegur Trench has ca. 800 km in length, stretching from the most southern tip of the South Zone is associated with the Alpine Fault, which is the right-lateral transform fault boundary separating the Puysegur Trench and the northern Kermadec Trench (Beavan, Haines 2001). Macquarie Ridge Complex (MRC) is a dominantly trans- lational structure accommodating right-lateral motion between the Australian and Pacific Plates and the Puysegur Trench, where Australian lithosphere subducts beneath the southwest corner of New Zealand on the Pacific Plate. The plate boundary south of New Zealand is located along the MRC which is crucial for understanding the tectonic structure of the region. Comparing to the Hikurangi, Puysegur/Hjort is younger (started at 16–8 Ma) and less developed (Sutherland et al. 2006). The Indo- -Australian Plate subducts beneath the Puysegur Bank and the Fiordland Massif forming Puysegur Trench.

## 2.3. Hjort Trench

Hjort Trench continues Puysegur Trench southwards from the Macquarie Island and extends until the Macquarie Triple Junction. It presents a linear topographic depression south of Macquarie Island in the southwest Pacific Ocean (Fig. 2). Hjort Trench lies in an area of transpression where plate boundary transitions from a transform boundary to a convergent one. Hence, this region shows how a transform boundary with a vertical (near-vertical) transform fault becomes an area of under-thrusting (Meckel et al. 2003). The deepest point of Hjort Trench is ca. 6.3 km b.s.l. Eastwards, the Hjort ridge follows the general curve of the Hjort Trench, separating it from the Hjort Plateau.

Hjort Trench is characterized by an oblique subduction zone geoid anomaly. Large 1924 earthquake occurred in the northern Hjort Trench which suggest a thrust focal mechanism and active subduction of young oceanic lithosphere beneath older oceanic lithosphere (Cazenave, Ruff 1985). Frequent seismic events, most less than 20 km deep, characterize the transpression along this plate boundary (Lodolo, Coren 1994). The southern segment of the Alpine Fault on the South Island continues into the Tasman Sea Basin and finishes at the Puysegur Trench (Fig. 2). The oceanic Indo-Australian plate subducts east- wards through the Puysegur Trench under the Pacific Plate.

Geologic events during the tectonic historical records of this region, such as Eocene-Oligocene rifting as well as Miocene-Quaternary strike-slip, crustal thinning in the Solander Basin, development of the oblique subduction zone in the Puysegur Trench, are studied by processing seafloor relief data and interpretation of the seismic and bathymetric cross-section profiles acquired over the Puysegur Trench area (Lamarche et al. 1997; Melhuish et al. 1999; Lamarche, Lebrun 2000).

# 3. Methods

## 3.1. Topographic mapping

The area selected for the data set lies in the southern Pacific Ocean and includes three trenches: Puysegur, Hjort and Hikurangi off New Zealand coast. The region is characterized by a geologically complex history and current situation with oblique subduction zone and subduction scissors. Such complex bathymetry exhibits considerable geomorphological variability among three trenches: there are differences caused by seamounts and seafloor obstructing natural curvatures of the trenches.

<figure><img src="image_7.png" /><figcaption>**Fig. 3.** Histogram equalization on the topography grids, ETOPO1 (ed. by author)</figcaption></figure>

<caption>**Ryc. 3.** Wyrównanie histogramu na siatkach topograficznych, ETOPO1 (oprac. autorki)</caption>

High-resolution bathymetric data is important for mapping trench shape in a cross-section and to identify clearly its geomorphology. For these reasons, GEBCO bathymetric grid (GEBCO Compilation Group 2020) was selected for topographic mapping (Fig. 1). Pixel size at a course resolution bathymetric maps (ETOPO5) may reduce accuracy. Hence, ETOPO1 and GEBCO datasets were chosen. Among the two, the GEBCO grid was used as the base geodata source due to its high resolution: 15- arc second. The GEBCO (https://www.gebco.net/) grid uses as a base Version 1 of the SRTM15+ data set (Olson et al. 2014) which in turn is based on version 11 of SRTM30+ (Becker et al. 2009; Sandwell et al. 2014), updated by
gridded bathymetric data sets. The geoid and gravity (Fig. 4 and 5) are modeled based on the Earth Gravitational Model EGM96 dataset (Lemoine *et al.* 1998).

<figure><img src="image_8.png" /><figcaption>**Fig. 4.** Geoid model visualization based on the EGM96: New Zealand region, Hikurangi, Puysegur and Hjort Trenches (ed. by author)</figcaption></figure>

**Ryc. 4.** Wizualizacja modelu geoidy na podstawie EGM96: region Nowej Zelandii, rowy oceaniczne Hikurangi, Puysegur i Hjort (oprac. autorki)

The quality of the two grids (GEBCO and ETOPO1) was compared and the data outputs assessed. Because the GEBCO grid has higher resolution than ETOPO1 (15 arc-second against 1 arc-minute, respectively), ultimately the GEBCO was selected as the base map for modelling and visualization

The assessment of the ETOPO1 grid was included visualization of the four subplots of histogram equalization (Fig. 3). The smoothness of the grids intensities for ETOPO1 was improved by passing the output of 'grdgradient' to 'grdhisteq'. Comparative histogram equalization was performed by key GMT module 'grdhisteq' to enhance visualization of the various ranges of the ETOPO1 grid (Fig. 3). Four subplots were generated to find values dividing grid files into equal area patches. The 'grdhisteq' module performs a histogram equalization of raster images. Using 'grdhisteq', the ASCII data values dividing the range of the initial raster data into cells segments was written to an output file. The '-C16' argument defines 16 cells. The resulting raster grid has an equal area in the images. Using 'makecpt' GMT module this output was then coloured according to the actual bathymetric values by following code: gmt makecpt -Crainbow -T 9000/3000 > t.cpt. The explanations for the subplot with four maps (Fig. 3) is as follows:

Top left: The original map (top left) visualizes initial raster (artificial cpt 'rainbow') to highlight changes in elevation; Top right: equalized raster grid; Low left: normalized raster grid derived using -N argument that stands for Gaussian output, used to to receive data with smooth Gaussian distribution. The default standard normal scores were used for grid normalization. Low right: quadratic equalization plotted using following snippet: gmt grdhisteq hpt_relief.nc -Gout.nc -Q. Here, the '-Q' argument is output selecting quadratic histogram equalization, unlike the default linear one. The '-T-9000/3000' argument means range of the topographic elevations. The image was then visualized using 'grdimage' module by code snippet: $gmt grdimage hpt_relief.nc -l+a45+nt1 -Ct.cpt -JM3i -Y6i -K-P-Bpxg5f5a10 -Bpyg4f2a8 -Bsxg5 -Bsyg4 -BWSne > $ps$.

In this code, the '-Ct.cpt' argument passes cpt created in the previous step for visualization; the '-JM3i' arguments explains the Mercator projection with 3 inches width; -Y6i' argument plots the map with 6 inches distance from the previous one by Y axis; -K' argument refers to the continuation of the code. The annotation was added using Unix 'echo' prog: echo $172 -33 Original" | gmt pstext -Rhpt_relief.nc -J-F+jBL+f12p-T-Gwhite@10 -Dj0.1i -O -K >> $ps$.

The 'grdhisteq' GMT module enables to write a raster grid with statistics based on cumulative distribution function. That means, after applying the 'grdhisteq' module, the output raster file has relative elevations in the same locations as the input file (that is, x, y). However, the values are modified to reflect their place in cumulative distribution with reference to the initial input file. This illustrates the principle of the equalization of the topographic grids by GMT module 'grdhisteq', as visualized on Fig. 3.

## 3.2. Digitizing cross-section profiles

Modelling and digitizing a series of the cross-section profiles along the trenches: Hikurangi, Puysegur and Hjort (Fig. 6 and 7) and plotting three graphs based on the retrieved tables (Fig. 8) was performed in GMT. Cross-section profiling is a technique used in geosciences to receive a sample of the selected segment in the study area and analyze variability of the studied elements along the track.

Automated methods have been explored in cartography, driven largely by the advantages of using machine-learning algorithms in cartographic routine, thus minimizing handmade routine, subjectivity in processes of the digitizing and vectorizing of the bathymetric data. Examples of such works is presented by Schenke, Lemenkova (2008); Lemenkova (2019e, 2019g, 2019h). GMT proposes more advanced solution in the automatization of the cross-sections through ML based digitizing that results in a series of the profile transects across the trench (Wessel, Smith 2018).
<figure><img src="image_9.png" /><figcaption>**Fig. 5.** Marine free-air gravity anomaly: Hikurangi, Puysegur and Hjort Trenches (ed. by author)</figcaption></figure>

**Ryc. 5.** Morska anomalia grawitacyjna (redukcja wolnopowietrzna – Faye'a): rowy Hikurangi, Puysegur i Hjort (oprac. autorki)

Two methods were tested in visualizing the profile: median and the mean (by GMT arguments '-Sm' for median and '-Sa' for mean). Of these two, median was selected as the best representing the empirical nature of the trench's shape. Although the 'mean' method shows fine interpolation, the 'median' approach shows the performance and visual representation of the trench within reasonable reflection of its geomorphology. On the contrary, mean values are notable for smoothing the splines rather as a mathematical functions which lesser reflects the geographic phenomena of the objects. The uncertainties of the actual geomorphology are expected to exceed the theoretical interpolation of the actual geomorphology represented on the graphs. The shape of the trenches is highlighted as median using '-Sm' argument, Fig. 6 and Fig. 8.

## 4. Results

Whilst it serves as a terrain variable in this study to examine the geomorphic landform, the variation of the geomorphic slopes were compared for the three trenches and following findings noted: Hikurangi Trench has a trough-like flat wide bottom, steeper gradient slope on the North Island flank (Fig. 6 and 8A).

<figure><img src="image_10.png" /><figcaption>**Fig. 6.** Digitizing cross-section profiles in Hikurangi Trench, North Island (ed. by author)</figcaption></figure>

**Ryc. 6.** Digitalizacja linii przekrojów w rowie Hikurangi, Wyspa Północna (oprac. autorki)

Puysegur Trench (Fig. 8B: middle plot) has an asymmetric V-form with steep gradient on the eastern slopes and more gentle slope on the west. Hjort Trench has a symmetric shape form with comparative gradients on both western and eastern slopes (Fig. 8C, lower plot). The results of the comparison of the median values (red line on Figure 8 for three sub-plots) of three trenches show that selected segment of the Hikurangi Trench has shallower depths with maximal values approximately -2,600 m (Fig. 8A), while Puysegur Trench is reaching up to -6,000 m (Fig. 8B). The deepest values >6,000 m for Hjort Trench (Fig. 8C). The surrounding relief of the Hjort Trench presents the most uneven terrain comparing to the other trenches. The neighboring terrain has a gentle slope on the oceanward side for Hikurangi Trench, and a steep slope on the eastern flank for Puysegur Trench, which is surrounded by more complex submarine relief along the Macquarie Arc (Fig. 2).

The statistical histograms for the transecting profiles of the Hikurangi, Puysegur and Hjort trenches are visualized on Figure 9. The evaluation of the descriptive statistics on bathymetry in three trenches and interpolation approaches shows following results. The shape of the histogram varies by the three trenches reflecting their geomorphology. Data distribution for the Hikurangi Trench
(Fig. 9B) demonstrates almost equal pattern for the depths
from -600 m to -2,600 m with the samples observations not
exceeding 60 for each sample bin (most data are detected
at around 30 to 40 samples for a bin <4%). Notable peak
have data located on the shallow areas (shallower than
-500 m) where maximal values are detected for the range
-400 to -300 m (258 samples). We can clearly see a rising
increase of data with depths below 500, that is a slope
of the North Island (frequency 5% to 12%).

<figure><img src="image_11.png" /><figcaption>**Fig. 7.** Digitizing cross-section profiles in Puysegur and Hjort trenches, Macquarie Island Arc (ed. by author)</figcaption></figure>

<caption>**Ryc. 7.** Digitalizacja linii przekrojów w rowach oceanicznych Puysegur i Hjort, łuk wyspowy Macquarie (oprac. autorki)</caption>

Puysegur Trench (Fig. 9A) has a bimodal type of data
distribution with two peaks. The first peak has three
notable bins range -4,250 to -4,500 m (373 samples
detected, data frequency 18%), range -4,000 to 4,2 (182
samples, data frequency 9,6%) and -4,500 to -4,750 m
(216 samples, data frequency 11,5%). The second peak
covers depths from -2,750 to -3,000 m with the data
frequency < 7,5%. The peak corresponds to the Macquarie
Arc bordering the trench slope. Data distribution for the
Hjort Trench (Fig. 9C) has a bell-shape form with a clear
peak of data at depths -3,250 to -3,500 m (364 samples,
30% of data frequency). The abrupt decrease in the
sample values off both flanks of the trench corresponds
to the steep slope of the trench west off Hjort Plateau.

Spreading fabrics can be seen (Fig. 7) eastwards off
the Puysegur Trench, together with minor ridges. This

geomorphology is particularly well expressed along
Macquarie Arc, between 51,5° and 54° where ridges
might form due to the sedimentation processes. The
ridges resembling elongated seamounts can be seen
on the north-west side off the Puysegur Trench (Fig. 7)
interspersed with minor troughs.

Geomorphic curvature and distribution of the
seamounts near the Puysegur, Hjort and Hikurangi Trenches
reflect the interplay between the complex tectonic
processes occurring at a subducting tectonic plates and
variations in the tension between the spreading ridges and
the transform faults. In the northwest region off Puysegur
Trench, GEBCO bathymetric data (Fig. 6 and 7) enable to
see complex submarine relief: linearly expressed ridge
geomorphology, a series of small elongated seamounts,
minor troughs and flat seabed areas. The average depth
of the seafloor deepens abruptly (Fig. 9A) from -4,750
(216 samples) to the -6,250 m (9 samples). The data
distribution has a clear bimodal way for the Puysegur
Trench with clear peaks at ranges -4,250 to -4,500
(373 samples) and at -2,750 to -3,000 m (140 samples).
The histogram for the Hjort Trench (Fig. 9C) has a classic
'bell-shape' form with one peak in data distribution at
range -3,250 to -3,500 m (364 samples).

The effect of using different histogram equalization
algorithms was examined using subplots for data on
ETOPO1 covering area for three trenches (Fig. 3).
Equalization compression for bathymetry grids were
tested as comparison for four grids: original, equalized,
normalized, quadratic algorithms. The results for this step
are demonstrated in Figure 3 showing a visual summary
of a grid equalization by different GMT algorithms.
Consistent cpt across all raster dataset grids where
applied for better comparison.

From the analysis of histogram equalization algorithms
it is notable that there are variations in the grids
values obtained depending on the method: equalized,
normalized, quadratic algorithms. This in itself means
that the topic is worthy of further elaboration. Through
the demonstrated example (Fig. 3) the effects of using
different algorithms varying with raster dataset grids
equalization can be notable. Cartographic functionality
of the GMT is assessed by technical visualization of the
produced maps, models and graphs as well as tested
variety of map projections. In this study, following various
cartographic projections were used for plotting maps:
Mercator, Mollweide pseudo-cylindrical homographic
equal-area, Eckert IV equal-area pseudo-cylindrical,
Lambert Azimuthal Equal-Area, Oblique Mercator.

**5. Discussion**

This study aimed to produce a set of the cross-
-section profiles for three deep-sea trenches varying in
geomorphology which could be utilized at similar works
for spatial marine data analysis and detailed seafloor
mapping. The comparison of the geomorphology and
highlighted differences are presented for three trenches. In that sense the study objectives were achieved. GMT is aiming to enable cartographic visualization and modelling of a high standards, high-quality maps based on the raster/vector datasets which can be effectively used for mapping the shape of the seabed and submarine landforms, thereby providing the knowledge base to detail the topography of the World Ocean.

<figure><img src="image_12.png" /><figcaption>**Fig. 8.** Comparative analysis on geomorphic cross-sections by three trenches: Hikurangi, Puysegur and Hjort (ed. by author)</figcaption></figure>

**Ryc. 8.** Analiza porównawcza profili batymetrycznych trzech rowów oceanicznych: Hikurangi, Puysegur i Hjort (oprac. autorki)

Approaches to the geological data analysis are diverse: ternary diagrams plotting (Reyes *et al.* 2010; Lemenkova 2019d), geophysical methods (Dahlin *et al.* 1999), swath-bathymetric mapping (Wells & Monahan 2002; Gauger *et al.* 2007; Nitsche *et al.* 2007), compression strength (Lindh 2004), various approaches to the data analysis, e.g. factor analysis, correlograms, cross-section plotting and visualization (Lemenkova 2018a, 2018b), geophysical and geomorphological modelling based on tectonic analysis and mapping (Serra *et al.* 2020; Gales *et al.* 2013; Lemenkova 2019c, 2019e). Apart from the statistical tools, a GIS data analysis is largely used in geological sciences. Comparing to the existing approaches based on various existing GIS software, e.g. ESRI ArcGIS (Suetova *et al.* 2005; Kuhn *et al.* 2006; Lemenkova 2011; Lemenkova *et al.* 2012; Klaučo *et al.* 2013a, 2013b, 2017), GMT is notable for its scripting based methodology. Plotting map in GMT evolves scripting and running a code from the console, unlike a GUI based GIS.

Modelling slope of the deep-sea trenches is important in relation to several reasons:

<figure><img src="image_13.png" /><figcaption>**Fig. 9.** Comparative analysis on data distribution by three trenches: Hikurangi, Puysegur and Hjort (ed. by author)</figcaption></figure>

**Ryc. 9.** Analiza porównawcza rozkładu danych według trzech rowów: Hikurangi, Puysegur i Hjort (oprac. autorki)

1. Geomorphology of the trench presents a crucial characteristics for benthic habitat and hence serves as an environmental variable: more specifically, the stability of sediments which directly depend on the geomorphic slope characteristics, affects the ability of deep-sea fauna species to dwell on sediments.

2. Slope gradient is relevant as a geomorphological concept, since it impacts the stability of the geologic sediments and grain size.

3. Geomorphic slopes are factors inducing acceleration of ocean deep currents which is related to the environmental characteristics, such as ecological chain: food supply and exposure for the deep-sea fauna species.

4. Slope landforms and specific forms of the trench geomorphology induces erosion, movement, fall and replacements of sediments depending on their size.

5. Geomorphic characteristics of slopes eventually influence submarine landforms of the deep-sea trenches.
A phenomenon of the tectonic plates subduction
explains the asymmetry of the deep-sea trenches.
Subduction of one lithospheric plate to the Earth's mantle
while another plate is being deformed induces a formation
of the oceanic trench which eventually forms through
filling the space between the plates. Necessarily, in case
of the triple junction, the complexity of the bathymetric
shape arises.

The depths of the Hikurangi, Puysegur and Hjort
trenches are influenced by a variety of geologic
processes and factors affecting their geomorphic shape
and structure. Of these, the tectonic plates movements
and slab geometry are the crucial factors controlling their
form, gradient steepness and depths. This can be seen
by the comparison of the visualized geophysical setting
(Fig. 4 and 5) and geomorphology of the trench's seafloor
(Fig. 6 and 7). Other factors include age and convergence
rate of the plates, intermediate slab dip, width of sinking
plate.

Generally, a strong correlation of the trench's axes
with borders of the three lithospheric tectonic plates
(Antarctic Plate, Pacific Plate and Info-Australian Plate)
can be noted, which underpins strong correlation of the
trench geomorphology with direction of the tectonic slab
lineaments, as plate movements, geologic lineaments and
extend of the fracture zones in the final end lead to the
formation of the trench axis through the plates motions.

Local geologic settings, linear extension of the tectonic
slabs, complex tectonic processes and sedimentation of
the Hikurangi, Puysegur and Hjort trenches might explain
variations in their geomorphic structure and shape of the
submarine landforms, in particular, a zone of Macquarie
Triple Junction in Southwest Pacific Ocean, Antarctic.

6. Conclusion

As the utility of the seafloor-mapping technology, a GMT
scripting was demonstrated as a case study for com-
parative analysis of the three trenches, methods of
visualization through GMT modules for thematic mapping
of the topographic and geologic settings (Fig. 1 and 2),
topographic statistical smoothing (Fig. 3) geoid and
gravity fields (Fig. 4 and 5), cross-section profile digitizing
(Fig. 6 and 7), geomorphic plotting (Fig. 8) and statistical
visualization (Fig. 9).

Applying GMT techniques to seafloor mapping on
Hikurangi, Puysegur and Hjort Trenches off New Zealand
enabled to model geomorphology of the three trenches
by tested methods (Lemenkova 2019f, 2020) and visu-
alize corresponding geologic conditions; each trench
was distinguished by specific geomorphic shape of the
submarine landform, geologic substrate, complexity of
the tectonic settings and historical development of the
lithospheric plates movements in this area.

The data on bathymetry has been modeled through
GMT based cross-section profiling for the three trenches,
respectively, and compared. The maximal depths in the

segments of the three trenches derived from digitized
GEBCO grid were used for comparative analysis and
visualized at histograms. Hikurangi Trench, which is also
often referred as trough proved to have more trough-
-like shape form in its cross-section, while Puysegur and
Hjort trenches have classic ‘V’-form. Of all three trenches,
Hjort Trench has the steepest slope gradient. The GMT
demonstrated to be is a powerful cartographic toolset
to visualize geological, geophysical and topographic
maps, model geomorphic cross-sections and perform
descriptive statistical analysis on the data retrieved from
the automatic digitizing.

Cross-section modelling approach is based on the
newly developed methods of the computed based data
analysis and visualization of the transect xyz grids in
topographical research (Harris et al. 2014; Hodgson
et al. 2014; Bursztyn et al. 2015; Niyazi et al. 2018;
Wessel, Smith 2018; Lemenkova 2019a, 2019b; Akan
et al. 2020; Brothers et al. 2020; McCalpin et al. 2020;
O'Brien et al. 2020; Trevisan et al. 2020), adapted to the
geomorphic mapping as a basis for mapping submarine
geomorphology. Automated cross-sectioning model is
based on primarily the 'grdtrack' module and considers
three principal variables: length of the transect segment,
distance between the samples, density of sampling,
which in this study were accepted as: track 400 km long,
spaces 20 km along the selected segment of the trench,
and density 2 km. These variables were selected for script
and then have shaped the current cross-section shapes
of the landforms and defined curvatures of the modeled
transects as median with errors visualized in three
trenches (Fig. 8). The X axis of the profiles (Fig. 8A, B, C),
reflects the perpendicular cross segment, the Y axis is
modeled based on the bathymetry data and elevation
characteristics by 'psxy' module. The graph is visualized
based on the numerical model received through the
digitizing of the cross-section profiles for each of the three
trenches.

Three types of the deep-sea trench shapes have been
then identified for the detailed seafloor mapping and
further exploration. The open-source GMT approach
represents a cost-effective approach to visualize seafloor
in a geographically remotely located areas such as hadal
trenches. The approach also delivers a knowledge base
upon which more detailed studies on links between
geology, tectonics and bathymetry can be identified
and founded. Hikurangi Trench presented unique
characteristics of the seafloor as trough-shaped form.

By recognizing the geomorphic shape and geologic
environments at the seabed, distinctly different from
Puysegur and Hjort Trenches, a gradual decrease of
depths along the slope of the North Island was observed.
Targeted seafloor mapping in cross-sections highlighted
active seafloor processes have created unique geomorphic
picture for the three trenches.
## Acknowledgements

The author gratefully acknowledges the anonymous referees for their comments and review which improved the initial manuscript. The research was performed during the author's study in Ocean University of China and funded by China Scholarship Council (CSC), State Oceanic Administration (SOA), Marine Scholarship of China, Grant Nr. 2016SOA002, People's Republic of China, and implemented in the framework of the Project Nr. 0144-2019-0011, Schmidt Institute of Physics of the Earth, Russian Academy of Sciences.

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