Statistical Analysis of the Mariana Trench Geomorphology Using R Programming Language

This paper introduces an application of R programming language for geostatistical data processing with a case study of the Mariana Trench, Pacific Ocean. The formation of the Mariana Trench, the deepest among all hadal oceanic depth trenches, is caused by complex and diverse geomorphic factors affecting its development. Mariana Trench crosses four tectonic plates: Mariana, Caroline, Pacific and Philippine. The impact of the geographic location and geological factors on its geomorphology has been studied by methods of statistical analysis and data visualization using R libraries. The methodology includes following steps. Firstly, vector thematic data were processed in QGIS: tectonics, bathymetry, geomorphology and geology. Secondly, 25 cross-section profiles were drawn across the trench. The length of each profile is 1000-km. The attribute information has been derived from each profile and stored in a table containing coordinates, depths and thematic information. Finally, this table was processed by methods of the statistical analysis on R. The programming codes and graphical results are presented. The results include geospatial comparative analysis and estimated effects of the data distribution by tectonic plates: slope angle, igneous volcanic areas and depths. The innovativeness of this paper consists in a cross-disciplinary approach combining GIS, statistical analysis and R programming.


Introduction
The goal of this study is to analyze factors affecting geomorphological structure of the Mariana Trench. Mariana Trench is a long and narrow topographic depression of the seafloor located in the west Pacific ocean, 200 km to the east of the Mariana Islands, east of the Philippines.

Processes of the deep-sea sedimentation
Processes of the deep-sea terrigenous sedimentation are formed by the transfer of the erosion materials from the adjacent land. The main processes include transportation, deposition and re-deposition of the sedimentation materials. The origin of the deep ocean sedimentation is diverse. In general, apart from the sediments from the rivers, the terrigenous material goes to the oceans through iceberg melting and glacial deposits transferred to the seafloor, as well as dusty material moved by the aeolian processes. Normally, the sediments transferred by rivers are deposited within the shelf sublittoral areas, and rarely reach deeper regions of the continental slope and, even less the abyssal basins. However, sediments deposited on the shelf may move to the deeper parts of the ocean including hadal trenches, due to further move from the shelf edge downwards, avalanche sedimentation, i.e. gravitational flows, which are caused by the gravity. For the case of the Mariana Trench, the deep currents flow through the trench ventilating its bottom water flowing through the West Pacific trenches originates from the Southern Ocean and flows northward (Warren & Owens, 1988), in a clockwise direction, passing through the trenches on the west of the Pacific (i.e. the Kermadec Trench and the Tonga Trench. Through the Samoan Passage, it flows northwest across the equator to the east Mariana Trench. Among other hadal trenches, Mariana Trench is the largest structural traps located in the continental margins. It stretches for hundreds kilometers and has a narrow depression on the ocean floor with very steep slopes and the depths of 3−5 km width of the bottoms rarely exceeding 5 km in breadth (Nakanishi & Hashimoto, 2011).
Therefore, the geomorphic conditions of Mariana Trench create ideal conditions for the sedimentation processes intercepting almost all clastic material originating from adjacent land. The accumulation of the terrigenous sedimentation on the Mariana Trench seafloor depends on various factors. These include climatic and hydrodynamic local characteristics, tectonics, structure of the seafloor bathymetry, geomorphic characteristics of the trench, type and size of particles and others. Large areas of active sedimentation processes can be distinguished in the areas where the speed of the sedimentation and their volumes are very high, as well as local areas of active sedimentation, or, on the contrary, dominating erosion areas. In general, sedimentation processes mainly occur in various sediment traps, however, some areas are noted by areal sedimentation. Therefore, the processes of the sedimentation within the Mariana Trench are highly uneven.

Bathymetry and the system of crack
Mariana Trench presents a strongly elongated, arched in plan and lesser rectilinear depression. Its transverse profile is asymmetric: the slope is higher on the side of the Mariana island arc. The slopes of the trench are dissected by deep underwater canyons. Various narrow steps are also often found on the slopes of the trench. On the longitudinal profiles of the bottom of the Mariana there are many deepwater detected transverse steps and thresholds connected by the movements of the earth's crust along transverse faults (Zhou, Lin, & Behn, 2015).
These thresholds can play important role in the evolution of the deep water trough, for example, to control the intensity of its filling by sedimental precipitation. In this process very important are the streams of the precipitation moving along the bottom from the part of the trough Electronic copy available at: https://ssrn.com/abstract=3447481 which is closer to the continent (Taira et al., 2004). At the bottom of the trough there is a transverse threshold, which can present kind of a dam, in front of which there is accumulation of a thick layer of sediment precipitation.
Mariana Trench has complicated steps of various shapes and sizes, caused by active tectonic and sedimental processes. The steepness of its geomorphic depth averages in 4−5 degrees, but its individual parts can be limited to steeper slopes as subjects to the gravitational flow system of the submarine canyons and valleys (Kawabe, 1993). Complex distribution of the various geomorphic material on the adjacent abyssal plains of the ocean contributes to the formation of the geomorphic features of the particular region of the Mariana Trench.

Igneous volcanic areas
Mariana Trench is an important integral feature of the active continental margins that naturally includes deep plate subduction. Subduction of slabs of oceanic lithosphere into the deep mantle involves a wide range of the geophysical and geochemical processes and is of major importance for the physical and chemical evolution of the Earth (Miller, Kennett, & Lister, 2004). Thus, the subduction and subduction-related volcanism are the major processes through which geochemical components are being recycled between the Earth's crust, lithosphere and mantle (Yoshioka, Torii, & Riedel, 2015). A large proportion of the world's earthquakes and volcanoes are related to the subduction (Kirby, Stein, Okal, & Rubie, 1996). Deep sea volcanism results from a range of processes including dehydration, melting and melt migration. The deepest known earthquakes occur in the subducted lithosphere at depths of 660-700 km but their cause is still not explained. In addition, the motion and velocities of the lithospheric plates at the Earth's surface are controlled largely by the buoyancy forces that drive subduction. Because of the wide variety of processes involved, subduction zones can be regarded as natural laboratories through which dynamic behaviour in the Earth's mantle can be studied.
Factors affecting plate subduction include hydrothermal factors (Yoshikawa, Okino, & Asada, 2012), buoyancy forces, rheology of mantle minerals, stabilities of hydrous minerals, partial melting, mechanisms and rates of melt migration, kinetics of phase transformations, mechanisms of deep earthquakes, geochemical recycling, and the processes of continental collision that result from subduction (Miller, Gorbatov, & Kennett, 2005). One fundamental problem concerns the depth to which subducted lithosphere penetrates into the mantle because this is related to the scale of mantle convection and the Earth's evolution.

Seafloor spreading
The seafloor spreading fabric in the Mariana Trench is obscured by the absence of magnetic anomaly lineations. Elongated topographic structures accompanied by plate  (Zhang, Lin, & Zhan, 2014).
The Japanese Lineation set is a Mesozoic magnetic anomaly lineation, it exists in the East Mariana Basin, east of the Mariana Trench (Nakanishi, Tamaki, & Kobayashi, 1992), which means that the subducting plate along the southern part of the Mariana Trench is a part of the Pacific plate formed in the Mesozoic. Other remarkable topographic feature of the Mariana Trench includes a set of many elongated ridges and escarpments accompanied by the plate bending on the outer slopes with two existing distinct strikes for these structures. The elongated structures have two strikes: N85°E and the same as the trench axis; N70°E. Most bending-related structures except those near the trench axis, were formed by the reactivation of the seafloor spreading fabric.
The presence of cracks is another distinguished geological feature of the Mariana Trench (Ogawa, Kobayashi, Hotta, & Fujioka, 1997). Mariana Trench has many open prominent cracks on its surface, up to a few meters deep and a few hundred meters long on the diatomaceous clayey sediment surfaces of its oceanward slopes. The shape of the cross-section is Y-shaped. More precisely, the bottom is a very narrow (1−3 km), yet in some places wide (several tens of kilometers) flattened. Electronic copy available at: https://ssrn.com/abstract=3447481

Methods and procedures
The methodological scheme includes four general steps of the statistical analysis of the morphology of the Mariana Trench: GIS processing of the geospatial data; creating crosssection profiles across the trench; converting coordinates to the UTM; reading depths of the observation points into the attribute table; Statistical analysis of data distribution: calculation and visualisation for regression analysis, histograms, boxplots with outliers, theoretical and sample quantiles (QQ); Comparative geospatial analysis by four tectonic plates: categorywise compositional bar charts on the depths distribution in observation points; multi-dimensional strip plots by four tectonic plates on maximal depth values, slope angle steepness, closeness of the igneous volcanic zones and thickness of the sediment layer; Clustering (by k-means method), correlation ellipses, data partition, grouping and sorting.
Here the geospatial analysis aims to extract a more regular impact factors of the geologic morphology development; whereas the cluster analysis and computing correlation matrices extracts the groups and classes in a total cloud of observation points. Statistical analysis has been performed by means of R (Borradaile, 2003). The R scripting is composed of separate written codes and an algorithm for data processing.
The R codes presented below generate a call for various statistical formulae and algorithms used by the machine for the data processing.

Data collection for the GIS project
The GIS part of the research is performed in the QGIS (Figure 1). Using QGIS plugins several complex tasks were separated into smaller and more manageable components (e.g. reading coordinates, crossing profile lines, etc). Various geospatial data have been uploaded into the GIS to form the GIS project: bathymetric features of the trench, sediment thickness, location of igneous volcanic zones, distribution of the tectonic plates, etc. The GIS project has been projected into the UTM cartesian coordinate system (square N-55). The GIS processing part consisted in following steps. Firstly, 25 1000-km long cross-section bathymetric profiles were digitized across the trench, as illustrated on Figure 2. The geometry of the first of the 25 profiles has been digitized across the Mariana Trench manually. Then, the line has been copied and re-entered for the next 24 profiles with a distance between every two neighbour lines of 100 km. The numbering of the profiles goes consequently from the north to the south, from Nr. 1 to Nr. 25, respectively. Hence, every profile contained 518 measurement points, XY coordinates, elevation depth data and thematic geological data (e.g. thickness of the sediment layer) stored in an attribute table. The QGIS tool plugin "Lat Lon Tools" adding projected coordinated has been installed to activate QGIS option of adding x and y values directly to the Spreadsheet. The total dataset comprises of large amount of 12 950 observations. The data were then copied into a table which was used further in this work for the statistical processing. The created profiles are visualized on Figure 3.

Analysis of data distribution
The data distribution for the bathymetric profiles has been computed using existing methods of the statistical analysis (Swan & Sandilands, 1995) using R programming language.

Histograms
The histogram plots ( Figure 4) show normal distribution of the depth observation data by the bathymetric crosssection profiles, as well as their outliers, skewness, median, mean, average, maximal, minimal and quartile distribution values. For each of 25 bathymetric profile various colours are taken for the following statistical data of depth values along the profile: "black" curves stands for normal distribution, "blue" curves -for density distribution. Vertical dashed lines: "purple" -median values, "green"mean values. The histograms have been drawn using R library{ggplot2}. On the first step a single histogram for each of bathymetric 25 profiles was created.

Regression analysis
To estimate the relationships between variables a regression analysis has been done using existing methods (Journel, 2000). Regression analysis and facetted plot wrapping for 25 bathymetric profiles were executed by R library {ggplot2}. Using non-parametric regression analysis the conditional expectation of the dependent variable (that is depth values) given the independent variables was estimated ( Figure 5). The confidence interval for each of 25 profiles has been done by four methods, visualized by the facetted plot wrapping for the series data comparison.
The regression analysis reveals how the typical value of the criterion variable changes when any one of the independent variables change, while the other independent variables are fixed. The formula describing regression equation describing the relationship between two variables used in this research is as follows: (1) The literature refers (Journel, 2000) to three major applications of the regression analysis including general loess method ("glm"), loess method ("lm") and loess method ("loess"), all of which were tested in this research.

Comparative geospatial analysis by four tectonic plates
Mariana Trench crosses four tectonic plates: Mariana, Philippine, Pacific and Caroline. Therefore, a comparative analysis of multidimensional data was performed to analyse interrelationships between the geographic location of the specific parts of the trench and factors that may impact changes in the geomorphic systems. Using existing methodology (Bretz, Hothorn, & Westfall, 2011), various dependences between the impact factors were tested in the current research by various approaches of the comparative analysis: Figures 7, 8 and 9.
First, the distribution of various environmental factors affecting the morphology of the trench were analysed: slope angle, sedimental thickness, depth and closeness of the igneous volcanic zones to the selected bathymetric profiles (Figure 7). Second, the changes in the trench deepest angle, calculated as tg(A/H), where A is the width, and H is the maximal depth of the profile, were calculated for each of the 25 bathymetric profiles and compared, respectively ( Figure 8).
Third, the depth distribution by four tectonics plates was visualized using multiple scatter function of R (Figure 9). A pairwise correlation of the environmental factors was performed by the scripting approach of R, which is convenient not only for looping over parts of the geomorphic model of the Mariana Trench, but also for pairwise iterating over bathymetric and geomorphic variables for the comparative analysis. Called functions "geom_smooth", "geom_point" and "geom_quantile" were used to draw smoothed conditional means and to perform regression analysis.

Multiple panels, divided by categories
The variation of the slope angle in the deepest point and depths by 25 bathymetric profiles of the Mariana Trench according to four tectonic plates that is crosses is illustrated on Figure 8 and Figure 9. The plots have been created using R code in 4 steps: # step-1. Creating data frame in R from the initial table (.csv) MDepths <-read.csv("DepthTect.csv", header=TRUE, sep = ", ") MDFl <-na.omit(MDepths) # delete possible NA values row.has.na <-apply(MDFl, 1, function(x){any(is.na(x))}) # check up NA values sum(row.has.na) # sum up NA values, receive: [1] 0 head(MDFl) # look up data frame.

Clustering (k-means method), correlation and data grouping
The next working step included finding correlations among the geomorphic factors that impact the morphological formation of the profiles. To this end, cluster analysis and correlation ellipses were created.

Clustering (k-means method) by R library{factoextra}
The k-means clustering, a machine learning technique for classification performs data partition into set up number of clusters, has been done using R library{factoextra}. The goal of the k-means clustering was to perform partition of the dataset of the observations across Mariana Trench into clusters, in which each depth observation belongs to the cluster with the nearest mean, serving as a prototype of the cluster. The performed clustering is sensitive to the initial random selection of the cluster centers. Therefore, several clusters has been tested: starting from 2 to 7. This Figure 18. Correlation ellipses and numerical correlation of the factors affecting Mariana Trench geomorphology function provides a solution using a hybrid approach by combining the hierarchical clustering and the k-means methods.
The workflow procedure include following steps: 1. Computed hierarchical clustering and cutting the tree in the k-clusters using R code (provided below); 2. Computed pairwise standard scatter plot of k-means cluster correlation (Figure 14).
3. Computed centres (2 to 7 were tested, in total 6 centres) of each cluster ( Figure 15); 5. Created correlation matrix (Figure 16). 6. Created groups have been tested according to their distributions by the tectonic plates ( Figure 17).
The K-means cluster analysis has been performed using set of cluster centres as the initial cluster centres. The algorithm worked iteratively to assign each profile to one of the groups (2 to 7) based on the morphometric features of the Mariana Trench across these profiles that were clustered based on their geomorphic feature similarity. The results of the k-means clustering are shown on the Figure 14 and Figure 15, the correlation matrix -on the Figure 16. The pairwise standard scatter plot of k-means cluster correlation distributed by four tectonic plates is shown on Figure 17.
The advantages of the k-means clustering applied for Mariana Trench consists in the algorithm nature: rather than defining groups before looking at the data, clustering enabled to find and analyse the groups in the profiles that have formed organically. As the structure of the tectonics and trench geomorphic properties are rather complex, clustering facilitated data partition and grouping. Figure 19. Normalized steepness angle (left); level plot of the sedimental thickness (right)

Discussion of GIS and R compatibility
The study demonstrated that the combined use of R Programming and QGIS is effective tool for the geospatial data processing and integration with further statistical analysis using R: the plugins installed for reading the coordinates, re-projecting the coordinate systems, layout visualization and attribute data conversion into xls and csv tables were efficient enough for this research. The overlapping function enables to map and visualize crossing various layers (tectonic plates, location of the volcanic igneous areas), as well as reading coordinates and depth observation points. The methodological scheme for the presented geomorphological analysis of the Mariana Trench contained a four-step approach: 1) GIS processing, 2) statistical analysis of data distribution, 3) comparative geospatial analysis, 4) data partition through cluster analysis (including k-means method and correlation ellipses).

Findings in data distribution
Statistical analysis revealed that the major depth observation points of the Mariana Trench are located in between the -3000 and -5000 meters (Figure 3), while the maximal depths reach up to -10000 in the current dataset, as can be drawn from the Figure 10: profiles 20, 21, 22 crossing mostly Philippine tectonic plate ( Figure 12). Another significant change is the decrease of depth in profiles 23, 24, 25, crossing Caroline tectonic plate, which may explain, among other factors the depth changes. Profiles Nr. 23 and 24 demonstrate the deepest depth data range.
Conversely, bathymetric profiles from 1 to 16 have gradual decrease in absolute depths (Figure 9), which can be noted in outliers sample location. A slight increase in absolute depths of the profiles #4-8 was also observed of the Figure 8. The majority of the observation points of Figure 20. Trench steepness angles: unsorted (left); sorted and grouped (right) the mentioned above profiles crosses the Pacific tectonic plate. The changes in bathymetry may, among others be explained due to the changed environmental factors of the underlying plate. Nevertheless, sedimental thickness changes notably both within the trench by profiles (1:25) and between four tectonic plates that Mariana Trench crosses: Philippine, Pacific, Mariana and Caroline. Since the tectonic properties and attribute values of them are not identical, the comparative analysis of how the data vary across four distinctive plates was performed. As can be seen on Figure 9, right, the majority of the observation points are located in the Pacific and Philippine plate, following my Marian plate, while Caroline plate only covers a few points (red coloured, Figure 12 left).
The density distribution as shown on a combined plot ( Figure 9) enables to compare the overlapping and maximal aptitude of the density curves both for the profiles and depth data distribution by four tectonic plates. Thus, the major trend of the trench angles located on the Pacific plate has downward general line trend. The Philippine tectonic plate, on the contrary, has a minimal peak by profiles #14-21, and then moving upwards.
The highest value for Caroline. Consequently, as can be drawn from the Figure 9, Mariana plate has the highest density of depth distribution values, followed by the Philippine plate, then Pacific and Caroline, respectively. From two multiple panel by groups (Figure 7 and Figure 8) we can compare the slope angles and depth distribution by tectonic plates, respectively, one can see the unique patters of these categories by four plates.
Summaries of the variations of the local polynomial regression of the bathymetric depths of the measured samples are presented on Figure 5. Upon a close examination of these summaries it can be observed that, with a mean depth value ranging from 5000 to of 3000 on the profiles, the widths of the confidence intervals are expanding more rapidly by the profiles 12 to 15 and 19 to 22 thus indicating on the large amplitude of the depths variations in this part of the Mariana Trench. The indication is that profile depth rather being affected by the local geographic conditions caused by the location on four different tectonic plates with varying environmental conditions.
On the other hand, profiles 22 to 25 crossing Caroline tectonic plate (again refer to Figure 12, left), suggests that the absolute depth in this region change to become shallower than the profiles crossing Philippine and Pacific plates, and this phenomenon has adverse implications for deep inter-connections between these factors.

Comparative geospatial analysis by four tectonic plates
Studies revealed that several environmental factors have distinct effect on the Mariana Trench morphology. Among them, findings indicate ( Figure 7) that sediment sources at the Mariana Trench are connected with trench tectonics where the values of the sedimental thickness lie between 120 and 140, decreasing to 50 mm. Thus, sedimentation processes differ significantly by four tectonic plates (Mariana, Pacific, Philippine and Caroline), due to the overall complexity of the sediment environmental processes and trigger factors and mechanisms. Among other triggers and key factors for sedimental thickness are turbidity caused by gravity sliding, biochemical deposits, closeness of seismic zones, igneous volcanic areas and differences in the sedimentation mechanisms. Besides, due to the funnelling effect, trench sediment deposits speed is faster and therefore, thickness is greater than that of the abyssal basins.

Findings in correlation, k-means clustering and data grouping
The results of k-means algorithm show groups across all 25 profiles, with the number of groups represented by the variable. We tested several possible clusters from 2 to 7, and found out the optical number, that is 5: the cluster circle contained the optimal number of the observations and the overlapping was reasonably minimal (Figure 15 and Figure 14). The correlation matrix is presented on Figure 16 showing crossing correlations in the combination of the environmental factors. Comparison of the bi-factor in-between the factors revealed pairwise correlation (Figure 17). Pairwise comparative analysis ( Figure 13) enabled to observe a marked influence on the environmental variables as bi-factors. Thus, in response to the decreasing sedimental thickness the slope angle goes in parallel; location of the volcanic igneous areas cause a cyclic repetition of the curve for the slope angles, as well as those of igneous volcanic areas have certain correlation between the slope angle and aspect degree. Therefore, according to the findings, four environmental variable factors, namely slope angle, sedimental thickness, aspect degree and location of volcanic igneous areas, are affecting the geomorphological structure of the trench.

Findings in data partition and ranking
Analysis of the angle steepness of the cross-section profiles along Mariana Trench revealed ( Figure 19) that a bunch of bathymetric cross-section profiles form cluster groups with similar geomorphic properties divided into five groups over the study area. Thus, profiles: 21, 22, 18 and 20 have all "strong slope" tg° angle degree, which is an average of 0.05. Similarly,profiles: 15,19,16,17,14 and 2, belonging to class "very strong slope", have an tg° angle of 0.057 to 0.058 ( Figure 20). When compared with third group in the study area, such as class "extreme slope" (profiles: 1, 11, 4, 5, 10 and 13), the average slope tg° angle fluctuating from 0.060 to 0.070. The forth group is class "steep slope" (profiles: 25, 12, 6, 8 3) with a slope tg° angle values from 0.070 to 0.075. Finally, the last group is notable for the highest steepness (profiles: 9, 7, 23, 24), with average slope tg° angle degree up to 0.079. Although the slope steepness is generally related to the slab subduction in this particular area, the nature of the slope expansion in the study area may also be associated with other factors such as topography, igneous closeness of the volcanic areas, and location (Pacific, Philippine, Mariana and Caroline plates).
Close examination of the slope degree statistical change revealed (Figure 20, left) that general trend has a scope of 0.03 (approximately from 0.05 to 0.08) of the steepness of the cross-section profiles along Mariana Trench. The reclassification of the slope angles across Mariana Trench ( Figure 20, right), as well as statistical normalization have a crucial role in the analysis of the slope fluctuations. For instance, the profiles #23 and 24 that are notable for the highest slope steepness, are located on the Philippine plate ( Figure 11, right). Generally, two large classes of the normalized degree angles were observed ( Figure 19): (1) below average degree (profiles # 1, 2, 11, 14-19, 21-22) and (2) below average degree (all the rest).
The spatial characteristics of the steepness distribution across trench have also been shaped by the components of the igneous volcanic areas in various profiles, as understood from Figure 13: profiles # 20, 22, 23, 24 with notable amount of igneous volcanic observation points (over 180) correlate with steepness angle. As a result of close examination, the groups of five classes of the slope steepness within trench are selected as best suitable due to the changed geomorphic properties along the trench (Figure 20 left). The Euler-Venn diagram enabled to analyse logical factors crossing and categories affecting morphology. It shows all possible logical relationships between a collection of data sets: four tectonic plates, sedimental thickness; geometric properties of the trench (that is slope angle, aspect class, hill shade group class derived as quantitative values from the GIS); morphology; volcanic closeness and depth values. As can be noticed (Figure 21, right) the area of the shape is proportional to the number of elements it contains, which is useful for explaining complex hierarchies and overlapping definitions as the case of factors affecting trench morphology. Mariana plate crosses all other plates, yet the most logical relationship has with Pacific plate. Comparing crossings between such categories as sedimental thickness and slope angle, as well as igneous zones distribution and trench slope angle. Thus, upon analysis of all possible combinations, intersections and similarities between categories, one can see the relationship between the mentioned above factors (Figure 21, right).
Finally, the integrated use of GIS, statistical methods, R programming applied for geological data processing aimed at a multi-disciplinary approach to study spatial distribution of the impact factors affecting trench geomorphology schematically represented on Figure 22, left. The interpretation and classification of the geospatial data by R were useful for estimating impact factors and triggers of the development and structure of the geomorphological structure of trench. A visual grouping of all methods, approaches and data as a cumulated flowchart is presented on Figure 22 (right) as a word cloud created by {word-cloud} library via R.
The studies of the ocean hadal trenches based on the profiles cross-section have been undertaken in the past (for instance, Murray, 1945), yet based on the technical methods of that time. Until now, little attempts has been available on application of R programming language and scripting libraries towards studies of ocean trenches in marine geology. Deep ocean trench formation is a very complex process that is known to be influenced by a variety of geomorphological and oceanological factors. These may not adequately explain the process of trench deep formation, its further development and what is the impact in a variety of factors affecting hadal structure of the ocean trenches. An improvement of the technical tools is therefore required in such studies.
Current analysis of the Mariana Trench geomorphology and dependence of the variability of the angle steepness from affecting factors indicate that the importance of geological factors (closeness of the nearby igneous volcanic areas, location of the part os of the trench on certain tectonic plates, angle aspect and bathymetry, depth and sediment layer thickness) are highly variable. The complex tectonic and geomorphic features of the Mariana Trench has been reviewed using a set of tested 25 cross-section profiles with unique geologic conditions located in four tectonic plates that Mariana Trench crosses. Current study demonstrated the dependences between the geomorphic factors and geology (slope angles and sedimental thickness, respectively) on the profile morphology. The quantified similarities between the distributional data distances were assessed using correlation matrices and cluster analysis (k-mean method).
The similarities and differences in the geomorphic structure (steepness of the slope angle degrees), geological characteristics (sediment thickness layer), geographic location of certain tectonic plates (Mariana, Caroline, Philippine and Pacific) and bathymetry (absolute minimal depths, means and median values) exist along the trench. Large gradients in variability occur within and among norther and southern part of the trench as well as in the eastern curve of its shape directed towards Magellan and Marcus-Wake transform lines. Hence, it enable to identify that geomorphological structure of the trench is mainly dominated by the following factors: the most dominated is geological factors: the closeness of the submarine volcanic areas and location of Philippine and Mariana tectonic plates, whereas sediment thickness is mainly geomorphic dominated. Thus, as a result of the undertaken study, it has been found that the middle part of the Mariana Trench (profiles: 14 up to 17), with very strong slopes, have roughly equal proportions of sediment thickness layer, which indicates that spatial locations and distributions of the volcanic areas and slope angle of the ocean trench are closely interrelated and affect sedimental thickness. The results of the research furthermore demonstrated spatial geomorphic unevenness of the Mariana Trench. Five unique regions across the trench length have been revealed, and the impact of various environmental factors affecting they morphology and characteristics were assessed by means of the applied statistics.
A contemporary perspective of R based geostatistical methods for the analysis of trench structure and formation is demonstrated in this research. The application of the statistical tools provided by functionality of R programming offer optimal prospects for better understanding of the bathymetry of the deep ocean trenches with a case study of Mariana Trench. A rigorous and quantitative quantitative data analysis performed by R and supported by GIS geospatial analysis methods is effective tool for Electronic copy available at: https://ssrn.com/abstract=3447481 investigation of such complex and large-scale geologic structures as deep ocean trenches. This paper demonstrated an example of such cross-disciplinary quantitative approach for geomorphological analysis. Through example of the presented research the powerful tool of the R scripting approach was shown. Using R for marine geoscience research does not only make geological modelling simpler and less error-prone. It may also facilitate more complex simulations involving, for instance, multi-dimensional modelling runs with varying geological parameters. It is also possible to apply the developed methods for extending testing of other deep ocean trenches.
Recent advances in the understanding of the hadal structure of the Mariana Trench have, so far, relied on the technologies that were unable to analyse correlations between various factors affecting its functioning and morphology. As demonstrated in this research, active using functionality of the programming languages for geoscience research provides effective tools to improve approaches to study hadal bathymetry. Development in statistical methods and using R scripting libraries in oceanographic studies make it possible to treat multi-source types of the marine geology data.
Full R codes and workflow of the statistical methods by R outlined in the current paper enable their repeatability and reuse for further testing in similar research. Hence, current paper contributed towards technical development of the quantitative and statistical methods in marine geomorphologic and oceanographic studies, in particular those aimed at the objective analysis of the complex interplay between the factors affecting ocean trench geomorphology.

Funding
The funding of this research has been provided by the China Scholarship Council (CSC) State Oceanic Administration (SOA), Marine Scholarship of China [Grant # 2016SOA002, 2016 for Doctoral (PhD) studies of Polina Lemenkova.

Author contributions
All part of the research has been performed by the author (Polina Lemenkova): GIS data capture, processing and mapping, statistical analysis, programming on R language, plotting and visualizing graphs, writing text.

Disclosure statement
There is no competing financial, professional, or personal interests from other parties.