Comparing Depth Values of GEBCO Bathymetry and

Comparing Depth Values of GEBCO Bathymetry and Wavelet Tomography Results in the Challenger Deep Point of Marianna Trench and Surroundings Fikret Doğru1, Oya Pamukçu2, Ayça Çırmık3,*

Abstract The deepest point of the world, Marianna Trench, is formed as a result of the thrusting Pacific Plate to the Philippines Plate. Mariana Trench stretches for more than 2,540 km with a mean width of 69 km. The greatest depths are reached in Challenger Deep (~11 km), a smaller steep-walled valley on the floor of the main trench southwest of Guam. In this study, depth values which are obtained from the General Bathymetric Chart of the Oceans (GEBCO) and by applying wavelet tomography to the World Gravity Map (WGM2012) Complete Spherical Isostatic gravity anomaly were compared. The most important convenience of the Wavelet Tomography method is that it does not require any inversion technique. As a result, the deepest point of the GEBCO data was obtained 10.8 km. The result of the wavelet tomography again reached a depth value of about 11 km. In addition, profiles were taken from different places for comparison and values were examined. In this study, it is seen that WGM2012 data will be informed about the basolateral fundus by applying wavelet tomography method. In this study, it is seen that WGM2012 data will have knowledge about base topography by applying Wavelet Tomography method. Keywords: Marianna Trench, Wavelet Tomography, GEBCO, WGM2012, Challenger Deep.

1. INTRODUCTION The Mariana Trench is an actively opening basin that lies at the eastern edge of the Philippine Sea plate. It is bounded by the West Mariana Ridge and the Mariana island arc (an active volcanic arc). The deepest part of Marianna Trench, the Challenger Deep, lies in the Southern Mariana Trench almost 360 km southwest of Guam Island and 2700 km south of the Japanese Islands [1], [2]. The location map is shown in the Fig. 1.

Fikret Doğru, [email protected], Ataturk University, Oltu Earth Sciences Faculty, Geophysical Engineering, 25400, Oltu, Erzurum 1

Oya Pamukçu, [email protected], Dokuz Eylul University, Engineering Faculty, Geophysical Engıneering, 35400, Buca, Izmir 2

Corresponding author: Ayça Çırmık, [email protected], Dokuz Eylul University, Engineering Faculty, Geophysical Engıneering, 35400, Buca, Izmir 3,*

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ICENS 4th International Conference on Engineering and Natural Science, 2-6 May 2018, Kiev, Ukraine

Figure 1. The location map of the study area (The figure exported from Google Earth Pro [3]).

The World Gravity Map (WGM 2012) which were compiled by the Bureau Gravimetrique International (BGI) with the support of the United Nations Educational Scientific and Cultural Organization (UNESCO) in association with the International Gravity Field Services (IFGS), computed from the Earth Spherical Model (EGM 2008) [4] instead of the conventional Bouguer slab correction and have a spatial resolution of ∼9 km [5], [6]. General Bathymetric Chart of the Ocean (GEBCO) [7] that has 30 arc-second resolution was generated by combining ship depth soundings, with the interpolation between the sounding points being guided by satellite gravity data [8]. GEBCO bathymetry mostly relied upon ship soundings and only 6.5% of all 30 arc-second depth cells are constrained by soundings, with the rest being indirectly mapped using some interpolation scheme [8]. Wavelet transform and its multi-scale tomography application have been used to localize the buried magnetic structures, to determine the depth of hydrothermal systems on self-potential data, edge detection signal processing [9], [10], [11], [12].

2. METHODS 2.1. Wavelet Transform The wavelet transform has contributed significantly to the study of many processes/signals in almost all areas of earth science. Different applications of wavelet transform have also shown its important role while dealing the complex behaviour of real geophysical data. Wavelet transform can be given following formula; 𝜓(𝑎, 𝜏)(𝑡) =

1 √𝑎

𝑡−τ 𝜓( ) 𝑎

(𝑎, τ ∈ R

a > 0)

(1)

where a is the dilation factor, τ is the translation factor and ψ(a,τ)(t), is the mother wavelet depending on parameters a and τ [13]. In the wavelet transform, instead of holding constant time and frequency resolutions, both can be used as a variable to obtain multi-resolution analysis in the time-frequency domain. Thus, increases in the frequency show improvement in time resolution. Likewise, decreases in frequency show improvement in the frequency resolution. 2.2. Continuous Wavelet Transform (CWT) The continuous wavelet transform was developed as an alternative approach to the short time Fourier transform (STFT) to overcome the resolution problem. The wavelet analysis is done in a similar way to the STFT analysis, in the sense that the signal is multiplied with a function, similar to the window function in the STFT, and the transform is computed separately for different segments of the time-domain signal. However, there are two main differences between the STFT and the CWT: 1. The Fourier transforms of the windowed signals are not taken, and therefore single peak will be seen corresponding to a sinusoid, i.e., negative frequencies are not computed. 2. The width of the window is changed as the transform is computed for every single spectral component, which is probably the most significant characteristic of the wavelet transform.

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Comparing Depth Values of GEBCO Bathymetry and Wavelet Tomography Results in the Challenger Deep Point of Marianna Trench and Surroundings, Fikret Doğru, Oya Pamukçu, Ayça Çırmık The continuous wavelet transform is defined as follows: 𝜓 𝜓 𝐶𝑊𝑇𝑥 (𝜏, 𝑠) = 𝛹𝑥 (𝜏, 𝑠) =

1

𝑡−τ ∫ 𝑥(𝑡) 𝜓 ∗ ( ) 𝑠 √𝑠

(2)

the transformed signal is a function of two variables, tau (τ) and s, the translation and scale parameters, 𝜓 respectively.𝛹𝑥 (𝜏, 𝑠) is the transforming function, and it is called the mother wavelet [14]. 2.3. Multi-Scale Wavelet Tomography (MSWT) In this study, complex Gaussian wavelet (cgau1) was used for estimation of the buried structure. Then wavelet modulus was calculated following formula: 𝑚𝑜𝑑 = √𝑟𝑒𝑒𝑙(𝑐𝑜𝑒𝑓(𝑐𝑤𝑡))2 + 𝑖𝑚𝑎𝑔(𝑐𝑜𝑒𝑓(𝑐𝑤𝑡))2

(3)

where reel and imag are reel and imaginer parts of the continuous wavelet transform. Local maximums were determined from coefficients of CWT. In addition, derivative of anomaly was calculated and then CWT was applied on this anomaly.

3. RESULTS In this study, WGM2012 Isostatic Bouguer Gravity (IBG) anomaly was used in the wavelet tomography application for determining the deepest point in the Marianna Trench. For this purpose, the wavelet tomography was applied on profiles that were taken from IBG anomaly and vertical derivative was applied on profiles then the wavelet tomography was carried out on these profiles. The results were compared with the GEBCO bathymetry data. In figure 2, Isostatic Bouguer Gravity anomaly and GEBCO bathymetry map are shown. The values changes -240 to 120 mGal in the Bouguer anomaly. The bathymetry values changes between -10804 to 263 meter in the GEBCO data (Fig 2a and 2b). The lowest anomaly values are on the collision boundary of the Pacific and Philippines Plates. Also the deepest point in this area is located in this collision boundary.

Figure 2. a) Isostatic Bouguer Gravity Anomaly, b) GEBCO bathymetry map.

In the wavelet tomography stage, three profiles were taken for comparison of depth values of GEBCO and obtained from wavelet tomography (Fig. 3). First profile, A-A', was taken from the deepest point ever known on earth, the Challenger Deep point. Then wavelet tomography applied on this profile and ~ 11km depth value was obtained. The deepest point in the GEBCO bathymetry data is 10.804 meter. Then, the other two profiles, B-B' and C-C', were taken and the same method was applied to these profiles. The wavelet tomography result of profile 1 shows that there is no solution but 11km depth value was obtained after the taken vertical derivative of profile 1. On the other hand, the wavelet tomography results of profiles 2 and 3 were almost obtained two times more than known. But vertical derivative improved the solutions of profile 2 and 3. The results are also shown in table 1.

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ICENS 4th International Conference on Engineering and Natural Science, 2-6 May 2018, Kiev, Ukraine

Figure 3. Profiles are shown in IBG anomaly.

Table 1. The comparison of the GEBCO bathymetry and the wavelet tomography results with and without derivative.

The Wavelet Tomograpy Results GEBCO (m)

Without Derivative (m)

With derivative (m)

Half of Without Derivative (m)

Profile 1

10804

-

11000

-

Profile 2

7700

15060

7320

7530

Profile 3

8463

16900

8290

8450

CONCLUSIONS In this study, wavelet tomography was applied to the profiles which were taken from Marianna Trench that was the deepest point in the world. Also obtained depth values from wavelet tomography were compared with the GEBCO bathymetry data. The results show there is not so much difference (not more than 380 meters) between GEBCO and wavelet tomography results (with derivative). The results also show that wavelet tomography without derivative gave 2 times more depth values than known from GEBCO. Half of the results are much closer the known values. The most important feature of wavelet tomography method is that it does not require a model such as a cylinder, sphere, etc. and without inversion technique to estimate depth value.

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Comparing Depth Values of GEBCO Bathymetry and Wavelet Tomography Results in the Challenger Deep Point of Marianna Trench and Surroundings, Fikret Doğru, Oya Pamukçu, Ayça Çırmık [4]. N.K., Pavlis, S.A., Holmes, S.C., Kenyon and J.K., Factor, An earth gravitational model to degree 2160: EGM2008. EGU General Assembly, 10, 13-18, 2008. [5]. G., Balmino, N., Vales, S., Bonvalot and A., Briais, Spherical harmonic modelling to ultra-high degree of Bouguer and isostatic anomalies. Journal of Geodesy, 86(7), 499-520, 2012 [6]. S., Bonvalot, G., Balmino, A., Briais, M., Kuhn, A., Peyrefitte, N., Vales, and M., Sarrailh, World Gravity Map, 1: 50000000 map. Eds. BGI-CGMW-CNES-IRD, 2012. [7]. J.J., Becker, D.T., Sandwell, W.H.F., Smith, J., Braud, B., Binder, J., Depner and R., Ladner, Global bathymetry and elevation data at 30 arc seconds resolution: SRTM30_PLUS. Marine Geodesy, 32(4), 355-371, 2009. [8]. R.L., Fisher, M.J., Jantsch and R.L., Comer, General bathymetric chart of the oceans (GEBCO). Canadian Hydrographic Service, Ottawa, Canada, 1982. [9]. G., Saracco, F., Moreau, P.E., Mathé, D., Hermitte and J.M., Michel, Multiscale tomography of buried magnetic structures: its use in the localization and characterization of archaeological structures. Geophysical Journal International, 171(1), pp.87-103, 2007. [10]. G., Mauri, G., Williams-Jones and G., Saracco, Depth determinations of shallow hydrothermal systems by selfpotential and multi-scale wavelet tomography. Journal of Volcanology and Geothermal Research, 191(3), pp.233- 244, 2010. [11]. F., Guo, Y., Yang, B., Chen and L., Guo, A novel multi-scale edge detection technique based on wavelet analysis with application in multiphase flows. Powder Technology, 202(1), pp.171-177, 2010. [12]. E., Foufoula-Georgiou and P. Kumar, Wavelets in geophysics. Vol. 4. Academic Press, 2014 eds. [13]. S.G.A., Mallat, Theory for multiresolution signal decomposition: the wavelet representation. IEEE transactions on pattern analysis and machine intelligence, 11(7), pp.674-693, 1989. [14]. I., Daubechies, Ten lectures on wavelets. Society for industrial and applied mathematics, 1992.

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