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Interpretation of ship-track magnetic data near Narcondam and Barren Island volcanoes revisited

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Abstract

We interpret the legacy ship-track magnetic and bathymetric profile data to investigate the role of the lithospheric scale West Andaman Fault (WAF) in the dormant Narcondam and active Barren Island volcanoes. We use data-based automated interpretation of total magnetic intensity (TMI) profiles using a contact model in order to delineate geometrical and physical parameters of several faults including the WAF and then investigate its implications in recent volcanism at the Barren Island. Our data-based interpretation of TMI data requires transformation of it into the first order analytical signal and tilt angle, which in turn, requires estimation of the first order horizontal and vertical derivatives of TMI data. We ensure robust estimation of the first order horizontal and vertical derivatives using Savitzky–Golay derivative filter and Hilbert–Noda transformation, respectively. We have identified several anomaly segments of the TMI anomaly profiles and used data-based quantitative interpretation in each segments with a contact model. We then make a comprehensive interpretation using bathymetry, geological setup and the results from quantitative data-based interpretation of magnetic data, and ascertain possible role of the WAF in Barren Island volcanism.

Research highlights

  • Quantitative data based interpretation of magnetic profiles across Narcondam and Barren Island seamounts.

  • Quantitative data based interpretation is based on analytical signal and tilt angle based transformation of magnetic data and modelling with a contact model.

  • Architectural settings of the West Andaman Fault are delineated and its implication in recent Barren Island volcanism is discussed.

  • A transpression signature of the West Andaman Fault near Barren Island volcano is identified.

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Acknowledgements

The author would like to thank both the anonymous reviewers for their illuminated reviews which help in improving the manuscript substantially. The current research is supported by Spaceage Geoconsulting, a research oriented consulting firm.

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Authors and Affiliations

Authors

Contributions

The principal author has contributed entirely in the paper that includes conceptualization, data processing, data modelling, interpretation and also preparation of the manuscript.

Corresponding author

Correspondence to Indrajit G Roy.

Additional information

Communicated by N V Chalapathi Rao

Appendix A: Formulation

Appendix A: Formulation

The horizontal and vertical gradients of the measured TMI response on the datum surface due to a buried contact model (figure A1), according to (Nabighian 1972; Roy 2013), are given as:

$$\begin{aligned} T_{x} (x) &= 2\,\kappa \,F \eta \, \sin \theta \, \frac{h \cos \phi + (x - x_{c}) \sin \phi }{h^2 + (x - x_{c})^2} , \end{aligned}$$
(A1)
$$\begin{aligned} T_{z} (x) &= 2\,\kappa \,F \eta \, \sin \theta \, \frac{(x - x_{c}) \cos \phi - h \sin \phi }{h^2 + (x - x_{c})^2} , \end{aligned}$$
(A2)

where \(T_{x}\) and \(T_{z}\) are the horizontal and vertical gradients, \(x_{c}\) is the horizontal location of the contact from the origin, \(\kappa \) is magnetic susceptibility contrast measured in SI unit, F is the geomagnetic field intensity, measured in nT. The product of magnetic susceptibility contrast \(\kappa \) and the field intensity F can be replaced with the magnetization \(J_{t}\), where is the total magnetization due to induced and remanent magnetization of the oceanic crust. It then turns out as

$$\begin{aligned} T_{x} (x) &= 2\,J_t \eta \, \sin \theta \, \frac{h \cos \phi + (x - x_{c}) \sin \phi }{h^2 + (x - x_{c})^2} , \end{aligned}$$
(A3)
$$\begin{aligned} T_{z} (x) &= 2\,J_t \eta \, \sin \theta \, \frac{(x - x_{c}) \cos \phi - h \sin \phi }{h^2 + (x - x_{c})^2} , \end{aligned}$$
(A4)

with

$$\begin{aligned} \eta &= 1 - \cos ^2 I \sin ^2 \alpha , \end{aligned}$$
(A5)
$$\begin{aligned} \phi &= 2\beta - \theta - 90^{\circ } , \end{aligned}$$
(A6)
$$\begin{aligned} \tan \beta &= \frac{\tan I}{\cos \alpha } , \end{aligned}$$
(A7)

where I is the inclination of geomagnetic field at a place and \(\alpha \) is the angle between magnetic north and the profile. From equation (A5), it can be said that \(0 < \eta \le 1\), where \(\eta \) takes on the maximum value 1 either at the geomagnetic pole or equator with \(\alpha = 0\). Please note firstly that the magnetization is normally expressed in terms of A/m while the TMI anomaly is measured in terms of nT, the conversion factor from nT to A/m being \(1\,\text {nT} = 0.7974 \times 10^{-3}\,\text {A/m}\), and secondly the magnetization \(J_t\) used in the formulas imply magnetization contrast instead of magnetization of individual rock type. With the conversion, as mentioned, the unit for horizontal and vertical gradients becomes \(\text {A/m}^2\). The close form formulae for the first order analytical signal and tilt angle are given as:

$$\begin{aligned} \mathcal {A}(x) = \frac{2\,J_{t}\,\eta \, \sin \theta }{\left[ h^2 + (x - x_{c})^2 \right] ^{1/2}} , \end{aligned}$$
(A8)

and

$$\begin{aligned} \delta (x) = \arctan \left[ \frac{(x - x_{c}) \cos \phi - h \sin \phi }{| (x - x_{c}) \sin \phi + h \cos \phi \, |} \right] , \end{aligned}$$
(A9)

where \(|\cdot |\) denotes the absolute value ensuring that the denominator of equation (A9) remains positive valued so that the TA lies between \(- 90^{\circ }\) and \(90^{\circ }\). Clearly from equation (A8) one finds that the first order analytical signal would attain peak maximum at \(x = x_{c}\). Following are the cases that hold.

Figure A1
figure 5

Schematic plot of a buried contact model and the total magnetic intensity (TMI) response.

Case 1: At the trace or edge of a contact, i.e., \(x = x_{c}\)

$$\begin{aligned} \mathcal {A}(x)\Big |_{x\,=\,x_{c}} = \frac{2\,J_{t}\,\eta \,\sin \theta }{h} . \end{aligned}$$
(A10)

From equations (A8 and A10), it is clear that the response of the first order analytic signal is symmetric and it attains a peak at the trace of the contact. Further, from equations (A6 and A9) with a little algebraic manipulation we write

$$\begin{aligned} \delta (x)\Big |_{x\,=\,x_{c}} = 90^{\circ } + ( \theta - 2\beta ). \end{aligned}$$
(A11)

Case 2: When TA attains zero value then using equations (A6 and A9), we write

$$\begin{aligned} x_{c} - x_{0} = h\,\cot (\theta - 2\,\beta ). \end{aligned}$$
(A12)

where \(x_{0}\) is the position corresponds to the zero value of the TA. Therefore, once \(x_{c}\) is determined from the position of the peak of \(\mathcal {A}(x)\) response the dip of the contact \(\theta \) can be determined using equations (A7 and A11), as the value of inclination I and azimuth \(\alpha \) are known. Further, on delineating the position of zero value \(x_{0}\) of TA the depth of burial of the contact can be easily determined and using equations (A7 and A12). The amplitude of magnetization \(J_{t}\) is readily determined from equation (A10) once all other parameters are either determined or known a priori.

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Roy, I.G. Interpretation of ship-track magnetic data near Narcondam and Barren Island volcanoes revisited. J Earth Syst Sci 130, 1 (2021). https://doi.org/10.1007/s12040-020-01500-2

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  • DOI: https://doi.org/10.1007/s12040-020-01500-2

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