Two-dimensional modelling of a towed transient magnetic dipole-dipole sea floor EM system
Article Sidebar
Main Article Content
Abstract
The discovery of massive sulphide deposits along mid-ocean ridges has prompted the development of towed sea floor electromagnetic mapping tools. One suitable configuration of transmitter and receiver is the in-line, coaxial, magnetic dipole-dipole. The step response of this system to a double half-space model has two distinct parts. The position in time of the initial event is indicative of the conductivity of the sea floor. A reduction in dimensionality greatly simplifies the analytic and numerical computation of more complicated cases. The transmitter is reduced to a pair of horizontal line sources carrying equal but opposite currents and separated by a small vertical distance. The transient responses of the simplified system and the coaxial system to the double half-space model are remarkably similar, even though the electromagnetic mode characterised by vertical current flow is excluded by the simplification. The analytic form of the sensitivity function enables a simple expression for a depth of investigation beneath the sea floor to be derived as a function of time. The magnetic effects of currents impressed in a two-dimensional conductive target embedded in the sea floor by a horizontal magnetic point dipole transmitter may be represented approximately by a system of vortex currents only. Since vortex current flow is the type of current flow induced in a two-dimensional target by a two-dimensional magnetic source, the principal characteristics of the three-dimensional problem can be studied by two-dimensional modelling. The scattered fields from a thin conductive dike and a thin conductive sill are evaluated by setting up and solving a boundary element integral equation in the electric field. Transient response curves are presented for a limited range of models. The sea floor conductivity is fixed at 1/30 that of seawater, a typical value for recent basalt. The array size and plate depth extent are fixed at 100 m and 25 m, respectively, while the depth of burial is allowed to vary from 4 m to 25 m. The ratio of the inductive response parameter of the plate to the response parameter of the crust, which determines the degree of influence of the plate conductor on the combined step response, is varied from 0.4 to 10. Increasing the relative effect of the target delays the onset and decreases the gradient of the initial part of the response. Pronounced minima in the response as a function of array location are observed when either the transmitter or the receiver cross over the target. The minimum field over a wide range of times is close to zero for a shallow dike due to the combined shielding effect of the dike and the seawater. The shallow dike may be distinguished from a shallow sill by the shape of the minima.
ARK: https://n2t.net/ark:/88439/y079019
Permalink: https://geophysicsjournal.com/article/123
Article Details
Authors who publish with this journal as of Vol. 63 agree to the following terms:
a. Authors share the copyright with this journal in equal parts (50% to the journal, 50% to the lead author), and grant the journal right of first publication, with the work after publication simultaneously licensed under Creative Commons Attribution License CC BY-NC-ND 4.0 that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this journal.
b. Authors may enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgment of its initial publication in this journal, and a reference to this copyright notice.
c. Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) during the submission process, as this can lead to productive exchanges and earlier and greater citation of published work and better sales of the copyright.
Author Self-archiving
Authors retain copyright and grant the Journal of Geophysics right of first publication, with the work three years after publication simultaneously licensed under the Creative Commons BY-NC-ND 4.0 License that allows others to share the work (with an acknowledgment of the work's authorship and initial publication in this journal), except for commercial purposes and for creating derivatives.
Authors can enter into separate, additional, but non-commercial contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository, but not publish it in a book), with an acknowledgment of its initial publication in this journal.
Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) before and during the submission process, as that can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
Additional Notes
This journal is one of a handful of scholarly journals that publish original scientific works under CC BY-NC-ND 4.0 - the only Creative Commons license affording the authors' intellectual property absolute worldwide protection.
Journal of Geophysics is published under the scholar-publishers model, meaning authors do not surrender their copyright to us. Instead, and unlike corporate publishers like Elsevier or Springer Nature that resell copyright to third-parties for up to $80,000 (per paper, per transaction!), the Journal of Geophysics authors share copyright equally with this journal.
Therefore, all the proceeds from reselling copyright to third parties get shared to equal parts (50% to the journal, 50% to the lead author). Under the Berne Convention, this protection is an inheritable right that lasts for as long as the rightsholder lives + 50 years.
By submitting to this journal, the lead author, on behalf of all co-authors, grants permission to this journal to represent all co-authors in negotiating copyright sales and collecting proceeds. The lead author should negotiate with his/her co-authors the modalities of distributing the lead author's portion of the proceeds. Usually, this is per pre-agreed percentage of each co-author's contribution to creating the copyrighted work. (more...)
References
Chave, A.D. (1983) Numerical integration of related Hankel transforms by quadrature and continued fraction expansion. Geophysics 48:1671-1686
Chave, A.D. (1984) The Frechet derivatives of electromagnetic induction. J. Geophys. Res. 89:3373-3380
Cheesman, S.J., Edwards, R.N., Chave, A.D. (1987) On the theory of sea floor conductivity mapping using transient EM systems. Geophysics 52:204-217
Davis, B., Martin, B. (1979) Numerical inversion of the Laplace transform: a survey and comparison of methods. J. Comp. Phys. 33:1-32
Edwards, R.N., Chave, A.D. (1986) On the theory of a transient electric dipole-dipole method for mapping the conductivity of the sea floor. Geophysics 51:984-987
Erdelyi, A., Magnus, W., Oberhettinger, F.G., Tricomi, F.G. (1954) Tables of integral transforms 1. McGraw-Hill, New York
Francheteau, J.H., Needham, H.D., Choukroune, P., Juteau, T., Seguret, M., Ballard, R.D., Fox, P.J., Normark, W., Carranza, A., Cordoba, D., Guerrero, J., Rangin, C., Bougault, H., Cambon, P., Hekinian, R. (1979) Massive deep-sea sulphide ore deposits discovered on the East Pacific Rise. Nature 277:523-528
Fullagar, P.K., Oldenburg, D.W. (1984) Inversion of horizontal loop electromagnetic frequency soundings. Geophysics 49:150-164
Hekinian, R., Fevrier, M., Bischoff, J.C., Picot, P., Shanks, W.C. (1980) Sulfur deposits from the East Pacific Rise near 21° N. Science 207:1433-1444
Inan, A.S., Fraser-Smith, A.C., Villard, Jr., O.G. (1986) ULF/ELF electromagnetic fields generated along the sea floor interface by a straight current source of infinite length. Radio Sci. 21:409-420
Knight, J.H., Raiche, A.P. (1982) Transient electromagnetic calculations using the Gaver-Stehfest algorithm. Geophysics 47:47-50
Koski, R.A., Normark, W.R., Morton, J.L. (1985) Massive sulfide deposits on the southern Juan de Fuca ridge: results of investigations in the USGS study area, 980-83. Marine Mining 5:147-164
Luke, Y.L. (1962) Integrals of Bessel functions. McGraw-Hill Book Co., New York
MalahofT, A. (1982) A comparison of the massive submarine polymetallic sulfides of the Galapagos Rift with some continental deposits. Marine Tech. Soc. J. 16:39-45
Normark, W.R., Morton, J.C., Koski, R.A., Clague, D.A., Delaney, J.R. (1983) Active hydrothermal vents and sulfide deposits on the southern Juan de Fuca ridge. Geology 11:158-163
Parker, R.L. (1977) The Frechet derivative for the one-dimensional electromagnetic induction problem. Geophys. J.R. Astron. Soc. 49:543-547
Rona, P.A. (1985) Hydrothermal mineralization at slow-spreading centers: Red Sea, Atlantic Ocean, and Indian Ocean. Marine Mining 5:117-146
Stehfest, H. (1970) Algorithm 368, numerical inversion of Laplace transforms. Commun. ACM 13:47-49
Tivey, M.K., Delaney, J.R. (1985) Sulfide deposits from the Endeavour segment of the Juan de Fuca ridge. Marine Mining 6:165-180
Wait, J. R. (1953) The fields of a line source of current over a stratified conductor. Appl. Sci. Res. 83:279-292
Wait, J.R. (1962) Theory of magnetotelluric fields. J. Res. NBS. Rad. Prop., 66D 5:509-541
Wolfgram, P.A., Edwards, R.N., Law, L.K., Bone, M.N. (1986) Polymetallic sulfide exploration on the deep sea floor: the feasibility of the Mini-Moses technique. Geophysics 51:1808-1818