ALBERT

Notes: New oceanic crust is being formed along active segments of the global mid-ocean ridge (MOR) system. The presence of an axial magma chamber and associated zones of partial melt and hydrothermal activity located up to several kilometres beneath the seafloor is central to almost all recently proposed theories of crustal formation. Seismic images of the top few kilometres beneath the fast spreading East Pacific Rise (EPR) have already been obtained. Reflection profiles place strong constraints on the geometry of the axial magma chamber but refraction data provide only coarse estimates of the subsurface temperature, distribution of partial melt and porosity, parameters required to distinguish between the proposed petrological models. Electrical conductivity is directly related to all these critical parameters and therefore electromagnetic experiments should be designed to help characterize the ridge environment.We determine the magnetic field B(t) on the seafloor caused by a sudden change in current in a 2-D electric dipole aligned perpendicular to the strike of the ridge. The finite element technique is used to solve the governing differential equation numerically in the Laplace s-domain. The transformation to the time domain is by the Gaver-Stehfest method. We show that the extraction of two basic parameters from the response curve Ḃ(t) can provide sufficient information to identify the more important features of the petrology. The parameters are the response amplitude Ḃmax, which is the maximum derivative of δtB(t), and the diffusion time γT, the time at which this maximum occurs. The behaviour of γ as a function of distance from the source is analogous to that of first arrival time in refraction seismology. The value of γ is a weighted integral of the conductivity along the most resistive path between the source and the receiver.A highly conductive, partially molten magma chamber beneath the ridge axis slows the rate of diffusion of electromagnetic fields across the ridge, increasing γ but also reducing Ḃmax at sites on the side of the ridge opposite the transmitter. A melt lens ponding as a thin layer on top of the chamber increases Ḃmax at the ridge crest and increases γ at sites on the far side. Hydrothermal fluid circulation in the uppermost 2 km of the crust reduces Ḃmax everywhere across the ridge but increases γ only at sites within 0–3 km of the ridge crest. Electromagnetic energy in this case can reach the more distant points via paths which by-pass the fluids.Inferences made from the results of 2-D modelling indicate that a practical experiment would require a 104 A m horizontal electric dipole (HED) transmitter located 5 km off-axis and receivers with a sensitivity of at least 1 pT s−1 over a time window up to 10 s.

Notes: Marine controlled-source electromagnetic experiments are designed to measure the electrical conductivity of the sea-floor. The apparatus consists of a transmitter, typically an electric current dipole, and a series of remote receivers. Variations in the current through the dipole cause correlated variations in the electric and magnetic fields at the receivers. The signals contain information about the electrical conductivity of the crustal rocks. Electrical conductivity is related to such critical physical parameters as porosity, temperature, composition, fluid content and texture.

Notes: A 2-D electromagnetic inverse problem relevant for geophysical exploration is considered. an exact theory is described which proves Fréchet differentiability of the data and the existence of optimal, or best-fitting, solutions. the earth is represented by a 2-D electrical conductivity structure with a known, horizontal strike direction and the data are surface measurements of electric field due to telluric earth currents flowing along-strike. First, the TE-mode equations governing the forward problem are cast in variational form. It is then shown that there exists at least one admissible conductivity that minimizes the discrepancy between the observations and variational solutions to the forward problem. Admissible conductivities are drawn from any compact subset of the class of bounded, positive functions. Standard techniques from elliptic partial differential equations, non-linear functional analysis and optimization play key roles in establishing the result. In particular, the Lax-Milgram lemma assures that a unique solution to the forward problem exists. an implicit function theorem approach is used to establish the regularity of the mapping from the conductivity to the data. the existence of optimal models follows from the well-known fact that a continuous functional attains its minimum when varied over a compact set. Previously, Fréchet differentiability and existence theories for geo-electromagnetic inverse problems have been limited to induction in 1-D media. However, characterization of the optimal models in two dimensions, analogous to Parker's D+ conductivity models in one dimension, is impeded by the lack of closed-form solutions to the forward problem.