V. S. Yakupov and S. V. Yakupov
Mining Research Institute for the Northern Territories, Siberian Division, Russian Academy of Sciences, Yakutsk
There is extensive literature on the thermal state of the deep-seated rocks of the Earth, including the papers reporting activities in the frameworks of important international projects. The ideas of temperature variation with depth, evaluated by some geoscientists as highly ambiguous [e.g., Lyubimova and Feldman, 1975], are based on the general physical concepts and indirect data. The common approach is to solve a thermal conductivity problem for a model of the crust and upper mantle, which is believed by a particular researcher to be most probable with various assumptions. A discrepancy between the calculations based on different models of the lithosphere averages 100% (of the least). Another approach is to use the variation of the electrical conductivity of rocks with depth, provided by the MTS, MVS, and other methods of electromagnetic sounding with the controlled sources of an electromagnetic field and compare it with the results of the experimental measurements of the variation of electrical conductivity with temperature and pressure. The most comprehensively developed models of a normal (standard) resistivity section, based on MTS data [Van'yan and Shilovskii, 1983; Zhamaletdinov, 1990], suggest a gradual growth of the electrical conductivity of rocks with depth with the mere variations of its gradient at the internal boundaries of the section. In this case, too, the order of conductivity uncertainty is great enough to produce differences between the models of different authors, amounting to one or two orders of magnitude. Another potential feasibility of estimating the temperature distribution in the Earth's crust is to use geophysical methods for locating temperature benchmarks - the boundaries at which a phase transition, accompanied by a change of some physical property of rocks, takes place, as some of the rock components or the interstitial solution (generally fluid) attains a phase-change temperature. Examples of these temperature benchmarks are the transformation of water to ice or to some supercritical state, the partial melting of rocks (basalt) in the asthenosphere, the transformation of ferromagnetic substances to paramagnetics as the temperature attains the Curie point, the transition of olivine to spinel, etc. The difficulty is that, for example, the temperatures of water transition to ice, or to a supercritical state [Smith, 1968], depend on the composition and concentration of substances, dissolved in it, and on pressure. Uncertainty of the same kind is encountered, for a number of reasons, in the cases of a partial melting zone in the asthenosphere and in the zone of olivine transition to spinel. In accordance with the hypothesis of the pyrolite composition of the Earth's mantle, and with the assumption of Fe/(Fe + Mg) 0.1, the temperature of this phase transition under pressure of 135 kb must be 1600o 50o C [Zharkov, 1978]. This temperature will be different in the case of any deviations of the olivine composition from the composition mentioned above. Akimoto and Fujisava  found the temperature of the phase transition of olivine to spinel at 43.8 kb to be ~1170o C. It follows that in the general case we are dealing with the temperature estimation of a particular phase transition from above or from below. Another important condition is the character of a change in the studied property of the rock during its phase transition: jumpwise, as follows from the general phase transformation theory, or the variation gradient of a given property changes with depth, as it is assumed for the upper boundary of the asthenosphere [Van'yan and Shilovskii, 1983].
The most widely used temperature benchmark is the zero isotherm based on the thickness of frozen rocks [Kalinin and Yakupov, 1989; Yakupov, 2000] and the isotherm of the Curie point of magnetite based on the depth of the bottoms of the magnetized bodies [Bulina, 1970; Volk et al., 1977a, 1977b]. A contact between thawed and frozen rocks is generally marked by the abrupt changes of electrical conductivity, dielectric constant, and, in the case of coarse-grained loose deposits and coarse-clastic hard rocks, of seismic velocity, or, in the general case, of electrical and acoustic impedances. The regions with fresh and salt subpermafrost water can be distinguished by the absence or presence of a stochastic correlation between the thickness of the permafrost rocks and the conductivity of a subpermafrost layer [Kalinin and Yakupov, 1989]. Therefore, in the regions of the coexistence of frozen rocks and fresh subpermafrost water, the position of the first of the above mentioned temperature benchmarks - t = 0o C - can be located reliably by the methods of electrical prospecting under favorable conditions with a mean relative error of ~10%. We succeeded to solve this problem for one of the largest water-bearing structures with salt subpermafrost water, the Olenek artesian water basin. We derived a temperature regression equation for the lower contact of the frozen rocks as a function of their thickness [Kalinin and Yakupov, 1989].
It is of interest to consider electrical resistivity at the boundary of a partial melting zone and in both of its sides in terms of a percolation theory. The rocks of the lower lithosphere and asthenosphere are polycrystalline formations. The arrangement of individual components in them is the compact packing of their chaotically distributed particles of different size and form. In this case the electrical conductivity of such a fairly large 3-D system can be described by the formula
where g1 is the conductivity of the asthenosphere above the partial melting zone, g2 is the conductivity of the melt, x is the relative melt content from 0 to 1, x c is the melt critical value, at which melt percolation takes place, this value being 0.25 in our case, and t is the critical index of electrical conductivity. Formula (1) is valid, as a first approximation, with an accuracy of a factor for g1 and g2 (we are interested in the behavior of the electrical conductivity of rocks in the vicinity of or at the melt percolation). Taking into account the sinuosity of the framework of an infinite melt cluster, proved for 3-D media, t = 1 + n, where n is the index of the correlation radius, equal to 0.8-0.9. It should be added that the formation of an infinite cluster is marked by g tending to be equal to g1. Hence, we arrive at
The threshold of percolation, as a constant of transportation processes, and the threshold of mechanical coherence in the system arising as a result of a phase transition may not coincide, and in this case the positions of the interfaces determined by electrometric and seismometric methods will be different (see, for example, [Yakupov, 2000]). Where the content of a new phase is small, the mechanical coherence of the initial rock remains intact, as does its homogeneity in terms of the related parameters.
1. The positions of the interfaces produced in the lithosphere by phase transitions in the individual components of the rocks, or in their interstitial fluids, control the positions of its temperature benchmarks. The temperatures of some phase transitions are known. In the case of the others it is controlled by the ratio or contents of the other rock components and pressure.
2. Some of the physical properties change jumpwise at the interfaces produced by the above mentioned phase transitions. Three models are proposed for their distribution in depth: models a, b, and c in Figure 1. These models can be used to determine the positions of these interfaces, in the case of their sufficient contrasts, using magnetotelluric sounding, magnetic variation measurements, and soundings using controlled field sources. This simplifies the interpretation of the results and makes them more reliable. Theoretically, this problem can be solved using radiolocation. Some technical means, though limited in their performance, are available.
3. Where the content of a new phase is sufficient, the interfaces may coincide in terms of percolation and mechanical coherence, and in this case its position can be located by electrometric and seismic methods. Where these thresholds differ, but have been achieved, the positions of the interfaces indicated by electrometry and seismic methods are different: the interface determined by electrometry must lie higher. Where the threshold of mechanical coherence is not attained, the physical properties of rocks remain intact.
4. The materialization of the ideas advanced in this paper will hopefully enhance our knowledge of the temperature distribution in the lithosphere, for instance, in the form presented in Figure 3.
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