A Model for the Generation of Precursory Electric and Magnetic Fields Associated with the Deformation Rate of the Earthquake Focus

We present a model for the generation of electric current in rocks under stress, involving the strain rate, (€) which is inf luenced by the motion of charge bearing dislocations. The relat ionship between current density and strain rate is demonstrated. On the basis of laboratory data, we estimate the deiormation rate necessary to generate an electr ic signal observable at distances far enough from the source, as to qual i fy i t as an electr ic earthquake precursor. Using this mechanism and the geometrical characterist ics of such a type of source we simulate the propagation of the electr ic and magnetic f ields and their "received" characterist ics as a function of the source-receiver separation. We find that the magnetic f ield is an effect ive indicator of the quali ty of the source, in part icular due to i ts spatial propert ies (azimuthal variat ion) and the relat ionship between the horizontal and vert ical components. We conclude that the expected signal waveforms at long distances from such a kind of source are similar to a class of signals (bay l ike waveforms), independently observed prior to earthquakes by several investigators. l . In t roduc t ion The generation of electr ic currents in rocks under stress has long been recognized by means of experiment. For instance, Whitworthl) has demonstrated such an effect in alkal i hal ides under pressure. In a more recent paper2), the generation of electr ic current in rocks under uniaxial compression is reported. The main result of these investigations is that the shape of the electr ic signal depends drastical ly on the rate of stress variat ion and specif ical ly, appears to fol low the f irst derivative ofthe external ly appl ied stress. From a theoretical point of view, two types of current generation mechanisms have been studied. The f irst is reported by Varotsos et al.3), and is related to polarization or depolarization effects. The second by Sl i fkina), is based on the concept of motion of charged dislocations. In the present paper, we discuss the avai lable data on the basis ofthe 288 F. VALLIANAToS and A. TzANrs moving charged dislocations (MCD) model. Furthermore, and assuming that the earthquake focus may be described by such a model, we make a first attempt to simulate the propagation of the resulting transient electric signal and describe its received characteristics at intermediate-long distances from the source (the earthquake in preparation). 2. A Current Generation Mechanism in Rocks under Pressure In a crystall ine structure, dislocations may be formed by an excess or absence of a half-plane of atoms. The edge of this half-plane comprises a dislocation l ine, around which the physical f ields related with it are concentrated. In an ionic structure there wil l be an excess or absence of a l ine row of ions along the dislocation l ine, with consequence that the dislocation becomes charged. We note thatthe jogs of edge dislocation can be ionically charged. Whitworthl) writes that a dislocation l ine "in a thermal equil ibriumwould be suruounded by a cloud of point defects of the opposite sign to maintain electric neutrality and its dislocation core presence would therefore affect the concentration of point defects in the crystal". However, in dynamic processes, when dislocations move, the electric neutrality can no longer be maintained. Let A+ be the density of edge dislocations of the type required to accommodate the uniaxial compression (or tension) and Abe the density of dislocation of the opposite type. The motion of charged dislocations produces a transverse polar izat ion: ' A r 6 x p= (A* A ) q t . #= 6L . q t . : + ( 1 ) r t , " ,12 . , 12 where q1 is the charge per unit length on the dislocation. If screw dislocations are ignored, the plastic contribution to the strain, when these dislocations of Burger vector D move through a distance 6x, is t . + , , a * . e ) r P = l n + A / . 2 The rate of change in polarization is equivalent to the electric urrent density, by definition , O P ( r ) , ( 2 ) . , . [ i q , : o A * + A tr=? utr=it. tr , p=fr; (3) where B is a constant usually between I and 1.5. Equation (3) shows that the observed transient electric variation is related to the non-stationary accumulation of deformation. Specifically, when the deformation rate increases at a variable