ANNALI DI GEOFISICA, Vol. XI., No 2, March 1997, pp. 435-443.
Key words: electromagnetic monitoring, seismo-electrical phenomena, magnetotelluric field, transfer functions, adaptive data processing
A second type of such phenomena is a direct generation of E.M. fields as a result of mechanic-electric energy transformation. A specific mechanism for such transformations depends on the structure and the composition of rocks and on the type of rocks deformation and consequently on the timephase during earthquake preparation. Evidently electrokinetic processes play a principal role under elastic deformations of water saturated rocks. In a first approximation the mecanic-electric transformation is linear in the case and the frequency spectrum of EM disturbances is a linear function of the mechanical field variations. In such a case the frequency band starts from some almost constant field, and reaches a few hundreds hertz. In contrast, under plastic deformations and failures mecanic-electric transformations can be not linear and the E.M. spectrum may run into kilo and megacycles (Sobolev, 1995).
At present, we achieved some relevant experience dealing with various modifications of the applications of E.M. monitoring. Sometimes, E.M. fields of internal origin in different frequency ranges are measured, sometimes a variation of geoelectrical sections is studied (Sobolev,1995). But unfortunately, both types of E.M. monitoring were separately applied. They provide, however, with independent information about geodynamic processes. We are presently designing low frequency modification of such monitoring wich can provide with an information about both types of seismo-electrical phenomena. The basic rationale is conceived as a continuous measurement of five components of the magnetotelluric field.
Here: Hx(t), Hy(t), Hz(t), Bx(t), By(t) - are the time varying magnetic and electric components, respectively; Zxx(t), Zxy(t), Zyx(t), Zyy(t), Izx(t), Izy(t) - are impulse responses of the impedance tensor Z and of the induction vector I components, respectively; and the sign * means a convolution. For instance, the first relation in (1) is a vector integral equation of convolution, with respect to the unknown impulse responses Zxx(t) and Zxy(t):
Usually, when performing an M.T. sounding such an equation is solved by transforming it into the frequency domain. We believe, however, that during continuous monitoring it is more effective to process and to interpret the data directly in the time domain (Svetov and Shimelevich, 1988). The similar opinion is expressed in the paper (Meloni et al, 1996). Such approach permits to exclude an operation of Fourier transform and to apply adaptive data processing methods, which allow to process the data in a quasireal time. But in reality we have to take into account that transfer functions (impulse responses) of M.T.field vary with changes of the geoelectrical section and of the current system in the ionosphere. Moreover, besides M.T. fields, there are E.M. fields of internal (geodynamic) origin. Therefore it is more correct to analyze a comparatively more complex equation:
The notation Z(t,t) emphasizes the possibility of the transfer functions variation with time of observation, while the term dEx(t) accounts for some eventual additional anomalous field with respect to M.T. one, that includes also the electrical field of internal origin. Evidently, such equation (3) has not a unique solution. It can be solved by assuming that the transfer functions changes are much slower than the E.M. field variations. After digitization of the function`s, the problem is reduced to solving a redundant system of linear algebraic equations (SLAE). In the Russian literature, a usual method for solving such a system is a minimization of the smoothing square functional formerly suggested by Tikhonov (Tikhonov and Arsenin,1977):
Here H is a matrix of SLAE coefficients (values of horizontal magnetic field at some given sequence of time instants), Ex is a column-vector of electric field values recorded at some given sequence of time instants, Z is a column-vector of unknown values of the impedance impulse response within a sequence of time delays, a is some regularization parameter and dt is a sampling-step of data. The unknown transfer functions can be found by the formula:
Here HT - is a transposed matrix H and I is the identity matrix. After calculating Z, one can evaluate the synthesized (predicted) electric field Es by a convolution of the horizontal magnetic field with the computed transfer functions:
The anomalous (residual) field is a difference between the total (the measured) field Ex and the predicted Exs one:
From our view point, however, iterative methods of solving SLAE appear better suited for the monitoring problem. They can be used in adaptive methods of data processing, and allow to renew the data at every step of the iteration (Widrow and Sterns,1985). After a number of iterations the computed transfer function get into a small vicinity of its exact value and following iterations only correct the function a little in accordance with the new variations of the M.T. field components. It is convenient to present the adaptive algorithm for data processing by means of the scheme on Fig. 1.
The scheme has 3 inputs and 2 outputs. Horizontal components of magnetic field Hx and Hy play a role of reference signals and enter two reference inputs and a component to be processed (e.g. electric componenet Ex) enters the main input. The components Hx and Hy are convoluted with impulse responses Zxx(t) and Zxy(t) respectively. In a discrete form each of the convolutions is expressed by the formula:
Here k and l mean sampled values of t and t in equation (3) and L is a length of the impulse responce Zkl expressed in dt values. Then both of the convolutions are added together and the sum is compared with the signal on the main input (Ex). As a preliminary the processed data are to be filtrated in a frequency band-pass with fmax/fmin <= 100 - 300. The algorithm for correction (AC) of the transfer function values is based on the iterative least square method (Widrow and Stearns, 1985). For equation (3) it can be written in the form:
Fig. 2 shows a one day (27.10.93) output of data processing for vertical component of magnetic field Bz.
Fig.2. Pattern of magnetic field data processing for a quiet-day - anomalous magnetic field and components of induction vector. The inscription Bz 27.10.93; RMS% = 19.63, L=500s. denotes the component of M.T. field, the date of observation, the relative RMS value of the residual field in percents and the length of impulse response in seconds.
In its upper part the graphs both of the predicted Bzs and of the residual (anomalous) dBz fields variations are represented. As a first approximation, they reflect variations of the external (MT) and of the internal (geodynamic) E.M. fields respectively. As follows from the latter graph in such a case the external MT field is well attenuated in dBz, the relative root-mean-square value of the anomalous field to the predicted one (RMS%) is equal to 19.63 percents. Below the graphs a spectral-time diagram of the anomalous field is shown. It permits to represent an information contained in the anomalous field in a more expressive form. On the diagram the time t of observation is along the horizontal axis, while the period of the residual field in minutes is along the vertical axis.The colour scale denotes the spectral density of the residual field. On the plot one can see some well-defined anomalies of the residual field. The lowest part of the picture shows the so called dynamic sections of impulse responses of induction vector components Izx and Izy. On such sections the time delay t of impulse responses Izx and Izy in seconds is along vertical axis and the colour scale denotes a magnitude of the impulse responses. The direction of t-axis corresponds to a rise of a depth of investigations with increasing of time delay. From such a plot, we can infer how much the transfer functions varies in time, and consequently how much the geoelectrical section changes. In the case the changes of geoelectrical section is not great. The values of impulse responses of transfer functions as well as of spectral density of an anomalous field are computed at every sampling-step, then they are averaged within 6 minutes intervals and are outputed on the plots.
The next picture (Fig.3.) is another dayly pattern (16.07.93) for vertical magnetic field.
Fig.3. Pattern of magnetic field data processing for disturbed day (16.07.93).
In the case the relative value of residual field is higher (RMS%=56.13) and there is a well-defined anomaly on the dynamic section of inductive vector component Izy.The anomaly of the spectral density is not so expressive in the case.
Fig.4 shows a pattern (27.10.93) of electric field processing for relatively quiet day.
Fig.4. Pattern of electric field data processing for quiet day - anomalous electric field and components of impedance tensor (27.10.93).
Here RMS%=24.67 and the impulse responses of impedance tensor elements change slightly. In contrast the dayly pattern on 07.10.93 is an example of disturbed anomalous electric field (fig.5).
Fig.5. Pattern of electric field data processing for disturbed day (07.10.93).
The impedance impulse responses change in a great extent in particular Zxy and the level of anomalous field increses up to 50.65%. In general, the quality of the electric field measurement and processing is worse than for the magnetic field. It is a result of a stronger interference in this case. It is important that in all the above-mentioned cases the residual field is not correlated with the predicted one and consequently it has other sources. But it cannot be reliably declared to be of internal (seismo-electrical) origin and to be connected only with geodynamic processes. Often it can also be of local industrial origin.
After averaging of the data on 3 hours intervals the dayly outputs of data processing are then synthesized into montly plots. Fig.6 is one such example for the vertical component of a magnetic field (for November,1993).
Fig.6. An example of a monthly plot for magnetic field after averaging the daily plots (11.93).
The graphs for both predicted and anomalous fields in the case are represented in the form of their intensity envelopes. As in the case of dayly patterns the residual field is not correlated with the predicted one, and consequently it provides an independent information. This picture also shows how the transfer functions change during some longer periods of time.
Fig.7. is the same monthly plot but for the electric field.
Fig.7. An example of electric field monthly plot (11.93).
Both anomalous field, and impedance transfer functions, appear much more disturbed than in the case of the magnetic field. Here the level of residual field is equal to 49.43% and there are pronounced anomalies of impedance impulse responces. Its duration is about several days. A special feature of the monthly patterns is that the anomalous field involves a pronounced daily harmonic. It is clearly seen on the graphs of the residual field and on its spectral-time diagrams (especially in the electric field). Since the data are presented in the periods band 20 sec - 1 hour, so such a phenomenon may be the result of field modulation only.
After 1 day averaging of 3 hour sampling data the monthly outputs of data processing are synthesized into a yearly plot. Fig.8 is an example of such plots for the vertical magnetic field.
Fig.8. Pattern of a yearly plot for magnetic field (1993).
The plot of the anomalous field does not appear expressive in such a form. Concerning the dynamic sections of the transfer functions, they show some anomalous zones. At present, its origin as well as the origin of anomalies on dayly and monthly plots are not clear. This is partly explained by the fact that during 1993 several weak seismic events occurred, although no powerful one. But the main cause is connected with the fact that the M.T. field observations were performed at one station only. Therefore, we cannot reliably interpret the observed disturbances of the residual field and of the transfer functions and locate a position of their source. Due to the same reason no trustworthy judjements can be passed about the correlation between E.M. disturbances and seismic events. For a reliable interpretation of the M.T. monitoring it appears essential to record simultaneously the E.M. field at several stations, and to correlate E.M. observations with other kinds of geophysical parameters.
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