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A model of apparent resistivity changes in earthquake preparational areas
Tectonophysics, 209 (1992) 297-299 Elsevier Science Publishers B.V., Amsterdam
297
Extended Abstract
A model of apparent resistivity changes in earthquake preparational areas Klaus Meyer a, Waldemar Jozwiak ’ and Laike M. Asfaw b a Seismological Department, Box 12019, S-750 12 Uppsala, Sweden b Geophysical Obseruatory, Box 1176, Addis Ababa, Ethiopia ’ Institute of Geophysics, Polish Academy of Science, Warsaw, Poland
(Received March 7, 1991; revised version accepted May 29, 1991)
Electric conductivity is highly sensitive to the evolution of microcracks in the vicinity of earthquake sources. Stress-induced crack development and subsequent threshold processes change the electric resistivity in the fault zone. An attempt was made to find a causal relation between temporal changes of apparent resistivity and stresses manifested in energy release by earthquakes. Any coherence would contribute to the understanding of the pre-seismic earthquake preparational phase. Site measurements were carried out in the central part of the Main Ethiopian Rift. In the field, simultaneous measurements of the magnetic field components H, D and 2 and telluric recordings of two electric lines, directed N-S and E-W (length 100 m) were carried out. Magnetic components induced the telluric fields E EW and ENS- The general relationship of electromagnetic induction in the frequency domain is the following:
[:;$y=[
Z,,(w) -we) H(w) (1) -G(w) G*(w) I[ D(w) 1
where: 2, the transfer nent E, (E, components
is an impedance tensor representing function between the telluric compo= E,,, E, = E,,) and the magnetic H, (H, = H, Hz = D).
Correspondence
to: K. Meyer, Seismological Department, 12019, S-750 12 Uppsala, Sweden.
0040-1951/92/$05.00
Box
The apparent resistivity p(w) is deduced from the impedance tensor, that is: PikCW)
=
I Zik(W) I ‘/Pm
(2)
where p is magnetic permeability. Laboratory results indicate that the state of stress may govern the evolution of microcracks in the earth’s crust. This could alter the resistivity in the focal area and, subsequently, the apparent resistivity measured on the surface. Thus, we expect a time dependence of apparent resistivity: Pik=Pik(W,
t,
(3)
example of a tentative variation of resistivity in the focal region of forthcoming earthquake is given in Figure Id. A dilatancy in dry or partly saturated rocks could lead to a resistivity increase. We might expect the same type ‘of resistivity increase in saturated rocks if a sector of compression is considered. In that case water out-flow is assumed. A resistivity drop (Fig. Id) occurs and a fracture plane is formed: the threshold process of crack evolution. In this phase water percolation starts a drastic decrease in resistivity. In order to get a rough indication of the resulting changes in the apparent resistivitias expected near fault zones we used a simple two-dimensional model of resistivity structure, including an elliptic fault zone (Fig. 2e). We calculated the apparent resistivity response for various resistivities in the fault zone. Four different periods were An
0 1992 - Elsevier Science Publishers B.V. All rights reserved
H‘.. pal
A time dependence for the apparent rcsistivity, and thus variations in the teliuric field, is obtained if we assume gradual changes in the resis~ivi~ in the fault zone, as assumed above (Fig. 11. The resulting time variations in apparent resistivities are displayed in Figure la-d for five
I I I I I I I I 012345ti?
oc
Lv
7
Time[days]
\ TIhE.days
---%-eT--
0
Fit& I. (a&-(c) Time dependence of apparent resistivity changes (s&are root) for temporal resistivity variations in the fault zone shown in fd). ~~tations are carried out for fauh zone model and assumed recording sites 1,2 and 3 as given in Fig 2, for four different periods: 24 h, 1 h, 60 s and 1 s, Note the strong influence of the site responses. t&d)Tentative modef of temporal resistivity changes in the earthquake fanit area prior to earthquake rupture. Gradual increase of resistivity in the dilatant epicentral zone is fohowed by a sharp decrease due to pemotation in the cracked rocks.
ii
used: 24 h, 1 h, 50 s and 1 s. The r~~~~t$ are disphyeb in Figure 2a-d and reveal rather clear apparent resistivity anomalies across the fault zone. Natural&, these resistkity zanomzdies would be r&&ted into the t&it&c field t&xi& &d~tion.
10
20
I
Fig. 2, Apparent resistivity response for viuious resistivit@s in the fault zone: I, 10, 100, 1001)and If&JO ohm-m. Tbiekness of superfieiai layer is 0.25 km, resistMy 2@ Ohmm. Fat& width 5 km, fault length iU km, dip angle 45”. gour periods are used: (a) 24 h, (b) 1 h, (cl 60 s and (d) 1 s. Apparent resistivity increases with increasing resistivity in the fault zone: lowest curves for 1 Ohm-m, uppermost curves for 1~ Qhm-m. fe) Two-dhnensionaf model used for ea%enh+ttingapparent resistivity changes, including ebiptic fatdt zone.
APPARENT
RESISTIVITY
CHANGES
MODEL
different periods: 24 h, 1 h, 60 s, 10 s, and 1 s. The apparent resistivities are computed for three sites on the Earth’s surface; one site just above the elliptic fault zone (site 3, Fig. 2), site 2, at the left,edge of the fault zone, and site 1, about 5 km from the left edge of the fault zone. In our example we found the largest changes in MT-induction at site 3 (H-polarization) which was expected. Temporal changes in the impedance tensor were of the order of several orders of magnitude for our particular example (Fig. 1). Our example only demonstrates the qualitative changes of apparent resistivity in the vicinity of a body where stress-induced crack development prevails. Any time dependence of apparent resistivities may be related to stress conditions and processes at different stages prior, during and after the occurrence of the seismic event (for instance: stress accumulation, crack orientation and crack density, percolation processes, and stress release). One measurable process is the stress release by earthquakes. We can estimate the amount of seismic energy released per unit time (even for microearthquake activity) and relate these measures to the time variation of apparent resistivities. Thus, we can generate two time series, describing the time variations of the apparent resistivity and seismic energy release. Any correlation between the two time series may suggest a causal relationship between tectonic stress (earthquake energy release) and crack development (resistivity changes) during an earthquake cycle. Numerical evaluation of a causal relationship may be achieved by crosscorrelation. The cross-
299
correlation function of two time series is a function of the mutual time shift, r.
where Xi, Yi are samples of the time series and 6,, 6, are the corresponding variances. This function is normalized, having values in the range 1 (perfect coherence) to - 1 (perfect coherence, but opposite phase). In addition, we can also calculate the telluric field from magnetic observations and the estimated apparent resistivities. The residual of the electrotelluric field (ETF) is obtained as the difference of the predicted and the observed telluric field. The investigation of the residual can easily reveal variations which have a different nature to those connected with electromagnetic induction. For instance, previous investigations have ascribed certain ETF anomalies to a source effect. Heterovalent impurities in ionic crystals cause interstitials which form electric dipoles. l3y changing the imposed stress field, the dipoles re-orientate into a new state of thermodynamic equilibrium, the time process of which may be fast under certain stress conditions. The resulting change of polarization is equivalent to the emission of an electric current. After a thorough discussion on possible sources of electric noise, the interpretation of the remaining residual may show anomalies which are connected with the generation of electric currents, such as those caused by crack development, creep motion or emission of electric currents.
297
Extended Abstract
A model of apparent resistivity changes in earthquake preparational areas Klaus Meyer a, Waldemar Jozwiak ’ and Laike M. Asfaw b a Seismological Department, Box 12019, S-750 12 Uppsala, Sweden b Geophysical Obseruatory, Box 1176, Addis Ababa, Ethiopia ’ Institute of Geophysics, Polish Academy of Science, Warsaw, Poland
(Received March 7, 1991; revised version accepted May 29, 1991)
Electric conductivity is highly sensitive to the evolution of microcracks in the vicinity of earthquake sources. Stress-induced crack development and subsequent threshold processes change the electric resistivity in the fault zone. An attempt was made to find a causal relation between temporal changes of apparent resistivity and stresses manifested in energy release by earthquakes. Any coherence would contribute to the understanding of the pre-seismic earthquake preparational phase. Site measurements were carried out in the central part of the Main Ethiopian Rift. In the field, simultaneous measurements of the magnetic field components H, D and 2 and telluric recordings of two electric lines, directed N-S and E-W (length 100 m) were carried out. Magnetic components induced the telluric fields E EW and ENS- The general relationship of electromagnetic induction in the frequency domain is the following:
[:;$y=[
Z,,(w) -we) H(w) (1) -G(w) G*(w) I[ D(w) 1
where: 2, the transfer nent E, (E, components
is an impedance tensor representing function between the telluric compo= E,,, E, = E,,) and the magnetic H, (H, = H, Hz = D).
Correspondence
to: K. Meyer, Seismological Department, 12019, S-750 12 Uppsala, Sweden.
0040-1951/92/$05.00
Box
The apparent resistivity p(w) is deduced from the impedance tensor, that is: PikCW)
=
I Zik(W) I ‘/Pm
(2)
where p is magnetic permeability. Laboratory results indicate that the state of stress may govern the evolution of microcracks in the earth’s crust. This could alter the resistivity in the focal area and, subsequently, the apparent resistivity measured on the surface. Thus, we expect a time dependence of apparent resistivity: Pik=Pik(W,
t,
(3)
example of a tentative variation of resistivity in the focal region of forthcoming earthquake is given in Figure Id. A dilatancy in dry or partly saturated rocks could lead to a resistivity increase. We might expect the same type ‘of resistivity increase in saturated rocks if a sector of compression is considered. In that case water out-flow is assumed. A resistivity drop (Fig. Id) occurs and a fracture plane is formed: the threshold process of crack evolution. In this phase water percolation starts a drastic decrease in resistivity. In order to get a rough indication of the resulting changes in the apparent resistivitias expected near fault zones we used a simple two-dimensional model of resistivity structure, including an elliptic fault zone (Fig. 2e). We calculated the apparent resistivity response for various resistivities in the fault zone. Four different periods were An
0 1992 - Elsevier Science Publishers B.V. All rights reserved
H‘.. pal
A time dependence for the apparent rcsistivity, and thus variations in the teliuric field, is obtained if we assume gradual changes in the resis~ivi~ in the fault zone, as assumed above (Fig. 11. The resulting time variations in apparent resistivities are displayed in Figure la-d for five
I I I I I I I I 012345ti?
oc
Lv
7
Time[days]
\ TIhE.days
---%-eT--
0
Fit& I. (a&-(c) Time dependence of apparent resistivity changes (s&are root) for temporal resistivity variations in the fault zone shown in fd). ~~tations are carried out for fauh zone model and assumed recording sites 1,2 and 3 as given in Fig 2, for four different periods: 24 h, 1 h, 60 s and 1 s, Note the strong influence of the site responses. t&d)Tentative modef of temporal resistivity changes in the earthquake fanit area prior to earthquake rupture. Gradual increase of resistivity in the dilatant epicentral zone is fohowed by a sharp decrease due to pemotation in the cracked rocks.
ii
used: 24 h, 1 h, 50 s and 1 s. The r~~~~t$ are disphyeb in Figure 2a-d and reveal rather clear apparent resistivity anomalies across the fault zone. Natural&, these resistkity zanomzdies would be r&&ted into the t&it&c field t&xi& &d~tion.
10
20
I
Fig. 2, Apparent resistivity response for viuious resistivit@s in the fault zone: I, 10, 100, 1001)and If&JO ohm-m. Tbiekness of superfieiai layer is 0.25 km, resistMy 2@ Ohmm. Fat& width 5 km, fault length iU km, dip angle 45”. gour periods are used: (a) 24 h, (b) 1 h, (cl 60 s and (d) 1 s. Apparent resistivity increases with increasing resistivity in the fault zone: lowest curves for 1 Ohm-m, uppermost curves for 1~ Qhm-m. fe) Two-dhnensionaf model used for ea%enh+ttingapparent resistivity changes, including ebiptic fatdt zone.
APPARENT
RESISTIVITY
CHANGES
MODEL
different periods: 24 h, 1 h, 60 s, 10 s, and 1 s. The apparent resistivities are computed for three sites on the Earth’s surface; one site just above the elliptic fault zone (site 3, Fig. 2), site 2, at the left,edge of the fault zone, and site 1, about 5 km from the left edge of the fault zone. In our example we found the largest changes in MT-induction at site 3 (H-polarization) which was expected. Temporal changes in the impedance tensor were of the order of several orders of magnitude for our particular example (Fig. 1). Our example only demonstrates the qualitative changes of apparent resistivity in the vicinity of a body where stress-induced crack development prevails. Any time dependence of apparent resistivities may be related to stress conditions and processes at different stages prior, during and after the occurrence of the seismic event (for instance: stress accumulation, crack orientation and crack density, percolation processes, and stress release). One measurable process is the stress release by earthquakes. We can estimate the amount of seismic energy released per unit time (even for microearthquake activity) and relate these measures to the time variation of apparent resistivities. Thus, we can generate two time series, describing the time variations of the apparent resistivity and seismic energy release. Any correlation between the two time series may suggest a causal relationship between tectonic stress (earthquake energy release) and crack development (resistivity changes) during an earthquake cycle. Numerical evaluation of a causal relationship may be achieved by crosscorrelation. The cross-
299
correlation function of two time series is a function of the mutual time shift, r.
where Xi, Yi are samples of the time series and 6,, 6, are the corresponding variances. This function is normalized, having values in the range 1 (perfect coherence) to - 1 (perfect coherence, but opposite phase). In addition, we can also calculate the telluric field from magnetic observations and the estimated apparent resistivities. The residual of the electrotelluric field (ETF) is obtained as the difference of the predicted and the observed telluric field. The investigation of the residual can easily reveal variations which have a different nature to those connected with electromagnetic induction. For instance, previous investigations have ascribed certain ETF anomalies to a source effect. Heterovalent impurities in ionic crystals cause interstitials which form electric dipoles. l3y changing the imposed stress field, the dipoles re-orientate into a new state of thermodynamic equilibrium, the time process of which may be fast under certain stress conditions. The resulting change of polarization is equivalent to the emission of an electric current. After a thorough discussion on possible sources of electric noise, the interpretation of the remaining residual may show anomalies which are connected with the generation of electric currents, such as those caused by crack development, creep motion or emission of electric currents.