Electromagnetic induction in regions under stress

Physics of the Earth and Planetary Interiors, 53 (1989) 187-193 Elsevier Science Publishers By., Amsterdam — Printed in The Netherlands

187

Electromagnetic induction in regions under stress S.O. Ogunade Department of Physics, Obafemi A wolowo University, Ile-Ife (Nigeria) (Received November 13, 1986; revision accepted August 20, 1987)

Ogunade, SO., 1989. Electromagnetic induction in regions under stress. Phys. Earth Planet. Inter.. 53: 187—193. The variations in the apparent resistivity due to a four-layer Earth model under stress have been studied with the aid of a numerical model. The effect of the stress produced by vertical uplifts of the bottom layer by as much as 1.5—20 m, for layer thickness h = 1.8—24 km, source period T= 1—60 mm and varying conductivity composition of the layers, has

been examined. The results reveal a gradual decrease in the apparent resistivity with increase in stress. This decrease in the apparent resistivity is particularly pronounced at shorter periods and for thicker layers. The change in apparent resistivity was also found to be enhanced when the first and third layers have conductivities much higher than that of the second layer.

1. Introduction The dilatancy—diffusion process is believed to be responsible for the change in Earth resistivity with stress (Brace and Orange, 1968). This process is known to cause an increase in volume of rocks under stress by opening new cracks which are subsequently filled with fluids. Nagata (1976) observed that mechanical stress in the Earth’s crust ought to cause a local distortion of the geomagnetic field in the focal area of an earthquake. Stress-induced changes have also been known to produce rock magnetization (Stacey and Banerjee, 1974; Rikitake, 1976; Smith and Johnston, 1976; Johnston et al., 1976). Particularly large-scale readjustments of regional stress are known to be reflected in the magnetic data (Smith et al., 1978). The possibility of a stress-induced magnetic change should be expected in regions where substantial stress variation occurs. Rikitake (1976) observed that a geomagnetic observation of micropulsations, storm sudden commencement (SSC), sudden impulse (SI) and other short-period variations is ideal for monitoring the conductivity anomaly associated with an earthquake of smaller magnitude, while geomagnetic variations having a period of a few 0031-9201/89/$03.50

© 1989 Elsevier Science Publishers B.V.

minutes may be useful for monitoring dilatant regions associated with large-magnitude earthquakes. Chinnery (1963), Press (1965), Rosenman and Singh (1973) and Johnston (1978) have used various numerical models to calculate stress distribution around dislocation on a vertical fault. Some of these models have also been used to determine the total magnetic field anomaly at the surface attributable to the stress distribution with depth. Assessment of the effects of conductivity in an extremely complex geological environment is much more difficult. Onyedim (1982) has computed the magnitudes of the maximum and minimum principal stress in a three-layer Earth model with a vertical fault. The objective of this work is to seek additional information on the effect of the spatial extent of dynamic stress fields, volume, geometry and conductivity difference of the composite layers of a four-layer Earth on changes in the apparent resistivity at the surface.

2. Numerical model The models considered are shown in Figs. 1 and 2. A uniform source field of ionospheric origin

188 A

E

B

5~ E ~ vanishes at infinity. Eax denotes the anomalous electric field, ~ denotes the normal electric field and E the total electric field. The values of ~ are used as starting values. Free boundary values are used as the impedance boundary condition at the boundaries, i.e. =

________

p 1 ~

o~c-~ ~

~

~

__.

~ ~

-—~~

—

kEax(Y, z)

i~

2 b

where k 0a, ~ 2~/T (T is the period of the source field), 1u0 is the permeability of free space, a is the conductivity and ~ is the direction of the outward normal. Equation (2) is obtained under the assumption that the anomalous fields diffuse outwards in the form of plane waves

~

~

=

~

~

~

~

l3~

08 32

90

•9~.97

.06

~~i~—~-----

T~1~~2L_

(2)

-~

=

(Schmucker and Weidelt, (2) yields as a condition at the1975). upperEquation edge of the air—Earth interface

92

aEax Fig. 1. A(a) High resistivity model p = ~ 50, 10, 0.02 t~m; B(a) Low resistivity model p = 40, 2, 0.4, 0.02 tI m. A(b) High resistivity finite difference model; B(b) Low resistivity finite difference model. A(c) Values of the maximum principal stress for d = 20 m (Onyedim, 1982); B(c) values of the maximum principal stress for d = 6 m.

—~-—— =

2.1. Earth models

The models designated A and B consist of four layers of varying thicknesses and resistivities given in Table I. Model A represents a newly uplifted

(1) with the boundary condition that the difference £~Eax(y,z)=i~io(~aEnx+aEax)

region with relatively little fluid in the resulting new cracks. Model B represents an uplifted region B

A ~

(3)

(i.e., a constant horizontal magnetic field). The iteration was carried out along columns using the Gauss—Seidel procedure with a successive relaxation factor to speed up convergence.

was assumed to be the inducing source field. The fields at the surface of the models were evaluated using the finite difference method of Ogunade (1982) (see Fig. lb). For the TE mode we have to solve the differential equation

P~5OQm

0

I~Qrn

_______

h I

~~5OO0m

—~--------~t

~

5ç?m 1

h

—~---Th--------

—~----1-~------~ —~-----~\-----

2 p500

m

~

h

2 P~5OOQ

m

~

h

S —~-------~----------

50

Fig. 2. (A) Conductivity model with p = 50, 500, 5 and 2 ~2 m; (B) p respectively.

=

500, 5, 50 and 2 t2 m from surface to bottom layer

189

and 0.02 ~2m from the surface layer downwards, while the layers of model B are assigned resistivi-

TABLE I Values of layer thickness and apparent resistivity Model

Uplift d (m)

First 5 10 20

6 12 24

1.5 3 6

2

ties ~ 40, 2, 0.4 and 0.02 ~ m from the surface layer downwards (see Fig. 1). In Fig. 2 the layers of model A are assigned resistivities p 50, 500, 5 and 2 ~ m from the surface layer downwards,

Layer Thickness h (km)

1.8 3.6 7.2

Second 6 12 24 1.8 3.6 7.2

=

Third

Fourth

8~ 16 32 j

Infinite

2.4\ 4.8 9.6

Infinite

=

while the layers of model B are assigned resistivities p 500, 5, 50 and 2 ~ m from the surface layer downwards. The lateral extent of the models =

J

considered is 700 km with the fault line occurring at 400 km. The intrusion resulting in vertical uplift of the structure on the left side (see Figs. 1 and 2)

Layer apparent resistivity p

occupies the region 0
(tl m)

A

Fig. 1 Fig. 2 Fig. 1 Fig. 2

B

1000 50 40 500

50 500 2 5

10 5 0.4 50

0.02 2 0.02 2

=

=

with the resulting cracks filled with fluid. The heights of the vertical uplifts are (1) d 5, 10 and 20 m and (2) d= 1.5, 3 and 6 m. In order to study the effect of conductivity difference the layers of model A are assigned resistivities p iO~,500, 10

=

=

=

200

—A

b

c

200

~

d~5m

~ 200

ll

i

I

_________________________________________________________________

—

—A

B

I

2.00

150

________________________ __--~~~~ I

2 00

—

~tS

I~ ~ 200

~

I

-—

I

1.50

I 200

_____________________________

2-00

d,20r,~

-

1—0c_

I

________________________i_~0

400

600

—~1—OC~ 1cm

I 200

400

600

‘i02 km

I 200

I 400

I 600km

Fig. 3. Apparent resistivity values for conductivity models in Fig. IA (full line), B (broken line) for vertical uplifts ci = 5, 10 and 20 m and (a) T = I mm, (b) 2 mm, (c) 5 mm.

190

2.02

—

d~Sm

~ 2.01

—

2m~

-

10 mr

h~5km

A

UNSTRS~~0~L_— —

—

2.01

h~5km

B

~ ~

—

I

200

d~Sm

~

~

I

2.00

1

—

I

400

I

600

km

—

I

200

I~i

400

600

km

—

-

15 mm 2.0(’

1—- 2-—

~

I

60mm 200

-

—

I

/.00

___~~!Z!

I

I

jL~—---~ 600 km

I

200

Fig. 4. Apparent resistivity values for vertical uplift (1) d and 60 nun for conductivity models A and B in Fig. 2. A

=

I

I

I

400

I km

600

5 m, (2) 1.5 m due to a uniform source field with period T = 1, 2, 5, 10, 15

B

2.O3~~NsTRESSEDj~ 1

-

drn10 m

h.

~ -

10km

I

d~10 m

-

h~10km

~i

E2O2~

~

1

2.00

200

i

I 400

I 600km

2.~—

I

I

200

400

600 km

200

400

600

I

I

I

—

~

~mi~”

200

400

600

km

Fig. 5. Apparent resistivity values for vertical uplift (1) d = 10 m, (2) 3 m and 60 nun for conductivity models A and B in Fig. 2.

km

due to a uniform source

field with period T = 1, 2, 5, 10, 15

191

amount of stress produced is directly proportional to the magnitude of the uplift.

function of lateral displacement is shown in Fig. 3a—c for vertical displacement d 5, 10 and 20 m and period T 1, 2 and 5 mm. The results show that the apparent resistivity is lower over the stressed region. The value of the apparent resistivity for the more conducting model is lower than that of the more resistive model over the stressed region. The values of the apparent resistivity tend to merge at some distance from the fault which is at 400 km. This observation, however, is not valid for d 20 m and T 1 mm where the thickness of =

=

3. Discussion of results Figure 3 shows the numerical results for a uniform inducing source over a vertical fault produced by vertical uplift of the basement layer. Two models with different resistivities were considered (see Fig. 1). The apparent resistivity as a

200~uNS:::~1h,20km

2.05

=

=

~imin21

~

-

2.03_

— -

1 2

d~20m 6

h~20km

LR’ISTRESSED

- —

~

I

201

200

I

400

I

600

~

~ ~

200 -

I

kmI

200

I

400

I

600

km I

~5mmn

~

~---~--_--

I

200

I

400

I

600

km

_ i~1

I

200

Fig. 6. Apparent resistivity values for vertical uplift (1) d and 60 nun for conductivity models A and B in fig. 2.

=

I

400

I

600

km

20 m, (2) 6 m due to a uniform source field with period T = 1, 2, 5, 10, 15

192

the layers, as well as the source period, make the anomalous apparent resistivity still observable at some considerable distance > 300 km from the fault. Models A(c) and B(c) in Fig. 1 show the magnitude of the maximum principal stress values obtained by Onyedim (1982) for a vertical fault. The higher values of the maximum principal stress are seen to be quite close to the fault whereas the minimum values of the apparent resistivity occur at 200 km to the left of the fault. Figures 4—6 show the effects of layer thickness, vertical uplift (see Table I), source period T 1, 2, 5, 10, 15 and 60 mm, and variation of the resistivity of the composite layers for conductivity models in Fig. 2. In Fig. 4 the value of the apparent resistivity over the region under stress increases with shorter periods. For the conductivity model A the apparent resistivity over the high resistive sediment (p iO~~ m) is higher for d 5 m than for d 1.5 m. However, for the conductivity model B the apparent resistivity for d 5 m and d 1.5 m over the low resistive sediment (p 5 ~2m) is of the same value over the stressed region and becomes distinct beyond the fault, with the apparent resistivity for d 1.5 m higher than that for d ~ m. Figure 5 shows the value of the apparent resistivity for d= 10 and 3 m and T= 1, 2, 5, 10, 15 and 60 mm. Again, the values are lower over the stressed region. The behaviours of the apparent resistivity for both conductivity models A and B are similar to that observed for d 5 and 1.5 m. In Fig. 6 the characterization of the apparent resistivity for d 20 and 6 m is shown. A considerable decrease in the apparent resistivity is observed at 200 km over the stressed region. Whereas the values are quite low over the entire region for d 6 m in model A there is a large increase for d 20 m over the high resistive sediment. This difference is not so pronounced in model B. The broken lines in Figs. 4—6 indicate the apparent resistivity values over an unstressed layered Earth as a function of lateral displacement. —

=

=

that the apparent resistivity values at shorter penods are lower than those at longer periods. These results tend to support Rikitake’s (1976) observations that shorter-period variations are ideal for monitoring the conductivity anomaly associated with an earthquake. The results also show that the apparent resistivities for thicker layers are lower than those for thinner ones. This is attributable to the fact that rock magnetization is directly related to the volume of the rock material. The lowering of apparent resistivity with increasing conductivity was also highlighted. The consequence of this effect is that the apparent resistivity is higher at the onset of vertical uplift and subsequently decreases as the new cracks are filled with fluid. The resistivity of the composite layers does play a role in the apparent resistivity observed at the surface.

=

=

=

Acknowledgement

=

=

=

=

=

=

—

=

=

4. Conclusion The apparent resistivity values over a region under stress have been obtained. The results show

The author acknowledges useful discussions with Dr. G.C. Onyedim on the modelling of fracture patterns. The support of an Obafemi Awolowo University research grant is also gratefully acknowledged.

References Brace, W.F. and Orange, A.S., 1968. Electrical resistivity changes in saturated rocks during fracture and frictional sliding. J. Geophys. Res., 73: 1433—1445. Chinnery, M.A., 1963. The stress changes that accompany strike-slip faulting, Bull. Seismol. Soc. Am., 53: 921—932. Johnston, M.J.S., 1978. Local magnetic field variations and stress changes near a slip discontinuity on the San Andreas fault. J. Geomagn. Geoelectr., 30: 511—522. Johnston, M.J.S., Smith, B.E. and R. Mueller, 1976. Tectonic experiments and observations in western U.S.A. J. Geomagn. Geoelectr., 28: 85—97. Nagata. T., 1976. Tectonomagnetism in relation to seismic activities of the Earth’s crust: seismo-magnetic effect in a possible association with the Niigata Earthquake in 1964. J. Geomagn. Geoelectr., 28: 99—111. Ogunade, SO. 1982. Electromagnetic response of a buried cylindrical conductor for sheet and line current sources. Pure AppI. Geophys., 120: 136—150. Onyedim, G.C., 1982. Computer Modelling of Fracture Patterns due to some Sub-surface Geological Features. Ph.D. Thesis, University of London.

193 Press, F., 1965. Displacements, strains and tilts at teleseismic distances. J. Geophys. Res., 70: 2395—2412. Rikitake, T., 1976. Crustal dilatancy and geomagnetic variations of short period. J. Geomagn. Geoelectr., 28: 145—156. Rosenman, M. and Singh, S.J., 1973. Quasi-static strains and tilts due to faulting in a viscoelastic half space. Bull, Seismol. Soc. Am., 63: 1737—1742. Schmucker, U. and Weidelt, P., 1975. Electromagnetic induction in the Earth. Lecture Notes, Inst. für Geophysik, University of Aarhus.

Smith, BE. and Johnston, M.J.S., 1976. A tectonomagnetic effect observed before a magnitude 5.2 earthquake near Hollister, California. J. Geophys. Res., 81: 3556—3560. Smith, B.E., Johnston, M.J.S. and Burford, R.O., 1978. Local variations in magnetic field, long-term changes in creep rate, and local earthquakes along the San Andreas fault in central California. J. Geomagn. Geoelectr., 30: 539—548. Stacey, F.D. and Banerjee 5K., 1974. The Physical Principles of Rock Magnetization. Elsevier, Amsterdam, pp. 146—155.