A fractal study of self-potential time series.

Transcription

1 A fractal study of self-potential tie series. F. Cervantes-De la Torre 1), A. Raírez-Rojas 2), C. G. Pavía-Miller 2,3) and F. Angulo-Brown 3) 1) Area de Sisteas Coputacionales, Departaento de Sisteas,División de CBI, Universidad Autónoa Metropolitana-Azcapotzalco. Av. San Pablo 180. Col. Reynosa Taaulipas. Delegación Azcapotzalco, 02200, MEXICO D. F., e-ail: telephone: (01) (55) , Fax: (01) (55) ) Area de Física de Procesos Irreversibles, Departaento de Ciencias Básicas,División de CBI, Universidad Autónoa Metropolitana-Azcapotzalco. Azcapotzalco, 02200, México D. F., MEXICO. 3) Departaento de Física, Escuela Superior de Física y Mateáticas, Instituto Politécnico Nacional, Edif.. N 9, U. P. México D. F., MEXICO Abstract In the current literature on seiso electroagnetic has been reported any earthquaes which present electroagnetic anoalies as probable precursors of their occurrences. Although this ethodology reains yet order discussion, it is considered interesting the study of any particular cases. In this wor we report a fractal analysis of electroseisic signals recorded in the Acapulco station during In October 24, 1993 occurred and earthquae (EQ) with M 6.5 an epicenter (16.54 N, W), 100K a way the entioned station. Here we calculate the so called Higuchi s fractal Diension and the Hurst exponent to signals during one onth before the EQ. We discuss the dynaical eaning of this analysis and its possible relation with the entioned EQ. 1. INTRODUCTION In any seisically actives zone around the world there exist research progras for the study of precursory phenoena of seiss (Lonitz, 1990; Riitae, 1976; Hayaawa, 1999).One of the techniques used in the search of phenoena precursors of seiss since ore twenty seven years ago consists in onitoring the so-called electric self-potential field. This field is studied through easureents of the ground electrical potential (the self-potential) by eans of shallow pairs of unpolarized electrodes buried in the ground generating a voltage tie series ΔV= ΔV(t). several authors have proposed a correlation between patterns of self-potential variations and the echanis of preparation of earthquaes (Varotsos and Alexoupoulos., 1948a; 1948b).

2 For soe years, we have taen registers of the fluctuations of electric self-potential of the ground in several sites of Mexico (Yépez et al., 1995; 1999), these registers were taen by eans of electric selfpotential stations Soe stations are located along the coast of Guerrero state, near the Middle Aerican Trench, which is the border between the Cocos and the Aerican tectonic plates. In this wor, we study the electric selfpotential tie series arising fro station of Acapulco (16.85 N, 99.9 W) lined to the Middle Aerican trench. In this typical station, thousands of data are taen each two (or four) seconds during periods in the scale of onths and years. Fig. 1. Typical segents of self-potential tie series collected at Acapulco station. The superior series is the N-S one and the down series correspond to the E-W line. Here two 5hr series are showed, with a sapling period of e seconds. The self-potential tie series corresponding to a 2 hr-file. 2. Scaling Law and Fractal Diension These tie series have been analyzed by eans of several ethods as the spectral ones (Yépez et al., 1995; 1999). In this paper, we report a study of our electric self-potential tie series by eans of the fractal diension D by using the Higuchi s algorith (Higuchi., 1988). In our study of electric self-potential tie series, we use the Higuchi s algorith for calculating their fractal diension D. Usually, the exponent is considered to be the index for representing the irregularity of a tie series, although the fractal diension D can be also used as index of irregularity. In fact, in any cases the usage of D is ore appropriate than the spectral exponent for deterining irregularity indices (Cervantes et al., 1999). The fractal technique developed by Higuchi (1988) gives stable indices even for a sall nuber of data. Higuchi (1988; 1990) considers a finite set of tie series observations taen at a regular interval: V 1, V 2, V 3,, V n. Fro the given tie series, he first constructs a new tie series, V, defined as follows. V : V, N, V, V 2,..., V. with = 1, 2,,, and where [ ] denotes the Gauss notation, and, are integers that indicate the initial tie and the tie interval respectively. For a tie interval equal to, one gets sets of new tie series. Higuchi defines (1988) the length of the curve associated to each tie series V as follows:

3 L N V i V ( ( i1) ) i1 N 1 N (1) where the ter N 1 represents a noralization factor, then the length of the curve for the tie interval N is taen as the average value L over sets of. If the average value obeys the following scaling law: L D, (2) L then the curve is fractal with diension D (Higuchi, 1988). This algorith can be applied even over tie series that are not stationary and this fact represents an advantage over the spectral techniques (Cervantes et al., 1999). Higuchi (1990) shows that if 1 3then the following liits are held, if 0 then D 2, (3) D (equation (2)) is held, he also shows that 5 2 which corresponds to uncorrelated white noise, while the second liit is: if 3then D 1. Since the values of the fractal diension D for our tie series are in the interval [1,2], the equations (1) and (2) can be used for their analysis. In figures 1a and 1b we show typical V t electric self-potential tie series for N-S and E-W electrode pairs respectively. For the calculation of the fractal diension D, by eans of the Higuchi algorith we divide the V t tie series data in 6 hrs-files (10800 V-points). To each file, we associate a fractal diension D taen fro (2), calculating the slope of the double log plot of L against. Applying the Higuchi s algorith to data of It is convenient to rear that in the studied series the calculation of the fractal diension D is statistically appropriate; that is, the correlation coefficient R 2 is near to one, and the associate errors of the fractal diension D are worthless. That is, the obtained graphs of log L vs. log for our electric self-potential tie series are always statistically straight lines. The Hurst exponent: The description developed by Harold Hurst hiself is as follows: E[R(n)/S(n)]=C n H, (4) The left hand side is also nown as the expected value of the rescaled range ( Hurst, ). R(n) is defined on a tie ΔVi, i=1, 2,, n as follows R(n)= Max(ΔVi) Min(ΔVi) (5) S(n) is the standard deviation and C an arbitrary constant. 3. Soe Results for Self-Potential Tie Series. In this wor, for our electric self-potential tie series, we have calculated the following invariant

4 quantities: Fractal Diension D (Higuchi s Algorith) and the Hurst exponent fro the rescaled range. For the Acapulco station we study the behavior of the Fractal Diension fro 1993; we study the teporal evolution of the fractal Diension D (figure 2). Fig. 2 Tie evolution of fractal diension D, The october 24, 1993 an earthquae of Mw=6,6 ocurred. In october 14 appears anoalous behavior of the fractal diension D, and of the Hurst exponent

5 4. Concluding rears By eans of ellectrotelluric tie series taen fro the Acapulco station, near of Middle Aerican trench, which is a very seiically active zone, we study the dynaical behavior of the fractal diension.we have to find that the critical behavior of the fractal diension (D 1.8) to be able is correlated with the occurrence the seiss with agnitude greater or equal than Mw 5.8. References [1.] Cervantes-De la Torre F., A. Raírez-Rojas, C. G. Pavia-Miller F. Angulo-Brown, E [2.] Yépez and J. A. Peralta. A coparison between spectral and fractal ethods in electrotelluric tie series, Rev. Mex. Fis., 45, , [3.] Hayaawa Masashi, Ito Tetsuya and Sirnova Natalia. Fractal analysis ULF geoagnetic data associated with the Gua Earthquae on August, 8, Geophysical Research Letters, Vol. 26, No. 18, , Septeber [4.] Higuchi T., Approach to an irregular tie series on basis of the fractal theory, Physica D, , [5.] Lonitz C. Fundaentals of Earthquae Prediction, John Wiley & Sons., [6.] Varotsos P. and K. Alexoupoulos, Physical Properties of the Variations of the electric field of the Earth preceding earthquaes I., Tectonophysics, 110, 73-98, 1984a. [7.] Varotsos P. and K. Alexoupoulos, Physical Properties of the Variations of the electric field of the Earth preceding earthquaes II., Tectonophysics, 110, , 1984b. [8.] Riitae T., Earthquae Prediction Developents in Solid Earth Geophysics 9, Elsevier Scientific Publishing Copany., [9.] Yépez E. F. Angulo-Brown, J. A. Peralta, C. G. Pavía-Miller and G. González-Santos, Electric field patterns as seisic precursors, Geophys. Res. Lett., 22, , 1995.