Application of GEOTIME Computer Environment to Space-Time Modelling of Earthquake Preparation Processes

A. V. Ponomarev, G. A. Sobolev
Institute of Seismology, UIPE, Russian Academy of Sciences, Moscow, Russia

V. G. Gitis
Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow, Russia

Zhang Zchaocheng, Wang Guixuan, and Qin Xinxi
Center for Analysis and Prediction, State Seismological Bureau, Beijing, China

Electronic version of the paper submitted for publishing in Journal of Earthquake Prediction Research
© Copyright 1997 by A. Ponomarev, G. Sobolev, V. Gitis, Zhang Zchaocheng, Wang Guixuan, and Qin Xinxi
© Copyright 1997 by Geophysical Center RAS (electronic version only)
Figures 7, Tables 2

Abstract

An approach to the space-time analysis of multidisciplinary geophysical observations is described in relation to the geodynamic process of intraplate earthquake preparation. The GEOTIME computer Environment is applied to test the hypotheses about earthquake precursors. The data are processed by three stages: (i) cleaning the time series of geophysical measurements of seasonal rhythms, non-linear trend, noises and signal standardisation; (ii) calculation of space-time dynamic fields using the time series from all analyzed stations; (iii) detection of nonstationarities, estimation of dynamic fields on significance level, and geophysical interpretation.

Retrospective predictions of Tangshan (July 28, 1976, M = 7.8) and Datong (October 19, 1989, M = 6.1) earthquakes are considered as an example. Daily time series obtained from 10 stations since 1972 for Tangshan and from 10 stations since 1981 for Datong were processed to model the process of earthquake preparation and to detect the earthquake precursors. The suggested space-time approach is shown to be effective for research on earthquake prediction.

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1. Introduction

The problem of reliable prediction of earthquakes still remains unsolved in spite of the tremendous efforts of scientists in many countries. The difficulty is largely due to the complicated task of identifying earthquake precursors from geophysical monitoring data.

The obstacles to the solution of the latter problem have several main causes:

Nonetheless, we may presume on the basis of a vast experience accumulated in many countries, that precursors were actually observed in a number of cases. On the observation station, their form can be approximated by several types of signals; i.e., the appearance of distortion of the trend, the baylike anomaly, the unipolar or double-polar impulse. It is also assumed that the precursors can occur and disappear repeatedly in the course of preparation of an earthquake.

A great amount of research was dedicated to the determination of the methods of recognition of earthquake precursors from seismological, geophysical, hydrogeological, geochemical, etc., data. We shall mention here but a few of the summarising works [Ma Zonglin, et al., 1989; Continental Earhquakes, 1993; Sobolev, 1993].

The representativity and completeness of data on the processes of earthquake preparation are determined primarily by the density of the measurement network and by the time longevity of synchronous observations. Apparently, the prognostic observations on intracontinental earthquakes accumulated in China are the most impressive by their volume and the time periods they cover. In contrast to the observations collected in the Benioff zones, in China it is possible to analyze the measurements of the stations surrounding the epicenter of an earthquake.

In the present paper we suggest an approach to the analysis of geodynamic processes from multidisciplinary data of geophysical monitoring and discuss the results of the tests with the methods of short-term earthquake prediction; we also make preliminary estimates (within the scope of the available experimental data) of the significance of geophysical anomalies preceding the Tangshan (north-eastern China, July 28, 1976, M=7.8) and Datong (October 19, 1989, M=6.1) earthquakes.

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2. Initial data

In the analysed region, there are about 50 stations at which the geophysical, hydrogeological and hydrochemical data were being recorded for several decades. All the time series have been selected from the data mass that had no equipment failures and conducted observations every day sta ting not later than on Jan. 1, 1972 for the Tangshan earthquake and not later than on Jan. 1, 1981 for the Datong earthquake. In all, only 16 time series of different geophysical parameters, obtained by the irregular measurement network, satisfy all these requirements.

Table 1 gives a total list of the series of diurnal values of geophysical, hydrogeological and hydrogeochemical parameters, which were used in the process of research.

The stations 1 to 10 were selected for the analysis of the Tangshan earthquake; the stations 7 to 16 were chosen for the analysis of the Datong earthquake.

In the course of the analysis, two major principles were strictly observed: I) we included data limited by one date of 24 hours before the earthquake to prevent using later data; 2) we applied observation series of equal length. In this way, the analysis of variations before the Tangshan earthquake was based on the observation period ranging from the beginning of 1972 till July 27, 1976 and from the beginning of 1981 till October 18, 1989 for the Datong earthquake.

When processing the time series, we used the simplified additive model of the signal. It was presumed that the measured signal X(t) is composed of the response to the geodynamic process S(t), periodic components of the seasonal rhythm U(t), and the high-frequency noise with the zero average V(t):

X(t) = S(t) + U(t) + V(t). (1)

Link to Fig. 1 Figure 1 (a) shows an example of the time series of diurnal values of tilts at station FS. Intensive seasonal variations of the annual period are apparent; they are complicated by greater high-frequency peaks; the beginning of the latter in July coincides with the periods of intensive rainfall, as indicated by meteorological data. The spectral analysis of the initial data shows that all seasonal variations have maximums of the annual period. Figure 1 (c) gives an example of the changes in the water level in the bore-hole at station TS. At this point the periodicity of the seasonal variations, though less distinct, still shows numerous one-day peaks, most of which were caused, apparently, by technogenic interference or random errors of the operators. In order to exclude the peaks for all signals, we conducted the median smoothing out with a 5-days interval.

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3. Methods

3.1. The procedure of data processing

The availability of spatially distributed synchronous observations allows one to apply the space-time approach realized in the GEOTIME computer environment [Gitis, et al., 1994; Gitis, et al., 1995]. The idea of this approach is based on the alternative of the method of data presentation. The time variations of geophysical parameters synchronously measured at different points of the region and the data of the earthquake catalogue are transformed into dynamic fields representing three-dimensional rasters with two spatial and one temporal co-ordinates. A sufficiently extensive set-up of space-time transformations over dynamic fields is realized in the GEOTIME medium; these transformations allow us to generate various secondary dynamic fields from the initial ones.

It is assumed that after elimination of seasonal rhythms in the absence of earthquake preparation the dynamic fields are inhomogeneous in space, but quasistationary in time. The appearance of a precursor, which occupies a certain related subset of elements of the raster, violates the stationarity of the process.

In order to determine the non-stationarity, the current observation interval is divided into two consecutive sub-intervals T1 and T2, of which the former is several times longer than the latter. The duration of both sub-intervals are determined by the researcher depending on the statistical properties of the background signal within the interval without precursor and on the expected duration of anomalous changes. The problem is reduced to testing the hypothesis of statistical homogeneity of two random sample sets. The hypothesis about the coincidence of parameters of the sample set distributions is tested by a certain statistics, which depends on the selected statistical model. In the case when several dynamic fields of different physical nature are jointly analyzed (the multidisciplinary approach), their values at raster points are multidimensional vectors, and multidimensional statistical models are used to verify the hypothesis.

In our case, the vector dynamic fields, computed from the time series of different types of the measured parameters, are not representative owing to the restricted number of stations. We, therefore, resort to a compromise by using the GEOTIME system to obtain a unified scalar dynamic field for all temporal series recorded at all available stations regardless of the physical nature of the measured values.

For this purpose, the signals from all stations should be first of all standardized (normalized by variances).

After standardization, the data processing is carried out by three stages, i.e., I - cleaning the time series of seasonal rhythms; II - calculation and transformation of dynamic field of precursors; III - calculation and analysis of dynamic fields of precursors' significance.

3.2. Stage I

In the course of the initial stage we proceeded from the generalized world experience of research on earthquake prediction; its basic facts are that earthquake precursors can be observed during several tens of years (long-term), several years and several months (middle-term), weeks and days (short-term), and a few hours and less (operative) before the moment of the actual earthquake.

The relatively short series of diurnal observations before the Tangshan and Datong earthquakes of about 5 and 9 years duration, correspondingly, did not allow us to analyze the long-term precursors, and we analyzed the possible appearance of only middle- and short-term precursors. The rather large and complicated by form variations of seasonal rhythms also provided little opportunity for identification of precursors with duration of more than a year. Consequently, at the present state of research, the analysis was aimed at finding anomalous changes of from one to several months duration.

The pattern of seasonal rhythm was estimated by the time series interval 2 years long. It was assumed that the seasonal rhythm remains unchanged during the next year (the year of prognosis). For example, the seasonal rhythm for the Tangshan earthquake was estimated by data of 1972 and 1973 and predicted for 1974. This procedure was repeated for every following year. In order to retain for analysis the whole observation series before the Tangshan earthquake since 1972, the image of the seasonal rhythms, based on the material of 1973-74 and 1974-75, was predicted backwards, i.e., for 1972 and 1973, respectively. The seasonal patterns computed for all these years were then subtracted from the initial time series.

Figure 1 (b, d) shows examples of signals obtained after subtraction of seasonal rhythms. It is obvious that these realizations contain not only anomalies associated with incomplete removal of the seasonal trend, but also other deviations of unknown nature and probably the earthquake precursors among them.

For different physical parameters the precursors can be both positive and negative anomalies, as illustrated, in particular, by the given examples. In 1975-76, at one of the stations, a lowering of the signal's level was recorded (Figure 1 (b)), whereas at another station (Figure 1 (d)) the level has risen, and both anomalies can be regarded as the possible precursors of the Tangshan earthquake.

3.3. Stage II

During stage II, the spatial interpolation is carried out for every time section of signals from all stations. The signals were squared to avoid mutual exclusion during interpolation of anomalies observed at different stations. For the dynamic field, the raster was adopted having 0.1o in latitudinal direction, 0.067o in meridian direction, and 5 days on the time coordinate. Interpolation was made by formula

Equation 2(2)

where Z(l, j, t) is interpolated value at point (l, j, t), Yn(t) is value of signal of n-station at moment t, rn is the distance from n-station to the point (l, j, t), with rn = 0,   Z(l, j, t) = Yn(t).

3.4 Stage III

The third stage is aimed at identifying precursors in time and in space. With this purpose in view, two statistical hypotheses were verified. The H0 hypothesis involves mathematical expectations of sequences in the first window T1 and in the second window T2Ha hypothesis presumes that the mathematical expectation of the sequence in the second window is greater than that in the first. If Ha hypothesis is applied, then it is assumed that a non-stationarity is observed in T2 interval. If H0 hypothesis is selected, then the process is recognized as stationary. The verifying criterion of H0 hypothesis against Ha hypothesis is based on calculation of statistics representing the difference of selected average values:

Equation 3(3)

where
Equation 3a

Equation 3b

T1 = 73, T2 = 6, which at 5-days step of the time co-ordinate corresponds to 365 and 30 days.

It is obvious that with H0 hypothesis the mathematical expectation of statistics G(a, j, t) is close to 0. But where as the counts down of the Z(a, j, t) signal are strictly correlated, the estimation of mean square deviations of the difference of selected averaged values, if H0 hypothesis is applied, meets with great difficulties. Let us assume that with H0 hypothesis the variance s2(a, j, t) of the signal is a slowly varying function of t and so it is the same in both windows T1 and T2. Then the upper limit of the root mean square of random variable G(a, j, t) is equal to 2s(a, j, t). It is convenient to normalize the G statistics by the statistical estimate of root mean square:

Equation 3(4)

where
Equation 3a

The u(a, j, t) statistics evaluates the degree of deviation from the stationary. With H0 hypothesis the statistics has the expectation close to 0 and the root mean square less than 1.

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4. Modelling

4.1. Tangshan

At selected duration of windows T1 and T2, the period of 1972 is entirely reserved to instructive material, and the first map of dynamic field of deviation statistics from the stationary refers to January 1973. The maps that followed were compiled with the 5-days shift. In total, 257 maps were prepared for deviation analysis; the latest map covers the period from June 24 to July 23, 1976.

The analysis of the maps reveal anomalies in July-August of some years owing to incomplete removal of the seasonal rhythm. The periods from September through June are free of this drawback, and their anomalies, apparently, had other causes including those of geodynamic character.

Link to Fig. 2 Unlike the two previous years, in September of 1975, a powerful anomaly with a maximum occurred over almost the entire studied area of northeastern China. It gradually attenuated and practically disappeared in April 1976. Only two anomalous stations remained, TS and SQ, in the region of the future Tangshan earthquake. In May 1976, the anomaly in the area of these stations grew intensively, as shown in Figure 2 (1) representing the map of that period. At the same time, a less intensive anomaly appears in the Beijing area. For easier orientation, Figure 2 (1) also shows tectonic faults and epicenters of the future Tangshan earthquake and of the two strongest aftershocks with magnitudes 6.9 and 7.0. There is a striking irregularity in the distribution over the territory of recording stations that supplied the initial observation series.

Link to Fig. 3 The next map in Figure 2 (2) represents the period from May 14 till June 13. At that time the anomaly in the Beijing area reached its maximum, and that in Tangshan was steadily growing. The map in Figure 2 (3) (May 29-June 28, 1976) shows the maximum of the anomaly in Tangshan region; after that time it gradually attenuates till the moment of the earthquake (Figure 2 (4) ). The dynamics of the development of anomalies along the A-B profile of latitudinal strike (Figure 2 (4)) can be followed in Figure 3 . The curves 1, 2, 3, 4 correspond to the periods of maps in Figure 1 (1, 2, 3, 4).

Link to Fig. 4 For comparison, Figure 4 shows 6 maps of the previous three years covering the period of the beginning (May 4-June 3) and the maximum (May 39-June 28) of the Tangshan anomaly. It is apparent that during all these years, in the Tangshan area, no significant anomalous changes were recorded in the field of the complex of studied parameters.

4.2. Datong

A similar processing was carried out for the time series referring to the Datong earthquake. In this case the first map of dynamic field of deviation statistics from the stationary refers to January 1982. The maps that followed were compiled with the 5-days shift. In total, 568 maps were prepared for deviation analysis; the latest map covers the period from September 15 to October 14, 1989.

Link to Fig. 5 An analysis of these maps shows that the dynamics of the field of the studied parameters largely differ from the dynamics before the Tangshan earthquake. This is evident from the series of maps in Figure 5. During the period from July 21 till August 20, 1989 (Figure 5a), in the region of Tangshan, an anomaly appears, which then grows in intensity and spreads west and east. The anomaly reaches its maximum in the period from August 20 till September 19 (Figure 5c), and then reduces (Figure 5d). In this case, the irregularity of distribution of measurement stations becomes apparent. In the southwest, there is only one TY station, and there are no data for the region of the Datong earthquake.

Link to Fig. 6 For comparison, a series of maps for the previous six years is demonstrated in Figure 6 (1983-1988) for August - September; during that period in 1989, the anomaly in the studied region reached its maximum. Apparently there no considerable anomalous changes in intensity and area at that time.

Link to Fig. 7 The dynamics of the development of the anomaly in 1989 before the Datong earthquake are shown in Figure 7. The plots 1, 2, 3, 4 along the latitudinal profile A-B correspond to the periods of corresponding maps in Figure 5a, b, c, d. The migration of the process is clearly traced in the western direction; it is less distinct in the eastern direction where the region is confined to the location of CL station. Unfortunately, the data of JX station hear Haichen were not available to the anthars for the period of the Datong earthquake.

4.3. Modelling of epicentral anomalies

4.3.1. Justification of the model
A comparison of dynamic fields (Figure 2 and Figure 5) shows that the shape and size of the anomaly that precedes the Tangshan earthquake greatly differs from the anomaly before the Datong earthquake. The Tangshan anomaly almost covers the region of the future epicentral earthquake zone, while the Datong anomaly covers practically the whole area on which the stations are located. We can suppose that these anomalies reflect different mechanisms of manifestation of precursors. The Tangshan anomaly shows that the generation of precursors has local character and is connected with the focus of the expected earthquake. But the Datong anomaly demonstrates the regional character of earthquake preparation, where precursors have on indirect association with the focus through the changes of tectonic stresses on a vast territory.

The epicentral character of manifestation of precursors was discussed in [Chen Yong, et al., 1992; Zhang Zhaocheng, et al., 1992], where retrospective data are given on the dependence between the relative number of stations that recorded the precursor and the distance to the earthquakes epicenters. For the earthquakes with magnitude 7, these data are given in Table 2.

Let us assume that at distances of the order of 1000 km, the precursors cease to bee observed and the amplitude of a precursor diminishes approximately by the same law as the number of stations that recorded the earthquake precursors. In this case, Table 2 can be approximated by the attenuation function

F(R) = A(exp(-0.02R) - 0.27) (5)

where A is the amplitude of the signal, R is the distance to the source of the signal in km.

In this part of the paper we shall make an attempt to model a generalized precursor of the Tangshan earthquake by using the attenuation model (5) to localize the future source.

Let us indicate the time series obtained on observation stations n = 1, 2, ..., N by u(n, t). We shall assume that, for any fixed moment of time, the center of the precursor's signal coincides with one of the points of the raster k = 1, 2, ..., K and that the values of the time series at the observation stations are expressed by relationship

un = AF(Rnk) + xn (6)

where A is the amplitude of the signal, k is the number of the raster point, in which the center of the signal is located; xn are the independent Gauss values with zero mathematical expectancy and the mean square deviation s.

4.3.2. Estimation algoritm
Let us estimate the parameters of the signal by the method of least squares. The estimations are obtained by minimizing the functional

Equation 7(7)

With known k = $\hat{k}$ and if the signal propagates from point $\hat{k}$, the estimation of the amplitude A($\hat{k}$) is determined by expression

Equation 8(8)

By sorting out all the possible values of k = 1, 2, ..., K, we obtain different values of A($\hat{k}$) and residual sums of squares

Equation 9(9)

In order to evaluate the center of the signal - the K point-, let us analyse the criterion of relation of square estimation of the measured signal to the square of discrepancy (signal/noise ratio)

Equation 10(10)

where
Equation 11(11)

We should note that the vectors of the signal F = (F(R1k), F(R2k), . . . , F(Rnk)) and of the discrepancy, obtained by the least squares method, are orthogonal and in sum compose the vector of observations u = (u1, u2, . . . , uN).

Therefore,
Equation 12(12)

and
Equation 13(13)

If we suppose that at the analysed moment of time the signal is absent, that is un = xn, then a(k) is the relation of the Gauss square value with zero mathematical expectancy and dispersion s2 to the sum of squares N-1 of Gauss values with the same parameters.

It is convenient, instead of a(k), to consider the monotonously associated with it value

Equation 14(14)

Value b(k) acquires the magnitude ranging from 0 to 1. The value b(k) = 1 corresponds to the situation when un = AkF(Rnk), i.e., the signal/noise ratio is equal to \infty. At b(k) = 0, the signal is absent. At b(k) \le 0.5, the discrepancy in parameter A evaluation is greater than the amplitude evaluation. Therefore, independently of the value of amplitude Ak estimation, we can admit that, in the studied region, the signal corresponding to the assumed model was not observed.

On the basis of these considerations, at b(k) \le 0.5, the estimation of the position of the signal $\hat{k}$ center we shall choose for the condition of the maximum of function b(k), k = 1, 2,..., K, i.e.,

Equation 15(15)

and $\hat{A}$($\hat{k}$) value shall be assumed as the estimation of the amplitude of the signal.

4.3.3. Modelling
The modelling of the epicentral anomaly of the Tangshan earthquake was carried out on the basis of the average diurnal time series obtained at stations 1 to 10 (Table 1). It was presumed that the Tangshan earthquake precursours are generated by one source located within the polygon (Figure 2), and the change of the signal is described by equation (5).

The first stage of processing, as in part 3, included standartization of series, suppression of the seasonal rhythms, and squaring. At the next stage, the time series of deviations for stationarity were calculated by formulas (3) and (4) with substitution in them of coordinates l, j by the number of the stations is at the value of parameter T1 = 365 days and T2 = 30 days. The last stage was the transition to the space-time model by estimation of parameters of the model $\hat{k}$ and $\hat{A}$($\hat{k}$) with 5 days interval.

Figure 7 shows plots of changes of criterion of the presence of signal b($\hat{k}$), estimation of its amplitude $\hat{A}$($\hat{k}$) and the distance r($\hat{k}$, C) between the center of signal $\hat{k}$ and the real earthquake epicenter. It is apparent that during almost the whole interval up to August 1975 b($\hat{k}$) < 0.5. This means that, according to our supposition, the epicentral precursor signal was either absent, or did not comply to the model (5). A year before the earthquake, since August-September 1975, the b($\hat{k}$) values sharply increased and exceeded 0.5. In other words, at that time interval, the suggested model conforms best with the set of real data. Concurrently, an essential increase of the signal's amplitude was recorded. Finally, since November 1975, the center of the modelled anomaly was shifted to the epicentral area of the Tangshan earthquake with deviations from the future epicenter reaching about 50 km.

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5. Conclusions

The present paper suggests a new technology of space-time analysis of geophysical series tested by real data. The study is based on transition from the analysis of time series to the analysis of trivariate rasters - with two spatial and one temporal coordinates.

Two approaches were realized:

  1. spatial interpolation of observation data and compilation of time sections;
  2. calculation from time sections of spatial anomalies according to a certain hypothesis about the geometry of the precursor.

The following preliminary conclusions can be drawn from the analysis of the initial data and maps at our disposal showing the complex of the studied geophysical, hydrogeological and geochemical parameters.

From May till July 1976, an anomaly was recorded in the region of the future Tangshan earthquake; its amplitude, probably, exceeded the random deviations of the background noise. The coincidence of the maximum of the anomaly with the Tangshan earthquake and the absence of such anomaly in the analyzed previous years does not contradict the hypothesis about its geotectonic origin. If that supposition is true, then the anomaly is a medium-short -term precursor that appeared in the vicinity of the earthquake's focus. Let us recall that precursors with duration longer than a year or less than a few days are not analyzed in this paper on account of restricted observation series.

On the other hand, the Datong earthquake of October 19, 1989, occurred against the background of regional anomaly covering a large part of north-eastern China and localized near the epicenter. We believe, that the earthquake proper is only indirectly connected with the observed anomaly in the field of geophysical parameters. Both events could have been caused by regional changes in the stress state of the environment the nature of which is as yet unknown.

We wish to emphasize that our conclusion is open to further revision, because it is based on obviously incomplete experimental data and extremely irregular observation network.

Other conclusions of the present research are as follows.

It is necessary to eliminate all possible errors of external origin in the initial data.

It is desirable to add to the analysis the available observation series from a larger set of stations preferably covering the area with greater regularity.

It seems expedient to carry out a formalized comparison of the available series of prognostic observations with similar series of certain meteorological parameters and, primarily, the air and soil temperature, the amounts of precipitation, and atmospheric pressure.

It is important to include into the processing the data on seismicity for better insight into the geodynamic process.

The prognostic features could be more readily identified by creation of models of space-time precursors formation based on the physics of the earthquake focus and on the experience of experimental observations.

Meanwhile, the elaborated variant of the GEOTIME system allows us to study the geodynamic process using a complex of heterogeneous data of prognostic observations. The experience of the present research has indicated the direction in which further development of the system should be continued.

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Acknowledgments

We extend our thanks to the collaborators at the Center for Analysis and Prediction, SSB, China, who have kindly made available the materials of experimental observations. The work was accomplished within the frame of the Agreement between the State Seismological Bureau of China and the Russian Academy of Sciences.

The research is supported by grants No. 97-05-65906 and No. 97-07-90326 from Russian Foundation for Basic Researches.

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References

1. Ma Zonglin, Fu Zhengxiang, Zhang Yingzhen et al., Earthquake Prediction. Seismol. Press: Springer, 1989, p.332.

2. Continental Earhquakes. Seismol. Press, Beijing, 1993, p. 576.

3. Sobolev G. A., Fundamentals of Earthquake Prediction. Nauka, Moscow, 1993, p. 311 (in Russian).

4. Gitis V. G., Osher B. V., Pirogov S. A., Ponomarev A. V. , Sobolev G. A., Jurkov E. F., A System for Analysis of Geological Catastrophe Precursors. Journal of Earthquake Prediction Research, Vol. 3, no. 4, 1994, pp. 540-555.

5. Gitis V. G., Osher B. V., Pirogov S. A., Ponomarev A. V. , Sobolev G. A., Jurkov E. F., Dynamic Fields Analysis System. Cahiers du Centre Europeen de Geodynamique et de Seismologie, Vol. 9, 1995, pp. 129-140.

6. Chen Yong,Wang Wei, Zhu Yueqing and Ji Ying., Multidisciplinary approach used in expert system for earthquake prediction in China. Journal of Earthquake Prediction Research, Vol. 1, no. 1, 1992, pp. 107-113.

7. Zhang Zhaocheng, Zheng Dalin, Luo Yongsheng and Jia Qing., Studies on earthquake precursors and the multidisciplinary earthquake prediction in China mainland. Journal of Earthquake Prediction Research, Vol. 1, no. 2, 1992, pp. 191-205.

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