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Performance evaluation of the M8 algorithm to predict M7+ earthquakes in Turkey

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Abstract

The M8 algorithm is one of the most reliable intermediate-term middle-range earthquake prediction algorithms. The present study evaluates the ability of the M8 algorithm and its modified versions for predicting major events (M7+) in Turkey. Thirty different algorithms were developed by changing the radius of circle of investigation (CI) and the lower magnitude cutoff of the M8 algorithm. These modified algorithms were executed all over the territory of Turkey, and the results were evaluated using the error diagram. Each modified algorithm was executed for consecutive half-year intervals over a specified period of time. Subsequently, the seismic catalog was updated, and failures-to-predict ratio and the fraction of alarm were considered. Results showed that the location of areas of alarm change gradually over consecutive intervals, and no sudden changes can be observed. In addition, the annual changes of areas of alarm are not random and follow a pattern. This study also showed that the modified algorithm having a three to six annual average of events and a 393-km CI radius is an efficient algorithm for predicting the future seismic events in Turkey. This algorithm predicted six out of six target events, retrospectively, with a confidence level of 96.4 %. According to the obtained results, it will be possible to rely on this modified algorithm to predict near future earthquakes of Turkey. Furthermore, this study proves that it is possible to alter the M8 algorithm for being used in regional studies.

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Author information

Authors and Affiliations

  1. School of Mining Engineering, College of Engineering, University of Tehran, Tehran, Iran

    Masoud Mojarab & Hossein Memarian

  2. Seismology Research Center, International Institute of Earthquake Engineering and Seismology (IIEES), Tehran, Iran

    Mehdi Zare

Authors
  1. Masoud Mojarab
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  2. Hossein Memarian
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  3. Mehdi Zare
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Corresponding author

Correspondence to Hossein Memarian.

Appendix 1 (M8 algorithm)

Appendix 1 (M8 algorithm)

The M8 algorithm consists of the following steps:

  1. 1.

    Determination of the target magnitude: The M8 algorithm is designed to predict the earthquakes greater than the magnitude of M 0. The magnitude range of target events is between M 0 and M 0 + Δm, where Δm is less than 1. In the case of having an adequately complete dataset, different overlapping ranges of M 0 with increments of 0.5 can be considered. However, sometimes, a natural cutoff magnitude is suggested by the actual distribution of earthquake size.

  2. 2.

    Determination of the investigation area: The understudy region is fully covered by overlapping circles of investigation, CIs, of a fixed radius (R(M 0) = (exp(M 0 − 5.6) + 1) × 111/2). CI of M8 algorithm is proportional to the linear dimensions of the target earthquakes and are about three to four times smaller of their preparation zone, e.g., R = 100.43M (Dobrovolsky et al. 1979).

  3. 3.

    Preparation of the catalog: Within each CI, the sequence of main shocks is considered. So, removing aftershocks and declustering of the events should be performed by means of a well-known algorithm, such as that of Keilis-Borok et al. (1980). Each main shock is characterized by the vector of [t i , m i , h i , b i (e)], where i (i = 1, 2, …) is the number of the main shock, t i is its origin time, m i is its magnitude, h i is its focal depth, and b i (e) is the number of aftershocks of magnitude M aft and above happening during the first e days. The sequence is normalized by the lower magnitude cutoff, M = M min (Ñ), where Ñ is a standard value of the average annual number of earthquakes in the sequence.

  4. 4.

    Computation of the main M8 functions: For each CI, in a sliding time window of (t-s, t) and magnitude range of [m, M 0), several average values should be computed to quantify the features of seismic sequence. These values are as follows:

    1. (i)

      N (t): The number of earthquakes of magnitude m or greater in the time window of (t-s, t). This function represents the rate of seismic activity; N (t) = N (t| m, s).

    2. (ii)

      L (t): The deviation of seismic activity from a longer-term trend over the period of (t 0, t); L(t) = L (t | m, s, t 0) = N (t | m, s) − N (t-s | m, t-s-t 0) × s/(t-s-t 0).

    3. (iii)

      Z (t): The linear concentration of main shock sources which is equal to the ratio of the average source diameter to the average distance between sources. This function indicates the linear concentration of earthquake sources; Z (t) = Z (t | m, M 0 − g, s, α, β)

    4. (iv)

      B (t): The maximum number of aftershocks, b i (e), among events of magnitude range of [M 0 − p, M 0 − q] during time interval of (t-s, t). Each of the functions of N, L, and Z are calculated twice for different magnitude cutoffs (M = M min (Ñ), for Ñ = 10 and 20). Therefore, the seismic sequence is characterized by average values of seven functions, including N 1, N 2, L 1, L 2, Z 1, Z 2, and B.

  5. 5.

    Determining TIPs “very large” values for each function are defined as the values higher than the Q percent of all of the encountered values. Whenever at least six out of seven abovementioned functions, including B, become very large, in a specified narrow time window of (t-u, t), a time of increased probability of earthquake of magnitude M 0+, TIP, starts. Also, this alarm or TIP should last for two successive time frames, t and t + 0.5. The following values of N (t), L (t), and Z (t) functions defined the original version of the M8 algorithm: D (M 0) = {exp (M 0 − 5.6) + 1} in degrees of meridian, which is equal to 384, 560, 854, and 1333 km for M 0 = 6.5, 7.0, 7.5, and 8, respectively; s = 6 years; s′ = 1 year; g = 0.5; p = 2; q = 0.2; u = 3 years; and Q = 75 % for B and 90 % for the other six functions. The value of 5.6 in the formula of D (M 0) is the normalizing value that makes D (M 0 = 8.0) = 12° in degrees of the Earth’s meridian, same as that of Keilis-Borok and Kossobokov (1987).

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Mojarab, M., Memarian, H. & Zare, M. Performance evaluation of the M8 algorithm to predict M7+ earthquakes in Turkey. Arab J Geosci 8, 5921–5934 (2015). https://doi.org/10.1007/s12517-014-1624-3

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