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The negative effects of natural disasters on human life exist from the foot and did not occur at a specific time but found since the creation of mankind. Humans coexist with extreme events all the time, only when the intensity of the event becomes greater than a certain level there is a resulting disaster. Small earthquakes occur all of the time with no adverse effects. Only large earthquakes cause disasters. Statistical analysis reveals that larger events occur less frequently than small events. Through the large number of seismic events, we find that at the end of the year may have a series of seismic events with different values depending on the strength of activity whether it is high or low on Richter scale and the assessment is only for the greatest value in a year even if recurring this value and the volume of dangerous increases and the frequency of their occurrence according to an ongoing activity, major disasters result from a small number of events and sustained results in a large and devastating event, and can be represented by these results and amounts On a log-scale which points are almost on a straight line and a clear indication of the evaluation event. Through previous data analysis we can understand the following events behavior for coordination and guidance on the development of evacuation plans on the expected future and use a Weibull equation to estimate the frequency of the event and the return again as a percentage for each event and the probability of the occurrence of a particular earthquake to some degree on the Richter scale in the sea during any period. Past records of earthquakes at the West Coast of the Kingdom of Saudi Arabia (Red Sea) for years 1913-2016 are used to predict future conditions concerning the annual frequency, the return period, the percentage probability for each event, and the probability of a certain-magnitude earthquake occurring in the region during any period.

The natural disaster damaged the old man’s life does not specify a period of time, and perhaps the most important “earthquakes” that threatens “human civilization”. The most destructive disaster of nature is a severe earthquake and its destroying effects. If the earthquake occurs in a populated area, it may cause many deaths and injuries and extensive property damage regions. The ultimate goal of seismic hazard assessment and risk evaluation for a particular site or area is to condense seism-tectonic knowledge and experience into parameters used for predicting seismic parameters which in turn can be applied by engineers in design and subsequent earthquake resistant construction.

Statistical surveys support researches on the likelihood of future earthquakes. A primary goal of earthquake research is to increase the reliability of earthquake probability estimates. With a greater understanding of the hazard parameters of earthquakes, we may be able to reduce damage and loss of life from this destructive event. Statistics help us to predict the future events based on previous events.

We find that in the western region of Saudi Arabia is growing concern on the volcanic activity associated with earthquakes in the Red Sea have been the work of affluent studies to assess the seismic risk level. Western Region of Saudi Arabia is considered to be a moderately active seismic zone as shown in

Red Sea is a body of water located between the western coast of the Arabian Peninsula and Africa. The overlooking countries on the Red Sea are: Saudi Arabia, Egypt, Sudan, Yemen, Eritrea and Djibouti. Its strategic movement of marine transportation as connection of the South Ocean through the Strait of Bab el Mandeb and extending north to reach the Sinai Peninsula, and there are branches off to the Gulf of Aqaba and the Gulf of Suez, which leads to the Suez Canal. The length of this sea 1900 kilometers and currently up in some areas to 300 km. The deepest point in the Red Sea up to 2500 m and the rate of decline is 500 m. Red Sea, an area of 450,000 km^{2}.

When looking around us to natural disasters, particularly earthquakes, we find they are warning of a disaster are taken into account in the event of predictable after a study and give warning of potentially harmful earthquakes in enough time to prepare appropriate for this disaster and minimize the loss of life and property [

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Earthquake prediction can be considered into two types. First is the statistical prediction which is based on previous events; Data are collected from the records. Second is deterministic prediction which is made from the earthquake signs.

Most extreme event analysis is concerned with the distribution of annual maximum or minimum values at a given site. These events are given a rank, m, starting with m = 1 for the highest value, m = 2 for the next highest and so on in descending order. Each earthquake magnitude is associated with a rank, m, with m = 1 given to the maximum magnitude over the years of record, m = 2 given to the second highest magnitude, m = 3 given to the third highest one, etc. The smallest earthquake magnitude will receive a rank equal to the number of years over which there is a record, n. Thus, the discharge with the smallest value will have m = n = 100.

There are several formulas for calculating the probability value. The Weibull formula will be used because of its ease of use. The US Geological Survey [

According to the Weibull equation [

Year | Number of Earthquakes | Minimum Magnitude | Range | Maximum Magnitude |
---|---|---|---|---|

1913 | 1 | 5.8 | 5.8 - 5.8 | 5.8 |

………. | ||||

1921 | 1 | 5.6 | 5.6 - 5.6 | 5.6 |

… | ||||

1962 | 2 | 4.8 | 4.8 - 5.3 | 5.3 |

………. | ||||

1964 | 1 | 4.8 | 4.8 - 4.8 | 4.8 |

1965 | 1 | 4.1 | 4.1 - 4.1 | 4.1 |

1967 | 28 | 4.1 | 4.1 - 5.6 | 5.6 |

1969 | 19 | 4.5 | 4.5 - 6.1 | 6.1 |

1970 | 3 | 4.5 | 4.5 - 4.8 | 4.8 |

1971 | 1 | 4.8 | 4.8 - 4.8 | 4.8 |

1972 | 1 | 5.1 | 5.1 - 5.1 | 5.1 |

………. | ||||

1974 | 3 | 4.4 | 4.4 - 5.1 | 5.1 |

1975 | 6 | 4.6 | 4.6 - 5.3 | 5.3 |

1976 | 6 | 4.3 | 4.3 - 4.8 | 4.8 |

1977 | 1 | 5.9 | 5.9 - 5.9 | 5.9 |

1978 | 4 | 4.4 | 4.4 - 5.1 | 5.1 |

1979 | 7 | 4.1 | 4.1 - 5.1 | 5.1 |

1980 | 11 | 4.3 | 4.3 - 5.4 | 5.4 |

………. | ||||

1982 | 2 | 4.6 | 4.6 - 4.8 | 4.8 |

1983 | 2 | 4.1 | 4.1 - 4.7 | 4.7 |

1984 | 9 | 3.1 | 3.1 - 4.7 | 4.7 |

1985 | 4 | 3.7 | 3.7 - 4.6 | 4.6 |

1986 | 3 | 3.4 | 3.4 - 4.7 | 4.7 |

1987 | 2 | 4.7 | 4.7 - 4.9 | 4.9 |

1988 | 16 | 3.8 | 3.8 - 5.3 | 5.3 |

1989 | 4 | 2.1 | 2.1 - 4.2 | 4.2 |

1990 | 4 | 4.2 | 4.2 - 4.8 | 4.8 |

1991 | 5 | 2.9 | 2.9 - 4.7 | 4.7 |

1992 | 11 | 2.4 | 2.4 - 4.5 | 4.5 |

1993 | 65 | 2.3 | 2.3 - 5.6 | 5.6 |

1994 | 21 | 2.3 | 2.3 - 4.9 | 4.9 |

1995 | 15 | 2.4 | 2.4 - 4.3 | 4.3 |

1996 | 41 | 2 | 2 - 5 | 5 |

1997 | 40 | 2.3 | 2.3 - 5.5 | 5.5 |

1998 | 25 | 2 | 2 - 4.2 | 4.2 |

1999 | 7 | 3.3 | 3.3 - 4.4 | 4.4 |

2000 | 77 | 1.5 | 1.5 - 4.9 | 4.9 |

2001 | 206 | 1.5 | 1.5 - 4.8 | 4.8 |

2002 | 477 | 1.3 | 1.3 - 4.5 | 4.5 |

2003 | 255 | 1 | 1 - 4.6 | 4.6 |
---|---|---|---|---|

2004 | 553 | 0.8 | 0.8 - 4.6 | 4.6 |

2005 | 386 | 0.7 | 0.7 - 4.3 | 4.3 |

2006 | 124 | 0.4 | 0.4 - 4.7 | 4.7 |

2007 | 616 | 0 | 0 - 4.5 | 4.5 |

2008 | 1037 | 0 | 0 - 4.2 | 4.2 |

2009 | 52 | 2.1 | 2.1 - 4.7 | 4.7 |

2010 | 66 | 0.1 | 0.1 - 4.4 | 4.4 |

2011 | 681 | 0.2 | 0.2 - 4.5 | 4.5 |

2012 | 117 | 1.3 | 1.3 - 4.5 | 4.5 |

2013 | 79 | 2.3 | 2.3 - 5.4 | 5.4 |

2014 | 25 | 3.1 | 3.1 - 4.1 | 4.1 |

2015 | 13 | 3.5 | 3.5 - 4.1 | 4.1 |

where: m = event ranking (in a descending order), and n = number of events in the period of record.

The percentage probability the (annual exceedence probability) for each magnitude is calculated using the inverse of the Weibull equation as follows:

From Equations ((1) and (2)) it is clear that P = 100/T%. For example, an earthquake equal to that of a 10- year one would have an annual exceedence probability of 1/10 = 0.1% or 10%. This would say that in any given year, the probability that an earthquake with a magnitude equal to or greater than that of a 10 year earthquake would be 0.1% or 10%. Similarly, the probability of an earthquake with a magnitude exceeding the 50 year one in any given year would be 1/50 = 0.02, or 2%. Note that such probabilities are the same for every year, but in practice, such an earthquake could occur next year, or be exceeded several times in the next 50 years.

Return period or Recurrence interval is the average interval of time within which a flood of specified magnitude is expected to be equaled or exceeded at least once. 100 year earthquake is an earthquake that is expected to occur, on the average, once every 100 years, or has a one percent chance of occurring each year.

A best-fit curve is drawn through the data points. From the best-fit curve, one can determine the earthquake magnitude associated with an earthquake with a recurrence interval of say 10 years, it is about 5.8 on Richter scale. This would be called the 10-year earthquake.

Similarly the recurrence interval associated with an earthquake magnitude of magnitude of 5 on Richter scale is about 17 year.

The annual peak information may also be presented with a logarithmic rather than a linear scale. This is often done to make the curve appear as a straight line and also to avoid a graph that will suggest either a zero or a one-

Rank (m) | Year | Maximum Magnitude | Probability (P) % | Period of return (T) |
---|---|---|---|---|

1 | 1969 | 6.1 | 0.961538462 | 104 |

2 | 1977 | 5.9 | 1.923076923 | 52 |

3 | 1913 | 5.8 | 2.884615385 | 34.66666667 |

4 | 1993 | 5.6 | 3.846153846 | 26 |

5 | 1967 | 5.6 | 4.807692308 | 20.8 |

6 | 1921 | 5.6 | 5.769230769 | 17.33333333 |

7 | 1997 | 5.5 | 6.730769231 | 14.85714286 |

8 | 2013 | 5.4 | 7.692307692 | 13 |

9 | 1980 | 5.4 | 8.653846154 | 11.55555556 |

10 | 1988 | 5.3 | 9.615384615 | 10.4 |

11 | 1975 | 5.3 | 10.57692308 | 9.454545455 |

12 | 1962 | 5.3 | 11.53846154 | 8.666666667 |

13 | 1979 | 5.1 | 12.5 | 8 |

14 | 1978 | 5.1 | 13.46153846 | 7.428571429 |

15 | 1974 | 5.1 | 14.42307692 | 6.933333333 |

16 | 1972 | 5.1 | 15.38461538 | 6.5 |

17 | 1996 | 5 | 16.34615385 | 6.117647059 |

18 | 2000 | 4.9 | 17.30769231 | 5.777777778 |

19 | 1994 | 4.9 | 18.26923077 | 5.473684211 |

20 | 1987 | 4.9 | 19.23076923 | 5.2 |

21 | 2001 | 4.8 | 20.19230769 | 4.952380952 |

22 | 1990 | 4.8 | 21.15384615 | 4.727272727 |

23 | 1982 | 4.8 | 22.11538462 | 4.52173913 |

24 | 1976 | 4.8 | 23.07692308 | 4.333333333 |

25 | 1971 | 4.8 | 24.03846154 | 4.16 |

26 | 1970 | 4.8 | 25 | 4 |

27 | 1964 | 4.8 | 25.96153846 | 3.851851852 |

28 | 2009 | 4.7 | 26.92307692 | 3.714285714 |

29 | 2006 | 4.7 | 27.88461538 | 3.586206897 |

30 | 1991 | 4.7 | 28.84615385 | 3.466666667 |

31 | 1986 | 4.7 | 29.80769231 | 3.35483871 |

32 | 1984 | 4.7 | 30.76923077 | 3.25 |

33 | 1983 | 4.7 | 31.73076923 | 3.151515152 |

34 | 2004 | 4.6 | 32.69230769 | 3.058823529 |

35 | 2003 | 4.6 | 33.65384615 | 2.971428571 |

36 | 1985 | 4.6 | 34.61538462 | 2.888888889 |

37 | 2012 | 4.5 | 35.57692308 | 2.810810811 |

38 | 2011 | 4.5 | 36.53846154 | 2.736842105 |

39 | 2007 | 4.5 | 37.5 | 2.666666667 |

40 | 2002 | 4.5 | 38.46153846 | 2.6 |

41 | 1992 | 4.4 | 39.42307692 | 2.536585366 |

42 | 2010 | 4.4 | 40.38461538 | 2.476190476 |

43 | 1999 | 4.4 | 41.34615385 | 2.418604651 |

44 | 2005 | 4.3 | 42.30769231 | 2.363636364 |
---|---|---|---|---|

45 | 1995 | 4.3 | 43.26923077 | 2.311111111 |

46 | 2008 | 4.2 | 44.23076923 | 2.260869565 |

47 | 1998 | 4.2 | 45.19230769 | 2.212765957 |

48 | 1989 | 4.2 | 46.15384615 | 2.166666667 |

49 | 2015 | 4.1 | 47.11538462 | 2.12244898 |

50 | 2014 | 4.1 | 48.07692308 | 2.08 |

51 | 1965 | 4.1 | 49.03846154 | 2.039215686 |

.............. | ||||

103 |

hundred percent exceedance probability. Moreover, a straight line curves are more easily allow extrapolation beyond the data extremes.

Percentage probability is determined by dividing one by the recurrence interval and multiplying by 100. For example, the probability that an earthquake magnitude will exceed the 100-year earthquake this year or any other year would be 1%.

Sometimes it is suitable to add a second X-axis to represent the return period to the first X-axis representing the annual exceedance probability.

From the fit line, one can determine the magnitude associated with an earthquake of a recurrence interval of say 30 years. This would be called the 30-year earthquake. The magnitude associated with the 30-year earthquake is about 5.8 Richter scale. Similarly the magnitude associated with an earthquake with a recurrence interval of 104 years (the 104-year earthquake) would have a measure of about 6.1 Richter scale.

The probability of a certain-magnitude earthquake occurring during any period t can be calculated using the following equation:

where P is the probability of occurrence over the entire time period, t, and P is the probability of occurrence in any year.

It is worth to apply Equation (3) for earthquakes of highest magnitudes which represent the most dangerous events in the location. The equation is applied for earthquakes of magnitudes 6.1, 5.9 and 5.8 Richter scale of probabilities of 0.96%, 1.92% and 2.88% respectively. The result is depicted in

A homeowner considering the costs of reinforcing a house against earthquakes will want to know how the risk varies during an average mortgage span of 30 years.

In this study, the statistical frequency analyses are applied to the recorded annual maximum earthquake magnitudes for Rea Sea province and the surrounding area in the westcoast of Saudi Arabia since 1913.

The risk of earthquakes, the return period and the probability of occurrence for a particular magnitude during any given year are calculated based on the analysis of data over a period of 104 years by applying Weibull equations.

The relation between magnitude and frequency and between magnitude and return period is represented as a curve in a linear scale graph and as a straight line on a logarithmic scale and variable scale graphs to facilitate the findings. The results lead to a general conclusion that Red Sea is considered to be located within the existing areas of the seismic belt and the region is exposed to earthquakes with strength ranging about 3.0 or less on the Richter scale with a high probability. The maximum magnitude is 6.1 with a return period of 100 years and probability of about 0.96%.

The conventional approach of hazard estimation based on magnitude frequency relationship is more useful when the dataset is complete for the entire time span and for the magnitude range. With good and complete datasets, the method is more appropriate and accurate for seismic hazard estimation.

Points for future researches can be summarized as follows:

・ To study in details the influence of missed data like that for the years in the intervals (1913-1921), (1921-1962), (1962-1964), (1965-1967), (1967-1969) and 1980-1982) on the earthquake parameters.

・ There are several methods of comparing the results of evaluation of earthquake parameters and can be applied in other areas in the Kingdom of Saudi Arabia

・ Can assess the risk parameters for a number of potential risks in Saudi Arabia, an example of the risks of landslides; severe storms; floods.

・ Drawing seismic maps of the areas in which they are registered seismic activity in Saudi Arabia each year for use in the evaluation and the likelihood of the occurrence of such activity on a long-term process.

Said Ali El- Quliti,Tawfiq Bin Saeed Al- Harbi,Mahdi Bin Salem Al- Yami,Ahmed Bin Matar Al- Ghamdi,Mohammed Bin Mattar Al- Shammari, (2016) Assessment of Main Parameters of Extreme Earthquakes in Red Sea, West Coast of Saudi Arabia. Open Journal of Earthquake Research,05,122-134. doi: 10.4236/ojer.2016.52010