توزیع بَرخالی (فرکتالی) لرزه‌خیزی القایی در مخزن سد مسجد سلیمان (جنوب غرب ایران)

Masjed Soleyman dam site is located in the Zagros Mountain of western Iran, which is one of the most seismically active zones of the Alpe-Himalayan belt. After impounding of dam, the seismicity of area increased considerably, showing the impact of reservoir (177 m height, 261 million m3) in changing the rate of seismicity in the area. We have analyzed the seismicity of area in terms of the spatial variation of fractal dimension and have compared it with the frequency-magnitude relation b-value. In the mid-2006, a digital seismograph network of five medium-band stations consist of Trillium-40T, 40 sec-50 Hz seismometer connected to 24 bit Nonometric Taurus recorder was established around the axis and reservoir of the Masjed Soleyman dam site by International Institute of Earthquake Engineering and Seismology (IIEES). The earthquake catalog of Masjed Soleyman network since June 1, 2006 to October 1, 2007 contains 3609 well-located events. As the epicenter of induced earthquakes are mostly within the 30 kilometers radius of dam and their hypocenter is located at depth less than 20 kilometers, therefore we selected only 1924 events which satisfied above selection criteria. During monitoring period, two large earthquakes with magnitude of 3.9 and 3.6 struck the area on November 23, 2006 and September 1, 2007, respectively. These earthquakes happened following a rapid change in water level of reservoir. The phenomenon such as earthquakes and faults are self-similar systems at any scale and can be described by a power-law relation. The exponent of this relation that shows the degree of complexity in a chaotic system is called the fractal dimension. Although the term of fractals was introduced to the world by Mandelbort in 1967, power-law relations in order to investigate the geophysical phenomena were used earlier.
Gutenberg and Richter defined a relationship between the frequencies and magnitudes of earthquakes in 1945. The slop of the plot of occurrence numbers against magnitudes is known as the b-value and has been used as the indicator of seismic activity of the studied region. In this study we try to understand the loading impact due to reservoir water impoundment on both D and b-value parameters. We used correlation dimension which is the most commonly method for calculation the fractal dimension of earthquake hypocenter. To map the variation of fractal dimension as a function of space, the entire area was set into 0.05° × 0.05° grids. An overlapping of 25% is made for a comprehensive picture of the map. The 23 grids were created interactively, and the region with events less than 40 did not used in this estimation. The number of events in each grid varied from 40 to 109. In this exercise, the fractal dimension value ranged from 0.40 to 0.93, but the values were less than 1. The number of earthquakes, N with magnitude greater than Mc is related to the magnitude by logN=a?bM, which is widely known as the Gutenberg–Richter relation. In this study, the b-value of the Gutenberg–Richter relation was estimated by a maximum likelihood method which is claimed to be a better estimation. The threshold magnitude of 0.9 has been found for the dam region by examining the log-linear plot of cumulative number of events versus magnitude. We have obtained that b-value in the area varies from 0.6–1.3. The low D value obtained here may have several explanations.
Seismic activity in the Masjed Soleyman reservoir site occurs in a small area, and the distances between mainshocks and aftershocks are very small (sometimes less than 3 km) which may result in a low D value. If we consider that the seismicity of the Masjed Soleyman region is due to the fault interactions and reservoir-triggered forces which generate earthquakes in small clusters, since our data are in protracted step of seismicity in the area and the main factors for occurrence of earthquakes in this step are seepage of fluid in the crust and increase in pore pressure diffusion, therefore high permeability and presence of fluids in the fault and surrounding area may reduce effective stresses and show relatively low D. The low D value could also be the effect of high pore fluid pressure in the region as pore fluid pressure reflects redistribution of stress in the substratum. When D tends to zero, the seismicity of the area may not be due to any particular fault but may be connected to the stress generated by high pore fluid pressure; this indicates the point source zone. Having high b-value in the studied region especially in the vicinity of dam indicates heterogeneous stress distribution in the crust whereas homogeneous stresses results in lower b-values. Gradual increase in pore pressure is the main factor in occurrence of induced earthquakes, whereas this increase could be the result of faults weakening due to pore pressure diffusion, therefore we could see a heterogeneous stress distribution in the area and high b-values. So the lower D values (D ? 0.6) and higher b-values (b ? 0.8) in some grids indicate that there is a heterogeneous structure in this area and it seems that dam region is susceptible for occurrence of induced earthquakes. The results show a desirable correlation between D and b-value that indicates on existing of induced seismicity in area. The impact of increasing pure fluid pressure on both parameters (fractal dimension D and b-value) is truly observable for this area.