We have written a new equation to study the statistics of earthquake distributions. We call this equation “the generalized logistic equation”. The Gutenberg-Richter frequency-magnitude formula was derived from the s...We have written a new equation to study the statistics of earthquake distributions. We call this equation “the generalized logistic equation”. The Gutenberg-Richter frequency-magnitude formula was derived from the solution of the generalized logistic equation as an asymptotic case for the approximation of large magnitudes. To illustrate how the solution of the generalized logistic equation works, it was used to approximate the observed cumulative distribution of earthquakes in four different geological provinces: the Central Atlantic (40N - 25N, 5W - 35W), Canary Islands, Magellan Mountains (20N - 9S, 148E - 170E), and the Sea of Japan. This approximation showed an excellent correlation between the theoretical curves and observed data for earthquakes of magnitudes 1 < m < 9.展开更多
The Gutenberg-Richter law (G-R law) of the magnitude-frequency distribution of earthquakes has been an important base in seismology for a long time. However, the actual magnitude-frequency distribution usually deviate...The Gutenberg-Richter law (G-R law) of the magnitude-frequency distribution of earthquakes has been an important base in seismology for a long time. However, the actual magnitude-frequency distribution usually deviates from the G-R law. Based on the experimental results of three different rock samples, which contain macro-asperity, compressional en-echelon fault and model-Ⅲ shear fault, the correlative coefficient (r) was calculated by fitting the sequences of the acoustic emissions with the G-R law in every scanning time window. We investigated the changes of the correlative coefficient, which describes the actual deviation of magnitude-frequency distribution of earthquakes from the G-R law within the specific scanning time window. According to the results of the rock samples containing macro-asperity and compressional en-echelon fault respectively, the value decreases prior to the rock fracture, meaning that the deviation of magnitude-frequency distribution from the G-R law tends to be larger. The result of the model-Ⅲ shear fault didn’t show obvious decrease before the final rock fracture. Actually, the studies of some earthquakes also show deviation before the occurrence of moderate earthquakes. The results obtained in this paper will provide us with some useful clues for studying precursors before the occurrence of moderate earthquakes with the data of regional earthquake activities.展开更多
文摘We have written a new equation to study the statistics of earthquake distributions. We call this equation “the generalized logistic equation”. The Gutenberg-Richter frequency-magnitude formula was derived from the solution of the generalized logistic equation as an asymptotic case for the approximation of large magnitudes. To illustrate how the solution of the generalized logistic equation works, it was used to approximate the observed cumulative distribution of earthquakes in four different geological provinces: the Central Atlantic (40N - 25N, 5W - 35W), Canary Islands, Magellan Mountains (20N - 9S, 148E - 170E), and the Sea of Japan. This approximation showed an excellent correlation between the theoretical curves and observed data for earthquakes of magnitudes 1 < m < 9.
基金This research was sponsored by the Joint EarthquakeScience Foundation,China (A07007)
文摘The Gutenberg-Richter law (G-R law) of the magnitude-frequency distribution of earthquakes has been an important base in seismology for a long time. However, the actual magnitude-frequency distribution usually deviates from the G-R law. Based on the experimental results of three different rock samples, which contain macro-asperity, compressional en-echelon fault and model-Ⅲ shear fault, the correlative coefficient (r) was calculated by fitting the sequences of the acoustic emissions with the G-R law in every scanning time window. We investigated the changes of the correlative coefficient, which describes the actual deviation of magnitude-frequency distribution of earthquakes from the G-R law within the specific scanning time window. According to the results of the rock samples containing macro-asperity and compressional en-echelon fault respectively, the value decreases prior to the rock fracture, meaning that the deviation of magnitude-frequency distribution from the G-R law tends to be larger. The result of the model-Ⅲ shear fault didn’t show obvious decrease before the final rock fracture. Actually, the studies of some earthquakes also show deviation before the occurrence of moderate earthquakes. The results obtained in this paper will provide us with some useful clues for studying precursors before the occurrence of moderate earthquakes with the data of regional earthquake activities.
