SCALING LAWS OF SEISMIC EVENTS — A MODEL WITH FRACTAL GEOMETRY

Fractals ◽  
1999 ◽  
Vol 07 (04) ◽  
pp. 341-351
Author(s):  
C. GODANO ◽  
M. L. ALONZO
Keyword(s):  
Fractal Dimension ◽  
Fractal Geometry ◽  
Scaling Laws ◽  
B Value ◽  
Seismic Events ◽  
Magnitude Distribution ◽  
Transitional State ◽  
Contact Points ◽  
Omori Law ◽  
Local Fluctuations

Most models of earthquakes attempt to reproduce the observed scaling laws of seismic events: the Gutenberg-Richter frequency magnitude distribution, but not the Omori law for aftershocks and the multifractal distribution of hypocenters location. Many of these models are based on the idea of Self-Organized Criticality (SOC). These are dynamic systems which organize themselves into a transitional state and can reproduce the Gutenberg-Richter distribution, but generally do not reproduce the space-time distribution. Here, we suggest a model based on a fractal geometry: the two sides of a fault are modeled by means of a fractal surface. As a first step, one of them is slipped of a random amount with periodic boundary conditions, then new contact points between the surfaces are found. The area surrounded by these points is assumed to be proportional to the area of the earthquake. The size distribution of events is in good agreement with the observed Gutenberg-Richter law and the local fluctuations of the b value are explained in terms of variations of the fractal dimension of the surface. Also the multifractal distribution of earthquakes in space is well-reproduced with global properties not depending on the fractal dimension of the surface. However, we are not able to obtain something similar to the Omori law simply because we do not control the time evolution of the model.

A grid-based b-value approximation through Southern and Northern Norway: preliminary results 

2021 ◽  
Author(s):  
Rodrigo Estay ◽  
Claudia Pavez
Keyword(s):  
B Value ◽  
Seismic Events ◽  
Online Database ◽  
Magnitude Of Completeness ◽  
Stress Regime ◽  
Magnitude Distribution ◽  
The Mean ◽  
Frequency Magnitude Distribution ◽  
Frequency Magnitude ◽  
Grid Based

<p>The Gutenberg – Richter’s b-value is commonly used to analyze the frequency-magnitude distribution of earthquakes, describing the proportion of small and large seismic events as the first estimation of seismic hazard. Additionally, the b-value has been used as a stress meter, giving some insights into the stress regime in different regions around the world. In this research, a grid-based spatial distribution for the b – value was estimated in three different areas of Norway: northern (74°-81° N/ 12°-26° E), southern (57°-64°N/3°-12° E), and the ridge zones of Mohns and Knipovich. For this, we used a complete catalog from the years 2000 to 2019, which was obtained from the Norwegian National Seismic Network online database. The magnitude of completeness was estimated separately for each zone both in time and space, covering a total area of ~425,000 km<sup>2</sup>. Our results show a regional variation of the mean b-value for northern (b<sub>north</sub> = 0.79) and southern (b<sub>south</sub> = 1.03) Norway, and the Ridge (b<sub>ridge</sub> = 0.73), which can be interpreted in terms of the predominant stress regime in the different zones. So far, a few calculations regarding the b-value were previously done in Norway to analyze local intraplate sequences. Then, according to our knowledge, this research corresponds to the first estimation of a regional spatial variation of the b – value in the country.</p>

scholarly journals Statistics of the earthquakes in the central Himalaya and its vicinity in last 56 years, with an emphasis in the 25 April 2015 Gorkha, Nepal earthquake

2021 ◽  
Vol 51 (4) ◽  
pp. 321-343
Author(s):  
Ram Krishna TIWARI ◽  
Harihar PAUDYAL
Keyword(s):  
Fractal Dimension ◽  
Statistical Analysis ◽  
High Stress ◽  
Large Earthquake ◽  
B Value ◽  
Earthquake Activity ◽  
Central Himalaya ◽  
Magnitude Distribution ◽  
Average Value ◽  
Central Nepal

To understand the variation of stress levels in the region 80°E – 89°E and 26°N – 31°N, the statistical analysis of earthquake frequency-magnitude distribution and spatio-temporal variation of fractal correlation dimension of earthquake epicenter distribution are estimated. The analysis is carried out on declusterised catalogue containing 1185 events of 56 years from February 1964 to November 2020. The study area is divided into three regions the western Nepal and vicinity (Region A), central Nepal and vicinity (Region B) and eastern Nepal and vicinity (Region C), respectively. The magnitude of completeness (Mc) varies from 3.6 to 4.0 for the study period. The spatial fractal dimension (Dc) and b-value are calculated as 1.89 ± 0.02 and 0.68 ± 0.03 for the western Nepal, 1.76 ± 0.01 and 0.60 ± 0.05 for the central Nepal, whereas they are estimated as 1.85 ± 0.02 and 0.63 ± 0.03 for the eastern part of the Nepal. The b-values obtained for all three regions are very low comparing to global average value of 1. The time clustering of the events in the respective regions are 0.26 ± 0.003, 0.31 ± 0.004 and 0.26 ± 0.02 as indicated by temporal fractal dimension (Dt). The higher Dc, lower b and Dt values associated with the regions indicate high stress concentration and stronger epicenter clustering in these regions. The strongly increasing trend of fractal dimension and strongly decreasing trend of b-value show the high probabilities of occurring the large earthquake in both central Nepal (82.5°E – 85.5°E and 27.5°N – 30°N) and eastern Nepal (85.5°E – 88.2°E and 26.45°N – 28.6°N) as compared to western Nepal (80°E – 82.5°E and 28°N – 30.5°N). This statistical analysis of spatial and temporal characteristics of the earthquake activity may give significant signs of the future seismic hazard along central Himalaya region.

Optimal Density Determination of Bouguer Anomaly Using Fractal Analysis (Case of study: Charak area,IRAN)

2005 ◽  
Vol 1 (1) ◽  
pp. 21-24
Author(s):  
Hamid Reza Samadi
Keyword(s):  
Surface Roughness ◽  
Fractal Dimension ◽  
Fractal Analysis ◽  
Fractal Geometry ◽  
Host Rock ◽  
Bouguer Anomaly ◽  
Research Area ◽  
Density Difference ◽  
Optimal Density

In exploration geophysics the main and initial aim is to determine density of under-research goals which have certain density difference with the host rock. Therefore, we state a method in this paper to determine the density of bouguer plate, the so-called variogram method based on fractal geometry. This method is based on minimizing surface roughness of bouguer anomaly. The fractal dimension of surface has been used as surface roughness of bouguer anomaly. Using this method, the optimal density of Charak area insouth of Hormozgan province can be determined which is 2/7 g/cfor the under-research area. This determined density has been used to correct and investigate its results about the isostasy of the studied area and results well-coincided with the geology of the area and dug exploratory holes in the text area

scholarly journals Characterizing microseismicity at the Rotokawa and Ngatamariki geothermal fields

2021 ◽  
Author(s):  
◽  
Chet Hopp
Keyword(s):  
Matched Filter ◽  
Fluid Pressure ◽  
B Value ◽  
Injection Well ◽  
Taupo Volcanic Zone ◽  
Reservoir Properties ◽  
Injection Wells ◽  
Small Magnitude ◽  
Magnitude Distribution ◽  
Geothermal Fields

<p>In this thesis, we construct a four-year (2012–2015) catalog of microearthquakes for the Ngatamariki and Rotokawa geothermal fields in the Taupō Volcanic Zone of New Zealand, and use these data to improve the knowledge of reservoir behavior. These microearthquakes occur frequently, often every few seconds, and therefore provide a tool that we use to assess reservoir properties with dense spatial and temporal resolution as well as to illuminate the underlying processes of seismogenesis. Using a matched-filter detection technique we detect and precisely relocate nearly 9000 events, from which we calculate 982 focal mechanisms.  At Ngatamariki, these results constitute the first detailed analysis of seismicity at a newly-developed resource. It has been commonly assumed that induced shear on fractures increases reservoir permeability by offsetting asperities on either fracture wall, thereby propping the fracture open. During stimulation treatments of two boreholes (NM08 and NM09), borehole permeability experiences logarithmic growth. At NM08, this growth occurs for eight days in the absence of seismicity, while at NM09 only nine microearthquakes are observed during the one-month treatment. This suggests that hydro-shear, the process of inducing seismicity through increased pore pressure at critically-stressed fractures, is not the dominant mechanism of permeability increase at many geothermal wells. Instead, aseismic processes, likely thermal and overpressure induced fracture opening, dominate well stimulation in high-temperature geothermal settings.  At Rotokawa, the earthquake frequency-magnitude distribution (b-value) is positively correlated with both proximity to major injection wells and depth. In an inferred pressure compartment near injection well RK23, b is ~1.18, but is <1.0 elsewhere, suggesting a connection between increased pore-fluid pressure and small-magnitude events. In addition, throughout the reservoir b increases from a value of ~1.0 at injection depth to almost 1.5 two kilometers below the reservoir, consistent with observations at volcanic areas elsewhere, but opposing the conventional wisdom that b-value is inversely proportional to differential stress.  Finally, the 982 focal mechanism observations that we invert for stress show a normal faulting regime throughout both reservoirs. At Rotokawa, a lowering stress ratio, v, after reintroduction of injection well RK23 (v drops from 0.9 to 0.2 over six months) indicates that anisotropic reservoir cooling affects the reservoir stress state through a process of preferential stress reduction.</p>

A Retrospective Analysis of b-Value Changes Preceding Strong Earthquakes

2021 ◽  
Author(s):  
Nicolas D. DeSalvio ◽  
Maxwell L. Rudolph
Keyword(s):  
B Value ◽  
Earthquake Precursors ◽  
Earthquake Catalog ◽  
Traffic Light ◽  
Magnitude Distribution ◽  
Parameter Combination ◽  
Definition Of ◽  
Value Changes ◽  
Frequency Magnitude Distribution ◽  
Optimal Set

Abstract Earthquake precursors have long been sought as a means to predict earthquakes with very limited success. Recently, it has been suggested that a decrease in the Gutenberg–Richter b-value after a magnitude 6 earthquake is predictive of an imminent mainshock of larger magnitude, and a three-level traffic-light system has been proposed. However, this method is dependent on parameters that must be chosen by an expert. We systematically explore the parameter space to find an optimal set of parameters based on the Matthews correlation coefficient. For each parameter combination, we analyze the temporal changes in the frequency–magnitude distribution for every M ≥ 6 earthquake sequence in the U.S. Geological Survey Comprehensive Earthquake Catalog for western North America. We then consider smaller events, those with a foreshock magnitude as small as 5, and repeat the analysis to assess its performance for events that modify stresses over smaller spatial regions. We analyze 25 M ≥ 6 events and 88 M 5–6 events. We find that no perfect parameter combination exists. Although the method generates correct retrodictions for some M 5 events, the predictions are dependent on the retrospectively selected parameters. About 80%–95% of magnitude 5–6 events have too little data to generate a result. Predictions are time dependent and have large uncertainties. Without a precise definition of precursory b-value changes, this and similar prediction schemes are incompatible with the IASPEI criteria for evaluating earthquake precursors. If limitations on measuring precursory changes in seismicity and relating them to the state of stress in the crust can be overcome, real-time forecasting of mainshocks could reduce the loss of lives.

What allows seismic events to grow big?: Insights from b-value and fault roughness analysis in laboratory stick-slip experiments

Geology ◽  
2017 ◽  
Vol 45 (9) ◽  
pp. 815-818 ◽  
Author(s):  
Thomas H.W. Goebel ◽  
Grzegorz Kwiatek ◽  
Thorsten W. Becker ◽  
Emily E. Brodsky ◽  
Georg Dresen
Keyword(s):  
B Value ◽  
Seismic Events ◽  
Stick Slip ◽  
Fault Roughness ◽  
Roughness Analysis

REVIEW AND A MODEL OF PRE-SEISMIC ELECTROMAGNETIC EMISSIONS IN TERMS OF FRACTAL ELECTRODYNAMICS

Fractals ◽  
2004 ◽  
Vol 12 (02) ◽  
pp. 243-273 ◽  
Author(s):  
K. EFTAXIAS ◽  
P. FRANGOS ◽  
P. KAPIRIS ◽  
J. POLYGIANNAKIS ◽  
J. KOPANAS ◽  
...  
Keyword(s):  
Critical Point ◽  
Scaling Laws ◽  
Critical Phenomenon ◽  
Crack Opening ◽  
Broad Band ◽  
Ground Surface ◽  
Band Spectrum ◽  
Omori Law ◽  
Transient Electromagnetic ◽  
Electromagnetic Emissions

We introduce a new model of the generation of pre-seismic electromagnetic emissions, which explains the observed phenomenology in terms of its geometry and fractal electrodynamics. Accumulated evidence indicates that an earthquake can be viewed as a critical phenomenon culminating in a large event that corresponds to a type of critical point. The principle feature of criticality is the fractal organization in both space and time. Earthquakes display a complex spatio-temporal behavior: in addition to the regularity in the rate of occurrence (e.g. Gutenberg-Richter law, Omori law), the spatial distribution of epicenters is fractal and earthquakes occur on a fractal structure of faults. Thus, the hypothesis that the fault develops as a fractal is reasonable. A mounting body of laboratory evidence suggests that micro-fracturing of rocks are associated with the appearance of spontaneous charge production and transient electromagnetic emissions (EME). The emitting, diffusing and recombination charge accompanying the micro-fracturing, can act as current generated during the crack opening. In this view, an active crack or rupture, can be simulated by a "radiating element." The idea is that a fractal geo-antenna (FGA) can be formed as an array of line elements having a fractal distribution on the ground surface as the critical point is approached. We test this idea in terms of fractal electrodynamics: we argue that the precursory VLF-VHF EM signals associated with recent earthquakes in Greece are governed by characteristics (e.g. scaling laws, temporal evolution of the spectrum content, broad band spectrum region and accelerating emission rate) predicted by fractal electrodynamics.

Fractal geometry of ammonoid sutures

Paleobiology ◽  
1995 ◽  
Vol 21 (3) ◽  
pp. 329-342 ◽  
Author(s):  
Timothy M. Lutz ◽  
George E. Boyajian
Keyword(s):  
Fractal Dimension ◽  
Fractal Geometry ◽  
Two Dimensional ◽  
Evolutionary Time ◽  
Linear Features ◽  
Divider Method ◽  
Richardson Method ◽  
Components Analysis ◽  
Box Method ◽  
Range Of Variation

Interior chamber walls of ammonites range from smoothly undulating surfaces in some taxa to complex surfaces, corrugated on many scales, in others. The ammonite suture, which is the expression of the intersection of these walls on the exterior of the shell, has been used to assess anatomical complexity. We used the fractal dimension to measure sutural complexity and to investigate complexity over evolutionary time and showed that the range of variation in sutural complexity increased through time. In this paper we extend our analyses and consider two new parameters that measure the range of scales over which fractal geometry is a satisfactory metric of a suture. We use a principal components analysis of these parameters and the fractal dimension to establish a two-dimensional morphospace in which the shapes of sutures can be plotted and in which variations and evolution of suture morphology can be investigated. Our results show that morphospace coordinates of ammonitic sutures correspond to visually perceptible differences in suture shape. However, three main classes of sutures (goniatitic, ceratitic, and ammonitic) are not unambiguously discriminated in this morphospace. Interestingly, ammonitic sutures occupy a smaller morphospace than other suture types (roughly one-half of the morphospace of goniatitic and ceratitic sutures combined), and the space they occupied did not change dimensions from the Jurassic to the late Cretaceous.We also compare two methods commonly used to measure the fractal dimension of linear features: the Box method and the Richardson (or divider) method. Both methods yield comparable results for ammonitic sutures but the Richardson method yields more precise results for less complex sutures.

Fractal Geometry and Properties of Doped BaTiO3 Ceramics

2010 ◽  
Vol 67 ◽  
pp. 42-48 ◽  
Author(s):  
V.V. Mitic ◽  
V.B. Pavlovic ◽  
L. Kocic ◽  
V. Paunovic ◽  
L. Zivkovic
Keyword(s):  
Fractal Dimension ◽  
Solid State ◽  
Fractal Geometry ◽  
Grain Shape ◽  
Grain Structure ◽  
Fractal Method ◽  
Ceramic Structure ◽  
New Approach ◽  
Fractal Modeling ◽  
Dielectrical Properties

Taking into account that the complex grain structure is difficult to describe by using traditional analytical methods, in this study, in order to establish ceramic grain shapes of sintered BaTiO3, new approach on correlation between microstructure and properties of doped BaTiO3 ceramics based on fractal geometry has been developed. BaTiO3 ceramics doped with various dopants (MnCO3, Er2O3, Yb2O3) were prepared using conventional solid state procedure, and were sintered at 1350oC for four hours. The microstructure of sintered specimens was investigated by SEM-5300. Using method of fractal modeling a reconstruction of microstructure configurations, like grains shapes, or intergranular contacts has been successfully done. Furthermore, the area of grains surface was calculated using fractal correction that expresses the irregularity of grains surface through fractal dimension. The presented results, indicate that fractal method for ceramics structure analysis provides a new approach for describing, predicting and modeling the grain shape and relations between the BaTiO3-ceramic structure and dielectrical properties.

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