Earthquake Size Distribution Research Articles

Deep borehole log evidence for fractal distribution of fractures in crystalline rock

Sonic velocity and electrical resistivity logs run to a depth of 3.5 km in crystalline rock near the San Andreas fault at Cajon Pass in southern California correlate over scale-lengths both small (sub-metre) and large (tens to hundreds of metres). No such correlations are seen with the more lithologically sensitive natural gamma intensity log. The correlation between the sonic velocity and electrical resistivity logs suggests that a non-lithologic property of the crystalline rock controls fluctuations. In situ fracture intensity is a logical candidate for the controlling rock property. The fluctuations of the individual sonic velocity and electrical resistivity logs are examined with the Hurst rescaled range parameter over borehole log intervals 1.5 m < L < 1500 m. For log fluctuations arising from a scale-invariant physical process the Hurst rescaled range scales with data interval as LH, 0 < H < 1. A purely random sequence of in situ fractures produces a scaling exponent H= 0.50. Fluctuations in the Cajon Pass sonic velocity and electrical resistivity logs yield H~ 0.70 evidence that in situ fracture sets tend to occur in clusters rather than at purely random intervals. The tendency for fracture clustering over log intervals 1.5 m < L < 1500 m suggests that fracture formation is a fractal process independent of length-scale in which larger fracture intervals form from clustering of numerous smaller fracture intervals. Seismic reflectivity derived from the borehole sonic velocity log is also scale independent over the range of data intervals 1.5m < L < 1500 m with a Hurst exponent H= 0.21. If we associate fracture clustering with crustal fault formation, the Cajon Pass borehole sonic velocity and electrical resistivity logs predict that crustal faults scale fractally with fractal dimension D̃ 2.30. The equivalent b-value for earthquake size distribution is b~D/2~ 1.15. On this hypothesis observed b-values < 1.15 indicate a tendency for earthquakes to cluster on existing (weak?) faults. A scale-independent mechanics for crystalline rock fracture formation in which larger scale fractures form as clusters of smaller scale fractures provides a mechanical link between the small pervasive stress aligned flaws, cracks and microfractures which can impart anisotropy to crystalline rock and the larger scale fractures associated with finite strain and faulting. Thus in crustal regions of active but low strain, fracture anisotropy is observed to be aligned with the inferred maximum principal stress, while in actively faulted crust, fracture anisotropy is observed to be more nearly fault parallel as if the fractures are aligned by the finite strain faulting process.

Relationship between the seismicity and geologic structure of the Blanco Transform Fault Zone

Morphologic studies of an oceanic transform, the Blanco Transform Fault Zone (BTFZ), have shown it to consist of a series of extensional basins that offset the major strike-slip faults. The largest of the extensional basins, the Cascadia Depression, effectively divides the transform into a northwest segment, composed of several relatively short strike-slip faults, and a southeast segment dominated by fewer, longer faults. The regional seismicity distribution (m b ≥4.0) and frequency-magnitude relationships (b-values) of the BTFZ show that the largest magnitude events are located on the southeast segment. Furthermore, estimates of the cumulative seismic moment release and seismic moment release rate along the southeast segment are significantly greater than that of the northwest segment. These observations suggest that slip along the southeast segment is accommodated by a greater number of large magnitude earthquakes. Comparison of the seismic moment rate, derived from empirical estimates, with the seismic moment rate determined from plate motion constraints suggests a difference in the seismic coupling strength between the segments. This difference in coupling may partially explain the disparity in earthquake size distribution. However, the results appear to confirm the relation between earthquake size and fault length, observed along continental strike-slip faults, for this oceanic transform.

Seismological and structural evolution of strike-slip faults

The mapped traces of strike-slip faults are commonly characterized by discontinuities that appear as steps in map-view. Here I present observations to show that the number of steps per unit length along the trace of major strike-slip fault zones in California and Turkey is a smoothly decreasing function of cumulative geological offset. When coupled with a growing body of evidence that indicates that steps in fault traces work to impede or arrest the propagation of earthquake ruptures, the apparent smoothing of fault traces with displacement is interpreted to suggest that the spatial distribution of strength properties on a fault plane is a function of cumulative geological offset. A consequence of this structural evolution is that faults may undergo a seismological evolution a well, whereby the size and frequency distribution of earthquakes is also a function of cumulative offset.

Earthquakes, quaternary faults, and seismic hazard in California

Data describing the locations, slip rates, and lengths of Quaternary faults are the primary basis in this work for constructing maps that characterize seismic hazard in California. The expected seismic moment M0e and the strength of ground shaking resulting from the entire rupture of each mapped fault (or fault segment) are estimated using empirical relations between seismic moment M0, rupture length, source to site distance, and strong ground motions. Assuming a fault model whereby the repeat time T of earthquakes on each fault equals M0e/M0g (where the moment rate M0g is proportional to fault slip rate), it is observed that the moment‐frequency distribution of earthquakes predicted from the geologic data agrees well with the distribution determined from a 150‐year historical record. The agreement is consistent with the argument that the geologic record of Quaternary fault offsets contains information sufficient to predict the average spatial and size distribution of earthquakes through time in California. The estimates of T for each fault are the foundation for constructing maps that depict the average return period of ≳ 0.1g peak horizontal ground accelerations, and the horizontal components of peak acceleration, peak velocity, and the pseudovelocity response (at 1‐period and 5% damping) expected to occur at the level of 0.1 probability during a 50‐year period of time. A map is also formulated to show the probability that ≳ 0.1g horizontal ground accelerations will occur during the next 50 years. The maps serve to illustrate the potential value of Quaternary fault studies for assessing seismic hazard. Interpretation of available slip rates indicates that the largest and most frequent occurrence of potentially destructive strong ground motions are associated principally with the San Andreas, San Jacinto, Calaveras, Hayward, and Ventura Basin fault zones. Other regions of similarly high hazard may yet remain unrecognized. This inadequacy results primarily from an incomplete data set. Numerous faults, for example, are mapped along the coastal region of northern California and within the Modoc Plateau, but relatively few studies relating to fault slip rate are reported. A similar problem exists for other stretches of coastal California where marine reflection studies provide evidence of active faulting offshore yet yield little or no information of fault slip rate. Geological and geophysical field studies can work to remove these deficiencies. A concerted effort to locate and define rates of activity on all faults in California is the most promising means to further quantify present levels of seismic hazard in California.

Hierarchy in earthquake size distribution : Fukao, Y; Furumoto, M Phys Earth Planet InterV37, N2–3, Feb 1985, P149–168

Hierarchy in earthquake size distribution : Fukao, Y; Furumoto, M Phys Earth Planet InterV37, N2–3, Feb 1985, P149–168

Hierarchy in earthquake size distribution

We propose a fault model in which there are a finite number of characteristic lengths between the smallest and the largest scales, e.g., between a grain size and a size of great earthquakes. A fault plane in one scale is segmented into blocks of statistically similar sizes by the barriers of statistically similar heights. Rupture expands by successively “climbing” the barriers. The average barrier height is proportional to the average block size which defines the characteristic length of the relevant scale. Stresses before and after rupturing are assumed to be independent of earthquake size. With these assumptions the probability for rupture to grow further is shown to be independent of the scale of barrier structure. The rupture in one scale, however, tends to grow more easily as it grows so that once the rupture exceeds some critical size, it no longer stops until it encounters the barriers in the next larger scale. Rupture grows by repeating this cycle, which starts with rupturing of a unit block in one scale and ends with one in the next larger scale. Our model involves two parameters which must be determined empirically. One is the length ratio r between two successive scales. The other is the critical number of blocks, n c, which defines the critical size for unstable rupture growth in one scale. We suggest values of ∼ 5 for both r and n c. With these values our model explains a diversity of earthquake phenomena such as the magnitude-frequency relation, the seismic gap and the magnitude gap, the magnitude difference between a main shock and its largest aftershock, the occurrence of multiplet earthquakes, the generation of high frequency seismic waves, the incoherency of the near field acceleration and the recent observation by Furumoto and Nakanishi that the main rupture is often preceded by a precursory rupture whose time duration, in general, scales with seismic moment.

Hierarchy in earthquake size distribution : Fukao, Yoshio and Muneyoshi Furumoto, 1985. Earth planet. Interiors, 37(2–3):149–168. Dept. of Earth Sci., Nagoya Univ., Chikusa, Nagoya 464 Japan

Hierarchy in earthquake size distribution : Fukao, Yoshio and Muneyoshi Furumoto, 1985. Earth planet. Interiors, 37(2–3):149–168. Dept. of Earth Sci., Nagoya Univ., Chikusa, Nagoya 464 Japan

Integration of geological and seismological data for the analysis of seismic hazard: A case study of Japan

Seismic hazard analyses are associated with large uncertainties when historical data are insufficient to define secular rates of seismicity. Such uncertainties may be decreased with geological data in areas where seismicity is shallow and produced by Quaternary faulting. To illustrate, we examine intraplate Japan. Large intraplate earthquakes in Japan characteristically produce surface ruptures along mappable Quaternary faults and show a systematic relation between seismic moment, M_0 and rupture length I (log M_0 = 23.5 + 1.94 × log I). It is observed that, within the bounds placed by geologically assessed slip rates, the mean regional moment release rate M_0 resulting from slip on mapped Quaternary faults is in accord with estimates of M_0 determined with the 400-yr record of seismicity. Recent work also shows that when the repeat time T of earthquakes on Quaternary faults in southwest Japan is assumed to equal M_0/M_0^g (where M_0 is estimated for rupture extended over the entire fault length and M_0^g is the geologically assessed moment release rate of each fault), the moment frequency distribution of earthquakes predicted from the geologic record is virtually identical to that seen with the 400-yr record of seismicity. These observations indicate that the geologic record of Quaternary fault offsets contains sufficient information to predict both the spatial and size distribution of intraplate earthquakes in Japan. A contour map of the average recurrence time of ground shaking of JMA intensity ≧V is thus computed using an empirical relation between seismic moment and the areal distribution of seismic intensity and assuming that the repeat time T of earthquakes on each Quaternary fault equals M_0/M_0^g. The map demonstrates how Quaternary fault data may be used to assess long-term seismic hazard in areas of active faulting where historical records of seismicity are relatively short or absent. Another shortcoming of conventional seismic hazard analysis is that hazard is not considered a function of the time since each fault in a region last ruptured. A simple procedure is used to demonstrate how the time-dependent nature of the earthquake cycle affects the evaluation of seismic hazard. The distribution of seismic shaking characteristic of large interplate earthquakes offshore of Japan is estimated from published isoseismal maps. The observed average repeat times of ruptures along specific segments of the plate boundaries then provide the basis to make probabilistic estimates of the next expected time of seismic shaking due to plate boundary earthquakes. When data are too few to document the average repeat times of rupture, the estimates of probability are calculated with data relating to the relative coseismic slip during past earthquakes and the rate of interseismic strain accumulation, interpreted within the framework of the time predictable model of earthquake occurrence. Results are displayed as maps of instantaneous seismic hazard: the probability that seismic shaking will occur conditional to knowledge of where in time each fault in a region presently resides with respect to the earthquake cycle.

Advances in Geophysics

Observations related to tsunami catalogs are reviewed and described in a phenomenological framework. An examination of scaling relationships between earthquake size (as expressed by scalar seismic moment and mean slip) and tsunami size (as expressed by mean and maximum local run-up and maximum far-field amplitude) indicates that scaling is significant at the 95% confidence level, although there is uncertainty in how well earthquake size can predict tsunami size (Rw 0.4–0.6). In examining tsunami Advances in Geophysics, Volume 53 2012, Published by Elsevier Inc. ISSN 0065-2687, Doi: http://dx.doi.org/10.1016/B978-0-12-380938-4.00002-1 35 j event statistics, current methods used to estimate the size distribution of earthquakes and landslides and the inter-event time distribution of earthquakes are first reviewed. These methods are adapted to estimate the size and inter-event distribution of tsunamis at a particular recording station. Using a modified Pareto size distribution, the best-fit power-law exponents of tsunamis recorded at nine Pacific tide-gauge stations exhibit marked variation, in contrast to the approximately constant power-law exponent for inter-plate thrust earthquakes. With regard to the inter-event time distribution, significant temporal clustering of tsunami sources is demonstrated. For tsunami sources occurring in close proximity to other sources in both space and time, a physical triggering mechanism, such as static stress transfer, is a likely cause for the anomalous clustering. Mechanisms of earthquake-to-earthquake and earthquake-to-landslide triggering are reviewed. Finally, a modification of statistical branching models developed for earthquake triggering is introduced to describe triggering among tsunami sources.