NG33B-01 INVITED
The Statistics of Wildfire Burned Areas and Landslides: Implications for Ecology, Erosion, Risk and Government Reporting
There is increasing evidence that the extremes of many natural hazards satisfy power-law or other heavy- tailed frequency-size statistics. Examples include earthquakes, volcanic eruptions, landslides, snow avalanches, forest and wildfires, meteorite impacts, and possibly floods. Although power-law distributions are commonly associated with the frequency-size distribution of small to large earthquakes, the frequency-size statistics of many other natural hazards are often associated with distributions that are more thin-tailed. The occurrence for large and very-large events using power-law frequency-size distributions is often much more conservative, with a greater chance of a large event occurring in a given period of time, compared to thinner tail distributions. The choice of the statistical distribution used or assumed has many implications to Earth Sciences research. In this paper we will present the frequency-size distributions for wildfires and landslides, both found to be robustly power-law for the medium and large events, and the implications of these statistics to erosion, ecology, risk and government reporting.
NG33B-02 INVITED
Missing Data in Aftershock Sequences: Explaining the Deviations From Scaling Laws
We extend the branching aftershock sequence (BASS) model to study the role of missing data at short times and small amplitudes after a mainshock, and apply this model which contains three parameters characterizing the missing data, to the magnitude and temporal statistics of four aftershock sequences in California. We find that the observed time dependent deviations of the frequency-magnitude scaling from the Gutenberg- Richter power law dependency can be described quantitatively by the model. We also show that for the same set of parameters, the model is able to explain quantitatively the observed magnitude dependent deviations of the temporal decay of aftershocks from Omori's law. In addition, we show that the same sets of data can also reproduce quite well the various functional forms of the probability density functions (pdf) of the return times between consecutive events with magnitudes above a prescribed threshold, as well as the violation of scaling at short and intermediate time scales.
NG33B-03 INVITED
Spatiotemporal clustering: A comparison between earthquake catalogs and models of seismicity
Describing and modeling the spatiotemporal organization of seismicity and understanding the underlying physical mechanisms of earthquake triggering have been proven challenging. To share new light on this issue, we follow a recently proposed method to characterize spatiotemporal clustering of seismicity by networks of recurrent events [Geophys. Res. Lett. 33, L1304, 2006] and compare the properties of earthquake catalogs to that of synthetic catalogs generated by different models of seismicity. In particular, we discuss the spatiotemporal clustering generated by the epidemic type aftershock sequence (ETAS) model and compare it to the clustering found in aftershock sequences like Parkfield.
NG33B-04
Occurrence Probability of Characteristic Earthquakes Based on a Renewal Model and Stress Interaction Effect in Central and Southern Apennines, Italy
We compute the effect of stress change due to previous historical earthquakes on the probability of occurrence of future earthquakes on neighboring faults, starting from the estimate of the probability of occurrence in the next 50 years for a characteristic earthquake through a time-dependent renewal model. Then, we apply a physical model for the Coulomb stress change caused by previous earthquakes on these structures. The influence of the stress change on the occurrence rate of characteristic earthquakes is computed taking into account both permanent (clock advance) and temporary (state-and-rate) perturbations. We apply this method to the computation of earthquake hazard for 35 seismogenic structures recognized in the Central and Southern Apennines region, for which both historical and paleoseismological data are available. This study provides the opportunity of reviewing the problems connected with the estimate of the parameters of a renewal model in case of characteristic earthquakes characterized by return times longer than the time spanned by the available catalogues, and the applicability of the concept of characteristic earthquake itself. An application of the decision tree approach has shown a wide variability of the probability of failure for all the characteristic sources in the next 50 years. The conclusion of this study is that the present status of both the methodology and the quality of input data for time-dependent earthquake hazard assessment in the study region are still at a premature stage for drawing results that can reliably substitute the time-independent Poisson hypothesis.
NG33B-05
Shoreline change and beach dynamics between June 2006 and June 2007 of the Outer Banks, North Carolina
Shorelines undergo continuous change, primarily in response to the action of waves. New technologies are enabling researchers to measure shoreline behaviors over a range of spatial and temporal scales. In June 2006 and June 2007, repeat NSF-funded LIDAR surveys were collected along a 175 km stretch of the Atlantic coast of the Outer Banks, North Carolina, United States by the National Center for Airborne Laser Mapping (NCALM). Analysis of annual shoreline position change determined from these new surveys will be presented. Our analysis of past annual surveys of the Outer Banks has documented nonlinear patterns in shoreline position change and strong correlations with preexisting beach width and annual dune retreat. Our work also documented spatial variability, where different regions of the Outer Banks exhibit different patterns of coastal change during the same time interval. The different regions have different shoreline orientations which correspond to different effective wave climates. The shoreline orientation has been shown to successfully model the spatial variations in observed shoreline change. The new 2006 and 2007 LIDAR surveys, combined with annual change determined from analysis of previous surveys of the same coastline segments collected by NASA in 1997, 1998, 1999, and 2000, will allow the analysis of patterns of shoreline change over time intervals ranging from one to ten years.
NG33B-06
Extreme Events in Space Weather: Long-Range Correlations and Clustering
Space weather is driven by the solar wind and many extreme geomagnetic events such as space storms and substorms are potential natural hazards. The statistical studies of these vents are complicated because of the turbulent nature of their driver, the solar wind. On the other hand archived data of geospace storms and substorms for very long periods are available and are amenable to detailed analysis using many techniques. For example, a database of substorms consisting of more than million events have been compiled for this study of the inherent statistical characteristics of extreme events in geospace. The auto- correlation and mutual-information functions are used to obtain the scaling exponents and they show the presence of long-term correlations and clustering. The scaling is represented by two exponents, the break arising due mainly to the turbulent nature of the solar wind driving the events. The auto-correlation functions show stronger long-term correlation than the mutual information functions, which represent correlations of all orders. The return intervals for varying thresholds show long-range correlations with decreasing strength for higher thresholds, similar to the case of multifractal systems. The techniques of detrended fluctuation analysis are used to further study of the long-range correlations and clustering of geospace events.
NG33B-07
Record-Breaking in Geophysics
The probabilistic theory of record-breaking was developed by Tata (1969), Nezvorov (1986) and others to describe the frequency of occurrence of record-breaking events in random trials. These results have been applied by Redner and Peterson (2006) in exploring the possible role of global warming on the statistics of record-breaking temperatures and by Newman and Turcotte (2008) to the rate of occurrence of record- breaking earthquakes. In addition, van Aalsburg et al. (2008) have derived the expected values of record- breaking earthquake magnitudes globally and compared this with cataloged observations. We review some of the underlying theory relevant to the distribution of events in time which we then extend to the spatial distribution of record-breaking events. In particular, we derive the distribution function associated with an otherwise random background of events and the emergence of spatial clustering in such situations. Moreover, we employ large-scale Monte-Carlo simulations to extend our analytic results to 2 and 3 dimensions. These results yield some remarkable scaling features including hierarchical behavior, resulting in power-law and fractal features, in situations where one would not intuitively expect to observe such pattern. Furthermore, they provide a "null-hypothesis" that can be used in testing the distribution and spatial scaling of real seismic events such as those studied by Davidsen and Paczuski (2005) and Davidsen, Grassberger, and Paczuski (2006, 2088). Tata, M.N., Z. Wahrscheinlichkeitstheorie verw. Geb. 12, 9- 20 (1969). Nezvorov, V.B., Theory, Prob. Appl., 32(2), 201-228, translated from Russian (2006). Redner, S. and Peterson, M.V., Phys. Rev. E 74, 061114 )2006). Newman, W.I. and Turcotte, D.L., 2008 Association of Pacific Rim Universities Symposium "Multi-Hazards around the Pacific Rim," University of California, Davis, August 21-22, 2008. Van Aalsburg, J., Newman, W.I., Turcotte, D.L., and Rundle, J.B., Fall AGU Meeting (this session). Davidsen, J. and Paczuski, M., Phys. Rev. Lett., 94, 048501 (2005). Davidsen, J., Grassberger, P., and Paczuski, M., Geophys. Res. Lett., 33, L11304 (2006). Davidsen, J., Grassberger, P., and Paczuski, M., Phys. Rev. E 77, 066104 (2008).
NG33B-08
The 2002 Mw 7.9 Denali Earthquake Aftershock Sequence: Statistical Analysis
Scaling properties of aftershocks of the 2002 Mw 7.9 Denali fault earthquake are studied. It is found that the sequence exhibits rather complex behavior in the magnitude, spatial, and temporal domains. The main shock was comprised of three subevents and raptured three faults with aftershocks mainly distributed along those faults. The frequency-magnitude statistics of aftershocks can be approximated by Gutenberg-Richter scaling with the obtained b-values that vary both spatially and in time. The magnitude distribution also has a pronounced change in behavior for the early aftershocks. The magnitude difference between the largest detected aftershock and the magnitude of the main shock which constitutes Bath's law is analyzed and discussed. The applicability of the modified Bath's law, where the inferred largest aftershock is obtained from the extrapolation of Gutenberg-Richter scaling, is studied as well. The frequency-magnitude statistics is also reported for the aftershocks generated by the preceding Mw 6.7 foreshock and background seismicity prior to the sequence. In the time domain, the decay rate can be approximated by the modified Omori's law and extends for several years after the main shock. The analysis of interoccurrence times between successive aftershocks reveal that the distribution can be explained in terms of non-homogeneous Poisson process statistics with the modified Omori's law as a rate. A collapse of rescaled interoccurrence time distributions with respect to several parameters indicates presence of a self-similar structure in the aftershock sequence both in the time and magnitude domains and signifies its universal scale-invariant behavior.