Stochastic Models Of Dynamic Balance State For The Morphological Patterns Of Cryolithozone Landscapes

The paper deals with mathematical modeling of a morphological pattern for a broad spectrum of cryolithozone landscapes in a state of a dynamic balance. The state of the dynamic balance means that all the elements of this morphological pattern are in continuous changing while its general parameters as a whole are stable. Two contradirectional processes at the same territory is a precondition for a state of dynamic balance.We developed a morphological pattern model for lacustrine thermokarst plains with fluvial erosion on the base of the mathematical morphology of landscape using the random process theory. The contra-directional processes here include thermokarst lakes appearing and increasing in size from one side and drainage of the lakes by fluvial erosion, from the other. Thus, the regularities of the structure and dynamics of each landscape morphological pattern are theoretically substantiated. The results of the mathematical modeling were empirically verified at some key sites.

Attenuation and source parameters of earthquakes in the Cascadia region

Digital ground-motion data recorded by the Western Canada Telemetered Network (WCTN) are used to examine the attenuation and source parameters of earthquakes in the Cascadia region of southwestern British Columbia and northwestern Washington. The data base is comprised of over 1000 vertical-component Fourier spectra, from earthquakes of magnitude 3 to 7 at distances from 10 to 500 km. Regression analyses determine the shape and coefficients of the regional attenuation curve and source spectra for 68 earthquakes. Seismic moment and stress drop are inferred from the amplitudes of the source spectra. Shallow (h < 10 km) earthquakes have an attenuation curve with a complex shape, exhibiting significant flattening (no apparent geometric spreading) in the distance range from 75 to 230 km; this shape is probably a result of strong reflected phases from mid-crustal discontinuities and the subducting slab. Events within the subducting slab and the lower crust exhibit a simple R−1 attenuation curve. The anelastic attenuation coefficient for the region as a whole is given by Q = 380f0.39. The duration of motion for each WCTN record is determined as the value that yields the observed relationship between time-domain and spectral-domain amplitudes, according to random process theory. These durations are approximately constant within 50 km of the source, then increase with distance as 0.07R. The high-frequency ground motions from Cascadia earthquakes are relatively weak. Cascadia source spectra are characterized by an average Brune stress drop of about 30 bars. This is significantly lower than the average California stress drop of 70 to 100 bars, and dramatically lower than the average eastern stress drop of 150 to 200 bars. It is concluded that there are significant regional variations in source parameters. Hazard estimates for the Cascadia region based on California groundmotion relations may be overly conservative.

A statistical model for ground motion produced by earthquakes at local and regional distances

To adapt random process theory techniques for statistical estimation of peak ground motion to more realistic earth models, we constrain the parameters of duration, geometrical spreading, and spectral shape by modeling the main ground motion as being the result of major contributions by the direct S wave and supercritically reflected S waves. The results of our modeling are constrained to be consistent with values from full-wave synthetics for the test models. The combination of estimation theory and theoretical amplitude spectrum of the main ground motion within the ergodic window successfully predicts the mean peak vertical ground displacements, velocities, and accelerations of the 1982 Miramichi earthquakes in New Brunswick, Canada. In addition, upon considering the effects of source depth and crustal structure for the November 25, 1988, Saguenay earthquake (M = 5.8) in Québec, Canada, the predicted mean peak horizontal ground accelerations match the observed data very well. The effects of source depth and crustal structure on the peak ground motion are complicated for different source sizes and at different epicentral distance ranges.

A Numerical Model for the Elastic Frictionless Contact of Real Rough Surfaces

A computer model for the dry, frictionless contact of real rough surfaces is presented. The model uses data directly recorded from a stylus measuring instrument and as a confirmation of the model it is shown to reproduce “smooth case” results with a high level of accuracy. Results are given for two important applications of the technique. The first considers the analysis of the contact pressure and displacements for a bearing surface including a debris induced dent in the contact zone. The results go someway to providing an explanation of early life failure often associated with debris contaminated oil. Secondly the relationship between load and real contact area is studied for a sample set of surface profiles. The results obtained are compared with random process theory. It is proposed that the numerical model represents a different approach to rough surface contact allowing certain assumptions about the nature of surface roughness to be relaxed.