A Pump-Probe Analysis of Nonlinear Elastic Behavior on the San Andreas Fault

Author(s):  
Andrew Delorey

<p>Fracture networks in the subsurface influence nearly every aspect of earthquakes and natural hazards.  These aspects, including stress, permeability and material failure, and are important for hazard assessment. However, our ability to monitor fracture behavior in the Earth is insufficient for any type of decision-making regarding hazard avoidance.  I propose a new method for probing the evolution of fracture networks in situ to inform public safety decisions and understand natural systems. </p><p>In heterogeneous, fractured materials, like those found in the Earth, the relationship between stress and strain is highly nonlinear.  This nonlinearity in the upper crust is almost entirely due to fractures.  By measuring to what extent Earth materials exhibit nonlinear elastic behavior, we can learn more information about them.  Directly, measuring physical properties may be more useful than just detecting that fractures are present or how they are shaped and oriented.  We measure nonlinearity by measuring the apparent modulus at different strains. </p><p>In this study we use a pump-probe analysis, which involves continuously probing velocity (as a proxy for modulus) while systematically straining the material.  We will use solid Earth tides as a strain pump and empirical Green’s functions (EGF) as a velocity probe.  We apply this analysis to the San Andreas Fault near Parkfield, California.  We chose Parkfield because there is a long-term deployment of borehole seismic instruments that recorded before and after a M6 earthquake.  We find evidence that nonlinear behavior is correlated with the seismic cycle and therefore it may contain information on the both the evolution and current state of stress on faults. </p>

2021 ◽  
Author(s):  
Andrew Delorey ◽  
Paul Johnson

<p>Rocks are heterogeneous materials that exhibit nonlinear elastic (anelastic) behavior in both the laboratory and Earth. In the laboratory, investigators have observed complex relationships between stress and strain that include hysteresis, finite relaxation times, and rate and stress path dependence.  These behaviors are linked to stress, porosity, permeability, material integrity and material failure, many of the characteristics we care about in the upper crust.  A limited number of studies in the Earth have confirmed that nonlinear elasticity can be measured in situ, but due to logistical challenges these investigations have not achieved the full potential of what can ultimately be learned from this type of investigation.  We adapted a ‘pump-probe’ type experiment common in laboratory studies, using solid earth tides as the low frequency pump and empirical Green’s function as the high frequency probe.  By probing the velocity at different points in the pump cycle, we constrain some important information about the stress-strain relationship.  Near the San Andreas Fault, we observe strongly nonlinear elastic behavior that increases with decreasing distance to the fault that characterizes the damage zone.  We also constrain important aspects of hysteretic behavior that are related to damage properties and possibly pore pressure.</p>


We consider three in situ processes which involve fluid flow in the crust: fault creep, aftershocks and dilatancy. Measurements of water level in wells suggest that creep events on the San Andreas fault are coupled with pore pressure changes. Readjustment of transient pore pressure, induced by large shallow earthquakes, possess the correct time constants and magnitudes to explain the occurrence of aftershocks. And finally, temporal changes of travel times in the Gram district (U.S.S.R.) imply that dilatancy may occur in situ.


1996 ◽  
Vol 118 (4) ◽  
pp. 445-451 ◽  
Author(s):  
G. S. Schajer ◽  
S. I. Green ◽  
A. P. Davis ◽  
Y. N.-H. Hsiang

This study illustrates how the highly nonlinear elastic behavior of artery wall material can cause unusual structural characteristics that do not occur with a linear-elastic material. An example mathematical model of an end-to-end anastomosis successfully predicts the experimentally observed area of elevated elastic compliance, called the “Para-anastomotic Hypercompliant Zone” (PHZ). The elastic hypercompliance is shown to occur because the anastomosis locally restricts the arterial diameter, thus forcing the adjacent material to remain in a lower strain, and correspondingly a lower stiffness, part of its non-linear stress-strain curve. Elevated elastic compliance can be avoided by locally matching both the arterial diameter and the elastic compliance within the physiological pressure range.


1993 ◽  
Author(s):  
Sandra S. Schulz ◽  
Robert E. Wallace

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