I would like to obtain the angle of rotation (?θ) of a detachment fault (https://www.whoi.edu/cms/images/lstokey/2005/1/v41n1-tucholke4en_5007.gif) after X meters of rock displaced during spreading at a mid-ocean ridge. I have a differential equation that can describe the elastic behavior of this fault:
[FONT=MathJax_Main]∇[/FONT][FONT=MathJax_Main]2[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_Math]D[/FONT][FONT=MathJax_Main]∇[/FONT][FONT=MathJax_Main]2[/FONT][FONT=MathJax_Math]w[/FONT][FONT=MathJax_Main])[/FONT][FONT=MathJax_Main]+[/FONT][FONT=MathJax_Math]ρ[/FONT][FONT=MathJax_Math]g[/FONT][FONT=MathJax_Math]w[/FONT][FONT=MathJax_Main]=[/FONT][FONT=MathJax_Math]p[/FONT]
with D the flexural rigidity, w the deflection, ρ the material density, g the gravitational constant, and p the load. Source and details: https://ic.ucsc.edu/~casey/eart150/Death%20Valley%20Reading/Buck,1988_Rolling%20Hinge.pdf
I am not quite sure how to handle this. My aim is to plot ?θ against X so that I get curve models showing an fast increased of fault rotation for a certain distance of spreading, and a steady-flat evolution afterwards (showing nearly no rotation happening anymore).
I never did any numerical modelling before but I'm able to work days/nights to get those curves.
If someone could give me a hint about the process (how to approach the problem mathematically or how to start), I would appreciate greatly.
[FONT=MathJax_Main]∇[/FONT][FONT=MathJax_Main]2[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_Math]D[/FONT][FONT=MathJax_Main]∇[/FONT][FONT=MathJax_Main]2[/FONT][FONT=MathJax_Math]w[/FONT][FONT=MathJax_Main])[/FONT][FONT=MathJax_Main]+[/FONT][FONT=MathJax_Math]ρ[/FONT][FONT=MathJax_Math]g[/FONT][FONT=MathJax_Math]w[/FONT][FONT=MathJax_Main]=[/FONT][FONT=MathJax_Math]p[/FONT]
with D the flexural rigidity, w the deflection, ρ the material density, g the gravitational constant, and p the load. Source and details: https://ic.ucsc.edu/~casey/eart150/Death%20Valley%20Reading/Buck,1988_Rolling%20Hinge.pdf
I am not quite sure how to handle this. My aim is to plot ?θ against X so that I get curve models showing an fast increased of fault rotation for a certain distance of spreading, and a steady-flat evolution afterwards (showing nearly no rotation happening anymore).
I never did any numerical modelling before but I'm able to work days/nights to get those curves.
If someone could give me a hint about the process (how to approach the problem mathematically or how to start), I would appreciate greatly.