\n",
"\n",
"This notebook is designed to understand the 2-dimensional strain relationships from motion on a buried (blind) fault derived from edge dislocations. The analytical expression in Segall's book for fault displacements is derived from the application of the traction form of Volterra's formula (1) to compute an infinitely long edge dislocation. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$\n",
"u_k(x) = \\int_{\\Sigma} s_i(\\xi) \\sigma^k_{ij}(\\xi, x)n_j d \\Sigma(\\xi) \\tag{1}\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This is a complex integral that describes the displacements in the k direction at a point x as a result of point force acting at $\\xi$. Here $\\sigma^k_{ij}(\\xi,x)$ describes the state of stress at $\\xi$ from the point force in the k direction acting at x. The $n_j$ term is used as a unit vector to determine sign based upon which side of the fault plane $\\Sigma$ that the point x resides. In order to reduce this integral to an analytical solution, we need to descritize the model, apply the plane strain Green's functions, and make some assumptions about the nature of the dislocation (namely that the line force is parallel to the fault plane $\\Sigma$). Below is a schematic of the physical system of a buried fault:"
]
},
{
"attachments": {
"Segall_2DEdgeDislocation.png": {
"image/png": 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"
}
},
"cell_type": "markdown",
"metadata": {},
"source": [
""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The above schematic shows a cross sectional view through a buried normal fault. The coordinate system denotes $x_1$ for the horizontal axis and $x_2$ for the vertical axis. The fault tip is buried at a depth $d$, and makes an angle $\\delta$ with the horizontal plane. Lastly, $s$ is defined as the long-term slip rate on the fault. Volterra's formula and the plane strain Green's functions combine to yield the analytical expressions for horizontal $(u_1)$ and vertical $(u_2)$ displacements:"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$\n",
"u_1 (x_1, x_2 = 0) = \\frac{s}{\\pi} \\left\\{ \\cos(\\delta) \\tan^{-1}(\\zeta) + \n",
"\\frac{\\sin(\\delta) - \\zeta \\cos(\\delta)}{1+\\zeta^{2}} \\right\\} \\tag{2}\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$ \n",
"u_2 (x_1, x_2 = 0) = - \\frac{s}{\\pi} \\left\\{ \\sin(\\delta) \\tan^{-1}(\\zeta) + \n",
"\\frac{\\cos(\\delta) + \\zeta \\sin(\\delta)}{1+\\zeta^{2}} \\right\\} \\tag{3} \n",
"$$ "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Here $s$ is the slip rate in mm/yr, and $\\zeta$ is a the distance between the observation point and the dislocation scaled by the depth (dimensionless term):"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$\n",
"\\zeta = \\frac{x_1 - \\xi_1}{d} \\tag{4}\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Recall that $x_1$ is the observation point in km, $\\xi_1$ is the position of the fault tip in the $x_1$ direction in km, and $d$ is the depth of the fault tip in km. This makes $\\zeta$ a dimensionless term that represents the effective distance from the edge dislocation. In this formulation, when $s$ is positive the motion along the dipping fault surface is normal, conversely if $s$ is negative the motion along the dipping fault surface is reverse. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"
Abstract the formulations to functions
"
]
},
{
"attachments": {
"simple2DStrainWorkflow.png": {
"image/png": 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"
}
},
"cell_type": "markdown",
"metadata": {},
"source": [
"The next cell holds the routines for computing the $u_1$ and $u_2$ displacements as described above. A simple workflow is provided to aid in visualizing the inputs.\n",
""
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"def u1(x1,s,d,xtip,angle):\n",
" '''\n",
" Function for computing the horizontal component of two dimensional edge dislocations\n",
" of a dipping fault.\n",
" INPUTS:\n",
" x1 - the profile location in the x1 (along fault dip) direction (km)\n",
" this variable can be a scalar or an array.\n",
" s - the slip rate (mm/yr)\n",
" d - depth to the top of the fault tip (km)\n",
" xtip - the xposition of the fault tip (km)\n",
" angle - angle the fault plane makes with the horizontal (degrees)\n",
" OUTPUT:\n",
" h - the horizontal displacement (mm/yr)\n",
" (+) means out of the page\n",
" (-) means into the page\n",
" '''\n",
" # dependencies\n",
" from numpy import sin,cos,arctan2,pi\n",
" \n",
" # constants\n",
" ang2rad = pi/180;\n",
" \n",
" # normalized depth\n",
" disl = (x1-xtip)/d;\n",
"\n",
" # break up the terms to make it easier to read/debug\n",
" term1 = cos(angle*ang2rad)*arctan2((x1-xtip),d);\n",
" term2 = (sin(angle*ang2rad) - disl*cos(angle*ang2rad))/(1+(disl**2));\n",
" h = (s/pi)*(term1 + term2);\n",
" \n",
" return h\n",
"\n",
"def u2(x1,s,d,xtip,angle):\n",
" '''\n",
" Function for computing the vertical component of two dimensional edge dislocations\n",
" of a dipping fault.\n",
" INPUTS:\n",
" x1 - the profile location in the x1 (along fault dip) direction (km)\n",
" this variable can be a scalar or an array.\n",
" s - the slip rate (mm/yr)\n",
" d - depth to the top of the fault tip (km)\n",
" xtip - the xposition of the fault tip (km)\n",
" angle - angle the fault plane makes with the horizontal (degrees)\n",
" OUTPUT:\n",
" v - the vertical displacement (mm/yr)\n",
" (+) up\n",
" (-) down\n",
" '''\n",
"\n",
" # dependencies\n",
" from numpy import sin,cos,arctan2,pi\n",
" \n",
" # constants\n",
" ang2rad = pi/180;\n",
" \n",
" # normalized depth\n",
" disl = (x1-xtip)/d;\n",
" \n",
" # terms for the vertical\n",
" term1 = sin(angle*ang2rad)*arctan2((x1-xtip),d)\n",
" term2 = (cos(angle*ang2rad) + disl*sin(angle*ang2rad))/(1+(disl**2))\n",
" v = -(s/pi)*(term1 + term2)\n",
" \n",
" return v\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"
Implement the functions to compute interseismic strain