altar.models.cdm.libcdm

Module Contents

Functions

altar.models.cdm.libcdm.cosd(angd)

altar.models.cdm.libcdm.sind(angd)

altar.models.cdm.libcdm.norm(v)

altar.models.cdm.libcdm.CDM(X, Y, X0, Y0, depth, ax, ay, az, omegaX, omegaY, omegaZ, opening, nu)

CDM calculates the surface displacements and potency associated with a CDM that is composed of three mutually orthogonal rectangular dislocations in a half-space.

CDM: Compound Dislocation Model RD: Rectangular Dislocation EFCS: Earth-Fixed Coordinate System RDCS: Rectangular Dislocation Coordinate System ADCS: Angular Dislocation Coordinate System (The origin of the RDCS is the RD centroid. The axes of the RDCS are aligned with the strike, dip and normal vectors of the RD, respectively.)

INPUTS X and Y: Horizontal coordinates of calculation points in EFCS (East, North, Up). X and Y must have the same size.

X0, Y0 and depth: Horizontal coordinates (in EFCS) and depth of the CDM centroid. The depth must be a positive value. X0, Y0 and depth have the same unit as X and Y.

omegaX, omegaY and omegaZ: Clockwise rotation angles about X, Y and Z axes, respectively, that specify the orientation of the CDM in space. The input values must be in degrees.

ax, ay and az: Semi-axes of the CDM along the X, Y and Z axes, respectively, before applying the rotations. ax, ay and az have the same unit as X and Y.

opening: The opening (tensile component of the Burgers vector) of the RDs that form the CDM. The unit of opening must be the same as the unit of ax, ay and az.

nu: Poisson’s ratio.

OUTPUTS ue, un and uv: Calculated displacement vector components in EFCS. ue, un and uv have the same unit as opening and the CDM semi-axes in inputs.

DV: Potency of the CDM. DV has the unit of volume (the unit of displacements, opening and CDM semi-axes to the power of 3).

Example: Calculate and plot the vertical displacements on a regular grid.

[X,Y] = numpy.meshgrid(-7:.02:7,-5:.02:5); X0 = 0.5; Y0 = -0.25; depth = 2.75; omegaX = 5; omegaY = -8; omegaZ = 30; ax = 0.4; ay = 0.45; az = 0.8; opening = 1e-3; nu = 0.25; import te[ [ue,un,uv,DV] = CDM(X,Y,X0,Y0,depth,omegaX,omegaY,omegaZ,ax,ay,az,… opening,nu); figure surf(X,Y,reshape(uv,size(X)),’edgecolor’,’none’) view(2) axis equal axis tight set(gcf,’renderer’,’painters’)

Reference journal article: Nikkhoo, M., Walter, T. R., Lundgren, P. R., Prats-Iraola, P. (2016): Compound dislocation models (CDMs) for volcano deformation analyses. Submitted to Geophysical Journal International Copyright (c) 2016 Mehdi Nikkhoo

Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the “Software”), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED “AS IS”, WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.

I appreciate any comments or bug reports.

Mehdi Nikkhoo Created: 2015.5.22 Last modified: 2016.10.18

Section 2.1, Physics of Earthquakes and Volcanoes Department 2, Geophysics Helmholtz Centre Potsdam German Research Centre for Geosciences (GFZ)

email: mehdi.nikkhoo@gfz-potsdam.de mehdi.nikkhoo@gmail.com

website: http://www.volcanodeformation.com

Converted from Matlab to Python April 2018 by Eric Gurrola Jet Propulsion Lab/Caltech

altar.models.cdm.libcdm.RDdispSurf(X, Y, P1, P2, P3, P4, opening, nu)

RDdispSurf calculates surface displacements associated with a rectangular dislocation in an elastic half-space.

altar.models.cdm.libcdm.CoordTrans(x1, x2, x3, A)

CoordTrans transforms the coordinates of the vectors, from x1x2x3 coordinate system to X1X2X3 coordinate system. “A” is the transformation matrix, whose columns e1,e2 and e3 are the unit base vectors of the x1x2x3. The coordinates of e1,e2 and e3 in A must be given in X1X2X3. The transpose of A (i.e., A’) will transform the coordinates from X1X2X3 into x1x2x3.

altar.models.cdm.libcdm.AngSetupFSC(X, Y, bX, bY, bZ, PA, PB, nu)

AngSetupSurf calculates the displacements associated with an angular dislocation pair on each side of an RD in a half-space.

altar.models.cdm.libcdm.AngDisDispSurf(y1, y2, beta, b1, b2, b3, nu, a)

AngDisDispSurf calculates the displacements associated with an angular dislocation in a half-space.