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|
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######################################################## |
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# |
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# Copyright (c) 2003-2012 by University of Queensland |
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# Earth Systems Science Computational Center (ESSCC) |
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# http://www.uq.edu.au/esscc |
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# |
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# Primary Business: Queensland, Australia |
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# Licensed under the Open Software License version 3.0 |
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# http://www.opensource.org/licenses/osl-3.0.php |
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# |
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######################################################## |
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|
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__copyright__="""Copyright (c) 2003-2012 by University of Queensland |
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Earth Systems Science Computational Center (ESSCC) |
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http://www.uq.edu.au/esscc |
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Primary Business: Queensland, Australia""" |
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__license__="""Licensed under the Open Software License version 3.0 |
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http://www.opensource.org/licenses/osl-3.0.php""" |
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__url__="https://launchpad.net/escript-finley" |
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|
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__all__ = ['DataSource','UBCDataSource','SyntheticDataSource','SmoothAnomaly'] |
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|
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import logging |
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import numpy as np |
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from esys.escript import * |
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from esys.escript.linearPDEs import * |
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import esys.escript.unitsSI as U |
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try: |
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from scipy.io.netcdf import netcdf_file |
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__all__ += ['NetCDFDataSource'] |
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except: |
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pass |
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|
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|
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class DataSource(object): |
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""" |
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A class that provides survey data for the inversion process. |
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""" |
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# this is currently specific to gravity inversion and should be generalised |
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|
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def __init__(self): |
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""" |
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""" |
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self._domain=None |
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self._pad_l=0.1 |
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self._pad_h=0.1 |
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self.logger = logging.getLogger('inv.%s'%self.__class__.__name__) |
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|
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def _addPadding(self, pad_l, pad_h, NE, l, origin): |
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""" |
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Helper method that computes new number of elements, length and origin |
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after adding padding to the input values. |
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""" |
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DIM=len(NE) |
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frac=[0.]*DIM |
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# padding is applied to each side so multiply by 2 to get the total |
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# amount of padding per dimension |
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if pad_l>0 and pad_l<1: |
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for i in xrange(DIM-1): |
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frac[i]=2*pad_l |
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elif pad_l>=1: |
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for i in xrange(DIM-1): |
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frac[i]=2*pad_l/float(NE[i]) |
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if pad_h>0 and pad_h<1: |
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frac[DIM-1]=2*pad_h |
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elif pad_h>=1: |
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frac[DIM-1]=2*pad_h/(float(NE[DIM-1])) |
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# calculate new number of elements |
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NE_new=[int(NE[i]*(1+frac[i])) for i in xrange(DIM)] |
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NEdiff=[NE_new[i]-NE[i] for i in xrange(DIM)] |
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spacing=[l[i]/NE[i] for i in xrange(DIM)] |
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l_new=[NE_new[i]*spacing[i] for i in xrange(DIM)] |
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origin_new=[origin[i]-NEdiff[i]/2.*spacing[i] for i in xrange(DIM)] |
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return NE_new, l_new, origin_new |
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|
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def _interpolateOnDomain(self, data, shape, origin, spacing, length): |
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""" |
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Helper method that interpolates data arrays onto the domain. |
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""" |
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dim=len(shape) |
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arrays=np.zeros(((len(data[0])-dim),)+tuple(shape)) |
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for entry in data: |
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index=() |
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for i in range(dim): |
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index=((entry[i]-origin[i])/spacing[i],)+index |
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for i in range(arrays.shape[0]): |
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arrays[i][index]=entry[dim+i] |
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dom=self.getDomain() |
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x=dom.getX() |
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delta=[length[i]/(shape[dim-i-1]-1) for i in xrange(dim)] |
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realorigin=[inf(x[i]) for i in xrange(dim)] |
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res=[] |
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for i in range(arrays.shape[0]): |
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res.append(interpolateTable(arrays[i], x[:dim], realorigin, delta, 1e9)) |
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return res |
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|
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def setPadding(self, pad_l=0.1, pad_h=0.1): |
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""" |
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Sets the amount of padding around the dataset. If pad_l/pad_h is >=1 |
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they are treated as number of elements to be added to the domain. |
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If 0 < pad_l;pad_h < 1, the padding amount is relative. |
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""" |
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self._pad_l=pad_l |
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self._pad_h=pad_h |
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|
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def getDomain(self): |
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""" |
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Returns a domain that spans the data area plus padding. |
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""" |
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if self._domain is None: |
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self._domain=self._createDomain(self._pad_l, self._pad_h) |
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return self._domain |
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|
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def getDensityMask(self): |
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""" |
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Returns the density mask data object, where mask has value 1 on the |
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padding area, 0 elsewhere. |
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""" |
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raise NotImplementedError |
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|
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def getGravityAndStdDev(self): |
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""" |
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Returns the gravity anomaly and standard deviation data objects as a |
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tuple. |
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""" |
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raise NotImplementedError |
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|
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def _createDomain(self, padding_l, padding_h): |
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""" |
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creates and returns an escript domain that spans the entire area of |
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available data plus a buffer zone. |
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""" |
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raise NotImplementedError |
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|
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|
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############################################################################## |
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class UBCDataSource(DataSource): |
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def __init__(self, domainclass, meshfile, gravfile, topofile=None): |
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super(UBCDataSource,self).__init__() |
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self._meshfile=meshfile |
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self._gravfile=gravfile |
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self._topofile=topofile |
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self._domainclass=domainclass |
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self._readMesh() |
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|
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def getDensityMask(self): |
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#topodata=self._readTopography() |
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#shape=[self.NE[1]+1, self.NE[0]+1] |
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#mask=self._interpolateOnDomain(topodata, shape, self._origin, self._spacing, self._meshlen) |
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#mask=wherePositive(self.getDomain().getX()[2]-mask[0]) |
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return self._mask |
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|
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def getGravityAndStdDev(self): |
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gravlist=self._readGravity() # x,y,z,g,s |
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shape=[self.NE[2]+1, self.NE[1]+1, self.NE[0]+1] |
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g_and_sigma=self._interpolateOnDomain(gravlist, shape, self._origin, self._spacing, self._meshlen) |
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return g_and_sigma[0]*[0,0,1], g_and_sigma[1] |
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|
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def _readMesh(self): |
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meshdata=open(self._meshfile).readlines() |
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numDataPoints=meshdata[0].split() |
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origin=meshdata[1].split() |
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self._numDataPoints=[int(x) for x in numDataPoints] |
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self._origin=[float(x) for x in origin] |
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self._spacing=[float(X.split('*')[1]) for X in meshdata[2:]] |
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# vertical data is upside down |
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self._origin[2]-=(self._numDataPoints[2]-1)*self._spacing[2] |
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|
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def _createDomain(self, padding_l, padding_h): |
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NE=[self._numDataPoints[i]-1 for i in xrange(3)] |
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l=[NE[i]*self._spacing[i] for i in xrange(3)] |
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NE_new, l_new, origin_new = self._addPadding(padding_l, padding_h, \ |
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NE, l, self._origin) |
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|
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self._meshlen=l_new |
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self.NE=NE_new |
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self._origin=origin_new |
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lo=[(self._origin[i], self._origin[i]+l_new[i]) for i in xrange(3)] |
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NEdiff=[NE_new[i]-NE[i] for i in xrange(3)] |
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try: |
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dom=self._domainclass(*self.NE, l0=lo[0], l1=lo[1], l2=lo[2]) |
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x=dom.getX()-[self._origin[i]+NEdiff[i]/2.*self._spacing[i] for i in xrange(3)] |
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mask=wherePositive(dom.getX()[2]) |
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|
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except TypeError: |
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dom=self._domainclass(*self.NE, l0=l_new[0], l1=l_new[1], l2=l_new[2]) |
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x=dom.getX()-[NEdiff[i]/2.*self._spacing[i] for i in xrange(3)] |
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mask=wherePositive(x[2]+self._origin[2]) |
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|
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M=2 # do not constrain bottom |
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#M=3 # constrain bottom |
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for i in xrange(M): |
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mask=mask + whereNegative(x[i]) + \ |
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wherePositive(x[i]-l_new[i]+NEdiff[i]*self._spacing[i]) |
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self._mask=wherePositive(mask) |
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|
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self.logger.debug("Domain size: %d x %d x %d elements"%(self.NE[0],self.NE[1],self.NE[2])) |
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self.logger.debug(" length: %g x %g x %g"%(l_new[0],l_new[1],l_new[2])) |
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self.logger.debug(" origin: %g x %g x %g"%(origin_new[0],origin_new[1],origin_new[2])) |
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|
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return dom |
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|
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def _readTopography(self): |
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f=open(self._topofile) |
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n=int(f.readline()) |
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topodata=np.zeros((n,3)) |
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for i in xrange(n): |
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x=f.readline().split() |
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x[0]=float(x[0]) |
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x[1]=float(x[1]) |
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x[2]=float(x[2]) |
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topodata[i]=x |
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f.close() |
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return topodata |
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|
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def _readGravity(self): |
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f=open(self._gravfile) |
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n=int(f.readline()) |
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gravdata=np.zeros((n,5)) |
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for i in xrange(n): |
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x=f.readline().split() |
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x[0]=float(x[0]) # x |
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x[1]=float(x[1]) # y |
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x[2]=float(x[2]) # z |
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x[3]=float(x[3]) # gravity anomaly in mGal |
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x[4]=float(x[4]) # stddev |
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# convert gravity anomaly units to m/s^2 and rescale error |
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x[3]*=-1e-5 |
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x[4]*=1e-5 |
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gravdata[i]=x |
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f.close() |
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return gravdata |
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|
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############################################################################## |
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class NetCDFDataSource(DataSource): |
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def __init__(self, domainclass, gravfile, topofile=None, vertical_extents=(-40000,10000,26), alt_of_data=0.): |
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""" |
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vertical_extents - (alt_min, alt_max, num_elements) |
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alt_of_data - altitude of measurements |
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""" |
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super(NetCDFDataSource,self).__init__() |
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self._topofile=topofile |
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self._gravfile=gravfile |
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self._domainclass=domainclass |
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self._determineExtents(vertical_extents) |
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self._altOfData=alt_of_data |
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|
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def getDensityMask(self): |
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#topodata=self._readTopography() |
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#shape=self._numDataPoints[1::-1] |
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#mask=self._interpolateOnDomain(topodata, shape, self._origin, self._spacing, self._meshlen) |
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#mask=wherePositive(self.getDomain().getX()[2]-mask[0]) |
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#rho=fill*(1.-mask) + RHO_AIR*mask |
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return self._mask |
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|
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def getGravityAndStdDev(self): |
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gravlist=self._readGravity() # x,y,z,g,s |
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shape=[self.NE[2]+1, self.NE[1]+1, self.NE[0]+1] |
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g_and_sigma=self._interpolateOnDomain(gravlist, shape, self._origin, self._spacing, self._meshlen) |
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return g_and_sigma[0]*[0,0,1], g_and_sigma[1] |
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|
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def _determineExtents(self, ve): |
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f=netcdf_file(self._gravfile, 'r') |
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NX=0 |
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for n in ['lon','longitude','x']: |
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if n in f.dimensions: |
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NX=f.dimensions[n] |
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break |
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if NX==0: |
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raise RuntimeError("Could not determine extents of data") |
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NY=0 |
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for n in ['lat','latitude','y']: |
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if n in f.dimensions: |
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NY=f.dimensions[n] |
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break |
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if NY==0: |
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raise RuntimeError("Could not determine extents of data") |
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|
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# find longitude and latitude variables |
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variables=f.variables |
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lon_name=None |
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for n in ['lon','longitude']: |
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if n in variables: |
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lon_name=n |
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variables.pop(n) |
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break |
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if lon_name is None: |
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raise RuntimeError("Could not determine longitude variable") |
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lat_name=None |
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for n in ['lat','latitude']: |
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if n in variables: |
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lat_name=n |
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variables.pop(n) |
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break |
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if lat_name is None: |
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raise RuntimeError("Could not determine latitude variable") |
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|
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# try to figure out gravity variable name |
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grav_name=None |
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if len(variables)==1: |
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grav_name=variables.keys()[0] |
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else: |
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for n in variables.keys(): |
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dims=variables[n].dimensions |
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if (lat_name in dims) and (lon_name in dims): |
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grav_name=n |
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break |
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if grav_name is None: |
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raise RuntimeError("Could not determine gravity variable") |
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|
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origin=[0.,0.,ve[0]] |
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lengths=[1.,1.,ve[1]-ve[0]] |
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try: |
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lon_range=f.variables[lon_name].actual_range |
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lat_range=f.variables[lat_name].actual_range |
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#origin[:2]=[lon_range[0],lat_range[0]] |
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lengths[:2]=[lon_range[1]-lon_range[0], lat_range[1]-lat_range[0]] |
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except: |
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try: |
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#origin[:2]=[f.geospatial_lon_min, f.geospatial_lat_min] |
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lengths[:2]=[f.geospatial_lon_max-origin[0], f.geospatial_lat_max-origin[1]] |
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except: |
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pass |
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|
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# hack |
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# grid spacing ~800m |
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SPACING_X=SPACING_Y=800. |
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lengths[0]=(NX-1)*SPACING_X |
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lengths[1]=(NY-1)*SPACING_Y |
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f.close() |
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self._numDataPoints=[NX, NY, ve[2]] |
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self._origin=origin |
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self._meshlen=lengths |
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self._spacing=[lengths[i]/(self._numDataPoints[i]-1) for i in xrange(3)] |
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self._lon=lon_name |
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self._lat=lat_name |
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self._grv=grav_name |
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|
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def _createDomain(self, padding_l, padding_h): |
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NE=[self._numDataPoints[i]-1 for i in xrange(3)] |
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l=self._meshlen |
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NE_new, l_new, origin_new = self._addPadding(padding_l, padding_h, \ |
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NE, l, self._origin) |
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|
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self._meshlen=l_new |
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self.NE=NE_new |
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self._origin=origin_new |
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lo=[(self._origin[i], self._origin[i]+l_new[i]) for i in xrange(3)] |
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NEdiff=[NE_new[i]-NE[i] for i in xrange(3)] |
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try: |
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dom=self._domainclass(*self.NE, l0=lo[0], l1=lo[1], l2=lo[2]) |
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# ripley may adjust NE and length |
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self._meshlen=[sup(dom.getX()[i])-inf(dom.getX()[i]) for i in xrange(3)] |
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self.NE=[self._meshlen[i]/(self._spacing[i]) for i in xrange(3)] |
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x=dom.getX()-[self._origin[i]+NEdiff[i]/2.*self._spacing[i] for i in xrange(3)] |
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mask=wherePositive(dom.getX()[2]) |
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|
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except TypeError: |
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dom=self._domainclass(*self.NE, l0=l_new[0], l1=l_new[1], l2=l_new[2]) |
| 361 |
x=dom.getX()-[NEdiff[i]/2.*self._spacing[i] for i in xrange(3)] |
| 362 |
mask=wherePositive(x[2]+self._origin[2]) |
| 363 |
|
| 364 |
M=2 # do not constrain bottom |
| 365 |
#M=3 # constrain bottom |
| 366 |
for i in xrange(M): |
| 367 |
mask=mask + whereNegative(x[i]) + \ |
| 368 |
wherePositive(x[i]-l_new[i]+NEdiff[i]*self._spacing[i]) |
| 369 |
self._mask=wherePositive(mask) |
| 370 |
|
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self.logger.debug("Domain size: %d x %d x %d elements"%(self.NE[0],self.NE[1],self.NE[2])) |
| 372 |
self.logger.debug(" length: %s x %s x %s"%(self._meshlen[0],self._meshlen[1],self._meshlen[2])) |
| 373 |
self.logger.debug(" origin: %s x %s x %s"%(self._origin[0],self._origin[1],self._origin[2])) |
| 374 |
|
| 375 |
return dom |
| 376 |
|
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def _readTopography(self): |
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f=netcdf_file(self._topofile, 'r') |
| 379 |
lon=None |
| 380 |
for n in ['lon','longitude']: |
| 381 |
if n in f.variables: |
| 382 |
lon=f.variables[n][:] |
| 383 |
break |
| 384 |
if lon is None: |
| 385 |
raise RuntimeError("Could not determine longitude variable") |
| 386 |
lat=None |
| 387 |
for n in ['lat','latitude']: |
| 388 |
if n in f.variables: |
| 389 |
lat=f.variables[n][:] |
| 390 |
break |
| 391 |
if lat is None: |
| 392 |
raise RuntimeError("Could not determine latitude variable") |
| 393 |
alt=None |
| 394 |
for n in ['altitude','alt']: |
| 395 |
if n in f.variables: |
| 396 |
alt=f.variables[n][:] |
| 397 |
break |
| 398 |
if alt is None: |
| 399 |
raise RuntimeError("Could not determine altitude variable") |
| 400 |
|
| 401 |
topodata=np.column_stack((lon,lat,alt)) |
| 402 |
f.close() |
| 403 |
return topodata |
| 404 |
|
| 405 |
def _readGravity(self): |
| 406 |
f=netcdf_file(self._gravfile, 'r') |
| 407 |
#lon=f.variables[self._lon][:] |
| 408 |
#lat=f.variables[self._lat][:] |
| 409 |
grav=f.variables[self._grv][:] |
| 410 |
f.close() |
| 411 |
lon=np.linspace(0, (grav.shape[1]-1)*self._spacing[0], num=grav.shape[1]) |
| 412 |
lat=np.linspace(0, (grav.shape[0]-1)*self._spacing[1], num=grav.shape[0]) |
| 413 |
lon,lat=np.meshgrid(lon,lat) |
| 414 |
lon=lon.flatten() |
| 415 |
lat=lat.flatten() |
| 416 |
grav=grav.flatten() |
| 417 |
alt=self._altOfData*np.ones(grav.shape) |
| 418 |
try: |
| 419 |
missing=grav.missing_value |
| 420 |
err=np.where(grav==missing, 1.0, 0.0) |
| 421 |
except: |
| 422 |
err=np.ones(lon.shape) |
| 423 |
err=1e-6*err |
| 424 |
grav=1e-6*grav |
| 425 |
gravdata=np.column_stack((lon,lat,alt,grav,err)) |
| 426 |
return gravdata |
| 427 |
|
| 428 |
class SmoothAnomaly(object): |
| 429 |
def __init__(self, lx, ly, lz, x, y, depth, rho_inner, rho_outer): |
| 430 |
self.x=x |
| 431 |
self.y=y |
| 432 |
self.lx=lx |
| 433 |
self.ly=ly |
| 434 |
self.lz=lz |
| 435 |
self.depth=depth |
| 436 |
self.rho_inner=rho_inner |
| 437 |
self.rho_outer=rho_outer |
| 438 |
self.rho=None |
| 439 |
def getMask(self, x): |
| 440 |
DIM=x.getDomain().getDim() |
| 441 |
m=whereNonNegative(x[DIM-1]-(sup(x[DIM-1])-self.depth-self.lz/2)) * whereNonPositive(x[DIM-1]-(sup(x[DIM-1])-self.depth+self.lz/2)) \ |
| 442 |
*whereNonNegative(x[0]-(self.x-self.lx/2)) * whereNonPositive(x[0]-(self.x+self.lx/2)) |
| 443 |
if DIM>2: |
| 444 |
m*=whereNonNegative(x[1]-(self.y-self.ly/2)) * whereNonPositive(x[1]-(self.y+self.ly/2)) |
| 445 |
if self.rho is None: |
| 446 |
alpha=-log(abs(self.rho_outer/self.rho_inner))*4 |
| 447 |
rho=exp(-alpha*((x[0]-self.x)/self.lx)**2) |
| 448 |
rho=rho*exp(-alpha*((x[DIM-1]-(sup(x[DIM-1])-self.depth))/self.lz)**2) |
| 449 |
self.rho=maximum(abs(self.rho_outer), abs(self.rho_inner*rho)) |
| 450 |
if self.rho_inner<0: self.rho=-self.rho |
| 451 |
return m |
| 452 |
|
| 453 |
class SyntheticDataSource(DataSource): |
| 454 |
def __init__(self, DIM, NE, l, h, features): |
| 455 |
super(SyntheticDataSource,self).__init__() |
| 456 |
self._features = features |
| 457 |
self.DIM=DIM |
| 458 |
self.NE=NE |
| 459 |
self.l=l |
| 460 |
self.h=h |
| 461 |
|
| 462 |
def _createDomain(self, padding_l, padding_h): |
| 463 |
NE_H=self.NE |
| 464 |
NE_L=int((self.l/self.h)*NE_H+0.5) |
| 465 |
l=[self.l]*(self.DIM-1)+[self.h] |
| 466 |
NE=[NE_L]*(self.DIM-1)+[NE_H] |
| 467 |
origin=[0.]*self.DIM |
| 468 |
NE_new, l_new, origin_new = self._addPadding(padding_l, padding_h, \ |
| 469 |
NE, l, origin) |
| 470 |
|
| 471 |
self.NE=NE_new |
| 472 |
self.l=l_new[0] |
| 473 |
self.h=l_new[self.DIM-1] |
| 474 |
|
| 475 |
if self.DIM==2: |
| 476 |
from esys.finley import Rectangle |
| 477 |
dom = Rectangle(n0=NE_new[0], n1=NE_new[1], l0=l_new[0], l1=l_new[1]) |
| 478 |
self._x = dom.getX() + origin_new |
| 479 |
self.logger.debug("Domain size: %d x %d elements"%(NE_new[0], NE_new[1])) |
| 480 |
self.logger.debug(" length: %g x %g"%(l_new[0],l_new[1])) |
| 481 |
self.logger.debug(" origin: %g x %g"%(origin_new[0],origin_new[1])) |
| 482 |
else: |
| 483 |
from esys.finley import Brick |
| 484 |
dom = Brick(n0=NE_new[0], n1=NE_new[1], n2=NE_new[2], l0=l_new[0], l1=l_new[1], l2=l_new[2]) |
| 485 |
self._x = dom.getX() + origin_new |
| 486 |
self.logger.debug("Domain size: %d x %d x %d elements"%(self.NE[0],self.NE[1],self.NE[2])) |
| 487 |
self.logger.debug(" length: %g x %g x %g"%(l_new[0],l_new[1],l_new[2])) |
| 488 |
self.logger.debug(" origin: %g x %g x %g"%(origin_new[0],origin_new[1],origin_new[2])) |
| 489 |
|
| 490 |
dz=l_new[self.DIM-1]/NE_new[self.DIM-1] |
| 491 |
self._g_mask=wherePositive(dom.getX()[0]-origin_new[0]) \ |
| 492 |
* whereNegative(dom.getX()[0]-(l_new[0]-origin_new[0])) \ |
| 493 |
* whereNonNegative(dom.getX()[self.DIM-1]-(l_new[self.DIM-1]+origin_new[self.DIM-1])) \ |
| 494 |
* whereNonPositive(dom.getX()[self.DIM-1]-(l_new[self.DIM-1]+(origin_new[self.DIM-1]+dz))) |
| 495 |
self._mask=whereNegative(self._x[self.DIM-1]) + \ |
| 496 |
wherePositive(self._x[self.DIM-1]-l[self.DIM-1]) |
| 497 |
for i in xrange(self.DIM-1): |
| 498 |
self._mask=self._mask + whereNegative(self._x[i]) + \ |
| 499 |
wherePositive(self._x[i]-l[i]) |
| 500 |
self._mask=wherePositive(self._mask) |
| 501 |
|
| 502 |
rho_ref=0. |
| 503 |
for f in self._features: |
| 504 |
m=f.getMask(self._x) |
| 505 |
rho_ref = rho_ref * (1-m) + f.rho * m |
| 506 |
self._rho=rho_ref |
| 507 |
|
| 508 |
return dom |
| 509 |
|
| 510 |
def getDensityMask(self): |
| 511 |
return self._mask |
| 512 |
|
| 513 |
def getReferenceDensity(self): |
| 514 |
return self._rho |
| 515 |
|
| 516 |
def getGravityAndStdDev(self): |
| 517 |
pde=LinearSinglePDE(self.getDomain()) |
| 518 |
G=6.6742e-11*U.m**3/(U.kg*U.sec**2) |
| 519 |
m_psi_ref=0. |
| 520 |
for i in range(self.DIM): |
| 521 |
m_psi_ref=m_psi_ref + whereZero(self._x[i]-inf(self._x[i])) \ |
| 522 |
+ whereZero(self._x[i]-sup(self._x[i])) |
| 523 |
|
| 524 |
pde.setValue(A=kronecker(self.getDomain()), Y=-4*np.pi*G*self._rho, q=m_psi_ref) |
| 525 |
pde.setSymmetryOn() |
| 526 |
psi_ref=pde.getSolution() |
| 527 |
del pde |
| 528 |
g=-grad(psi_ref) |
| 529 |
sigma=self._g_mask |
| 530 |
return g,sigma |
| 531 |
|
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