esys.downunder.forwardmodels.acoustic Package¶
Forward model for acoustic wave forms
Classes¶
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class
esys.downunder.forwardmodels.acoustic.AcousticWaveForm(domain, omega, w, data, F, coordinates=None, fixAtBottom=False, tol=1e-10, saveMemory=True, scaleF=True)¶ Bases:
esys.downunder.forwardmodels.base.ForwardModelForward Model for acoustic waveform inversion in the frequency domain. It defines a cost function:
Math: defect = 1/2 integrate( ( w * ( a * u - data ) ) ** 2 )where w are weighting factors, data are the measured data (as a 2-comp vector of real and imaginary part) for real frequency omega, and u is the corresponding result produced by the forward model. u (as a 2-comp vector) is the solution of the complex Helmholtz equation for frequency omega, source F and complex, inverse, squared p-velocity sigma:
Math: -u_{ii} - omega**2 * sigma * u = FIt is assumed that the exact scale of source F is unknown and the scaling factor a of F is calculated by minimizing the defect.
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__init__(domain, omega, w, data, F, coordinates=None, fixAtBottom=False, tol=1e-10, saveMemory=True, scaleF=True)¶ initializes a new forward model with acoustic wave form inversion.
Parameters: - domain (
Domain) – domain of the model - w (
Scalar) – weighting factors - data (
escript.Dataof shape (2,)) – real and imaginary part of data - F (
escript.Dataof shape (2,)) – real and imaginary part of source given at Dirac points, on surface or at volume. - coordinates (
ReferenceSystemorSpatialCoordinateTransformation) – defines coordinate system to be used (not supported yet) - tol (positive
float) – tolerance of underlying PDE - saveMemory (
bool) – if true stiffness matrix is deleted after solution of PDE to minimize memory requests. This will require more compute time as the matrix needs to be reallocated. - scaleF (
bool) – if true source F is scaled to minimize defect. - fixAtBottom (
bool) – if true pressure is fixed to zero at the bottom of the domain
- domain (
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getArguments(sigma)¶ Returns precomputed values shared by
getDefect()andgetGradient().Parameters: sigma ( escript.Dataof shape (2,)) – a suggestion for complex 1/V**2Returns: solution, uTar, uTai, uTu Return type: escript.Dataof shape (2,), 3 xfloat
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getCoordinateTransformation()¶ returns the coordinate transformation being used
Return type: CoordinateTransformation
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getDefect(sigma, u, uTar, uTai, uTu)¶ Returns the defect value.
Parameters: - sigma (
escript.Dataof shape (2,)) – a suggestion for complex 1/V**2 - u (
escript.Dataof shape (2,)) – a u vector - uTar (
float) – equalsintegrate( w * (data[0]*u[0]+data[1]*u[1])) - uTai – equals
integrate( w * (data[1]*u[0]-data[0]*u[1])) - uTu (
float) – equalsintegrate( w * (u,u))
Return type: float- sigma (
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getDomain()¶ Returns the domain of the forward model.
Return type: Domain
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getGradient(sigma, u, uTar, uTai, uTu)¶ Returns the gradient of the defect with respect to density.
Parameters: - sigma (
escript.Dataof shape (2,)) – a suggestion for complex 1/V**2 - u (
escript.Dataof shape (2,)) – a u vector - uTar (
float) – equalsintegrate( w * (data[0]*u[0]+data[1]*u[1])) - uTai – equals
integrate( w * (data[1]*u[0]-data[0]*u[1])) - uTu (
float) – equalsintegrate( w * (u,u))
- sigma (
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getSourceScaling(u)¶ returns the scaling factor s required to rescale source F to minimize defect
|s * u- data|^2Parameters: u ( escript.Dataof shape (2,)) – value of pressure solution (real and imaginary part)Return type: complex
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getSurvey(index=None)¶ Returns the pair (data, weight)
If argument index is ignored.
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rescaleWeights(scale=1.0, sigma_scale=1.0)¶ rescales the weights such that
Math: integrate( ( w omega**2 * sigma_scale * data * ((1/L_j)**2)**-1) +1 )/(data*omega**2 * ((1/L_j)**2)**-1) * sigma_scale )=scale
Parameters: - scale (positive
float) – scale of data weighting factors - sigma_scale (
Scalar) – scale of 1/vp**2 velocity.
- scale (positive
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setUpPDE()¶ Creates and returns the underlying PDE.
Return type: lpde.LinearPDE
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class
esys.downunder.forwardmodels.acoustic.ForwardModel¶ Bases:
objectAn abstract forward model that can be plugged into a cost function. Subclasses need to implement
getDefect(),getGradient(), and possiblygetArguments()and ‘getCoordinateTransformation’.-
__init__()¶ Initialize self. See help(type(self)) for accurate signature.
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getArguments(x)¶
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getCoordinateTransformation()¶
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getDefect(x, *args)¶
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getGradient(x, *args)¶
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Functions¶
Others¶
- HAVE_DIRECT