# TemporalModeling¶

class pysit.modeling.TemporalModeling(solver)[source]

Bases: object

Class containing a collection of methods needed for seismic inversion in the time domain.

This collection is designed so that a collection of like-methods can be passed to an optimization routine, changing how we compute each part, eg, in time, frequency, or the Laplace domain, without having to reimplement the optimization routines.

A collection of inversion functions must contain a procedure for computing: * the foward model: apply script_F (in our notation) * migrate: apply F* (in our notation) * demigrate: apply F (in our notation) * Hessian?

Attributes: solver : pysit wave solver object A wave solver that inherits from pysit.solvers.WaveSolverBase

Attributes Summary

Methods Summary

 adjoint_model(self, shot, m0, operand_simdata) Solves for the adjoint field. forward_model(self, shot, m0[, …]) Applies the forward model to the model for the given solver. linear_forward_model(self, shot, m0, m1[, …]) Applies the forward model to the model for the given solver. linear_forward_model_kappa(self, shot, m0, m1) Applies the forward model to the model for the given solver, in terms of a pertubation of kappa. linear_forward_model_rho(self, shot, m0, m1) Applies the forward model to the model for the given solver in terms of a pertubation of rho. migrate_shot(self, shot, m0, …[, …]) Performs migration on a single shot.

Attributes Documentation

modeling_type
solver_type

Methods Documentation

adjoint_model(self, shot, m0, operand_simdata, imaging_period=1, operand_dWaveOpAdj=None, operand_model=None, return_parameters=[], dWaveOp=None, wavefield=None)[source]

For constant density: m*q_tt - lap q = resid, where m = 1.0/c**2 For variable density: m1*q_tt - div(m2 grad)q = resid, where m1=1.0/kappa, m2=1.0/rho, and C = (kappa/rho)**0.5

Parameters: shot : pysit.Shot Gives the receiver model for the right hand side. operand_simdata : ndarray Right hand side component in the data space, usually the residual. operand_dWaveOpAdj : list of ndarray Right hand side component in the wave equation space, usually something to do with the imaging component…this needs resolving operand_simdata : ndarray Right hand side component in the data space, usually the residual. return_parameters : list of {‘adjointfield’, ‘ic’} dWaveOp : ndarray Imaging component from the forward model. retval : dict Dictionary whose keys are return_parameters that contains the specified data.

Notes

• q is the adjoint field.
• ic is the imaging component. Because this function computes many of
the things required to compute the imaging condition, there is an option to compute the imaging condition as we go. This should be used to save computational effort. If the imaging condition is to be computed, the optional argument utt must be present.
Imaging Condition for variable density has components:
forward_model(self, shot, m0, imaging_period=1, return_parameters=[])[source]

Applies the forward model to the model for the given solver.

Parameters: shot : pysit.Shot Gives the source signal approximation for the right hand side. m0 : solver.ModelParameters The parameters upon which to evaluate the forward model. return_parameters : list of {‘wavefield’, ‘simdata’, ‘dWaveOp’} retval : dict Dictionary whose keys are return_parameters that contains the specified data.

Notes

• u is used as the target field universally. It could be velocity potential, it could be displacement, it could be pressure.
• utt is used to generically refer to the derivative of u that is needed to compute the imaging condition.

Forward Model solves:

For constant density: m*u_tt - lap u = f, where m = 1.0/c**2 For variable density: m1*u_tt - div(m2 grad)u = f, where m1=1.0/kappa, m2=1.0/rho, and C = (kappa/rho)**0.5

linear_forward_model(self, shot, m0, m1, return_parameters=[], dWaveOp0=None)[source]

Applies the forward model to the model for the given solver.

Parameters: shot : pysit.Shot Gives the source signal approximation for the right hand side. m0 : solver.ModelParameters The parameters upon where to center the linear approximation. m1 : solver.ModelParameters The parameters upon which to apply the linear forward model to. return_parameters : list of {‘wavefield1’, ‘dWaveOp1’, ‘dWaveOp0’, ‘simdata’} Values to return. u0tt : ndarray Derivative field required for the imaging condition to be used as right hand side. retval : dict Dictionary whose keys are return_parameters that contains the specified data.

Notes

• u1 is used as the target field universally. It could be velocity potential, it could be displacement, it could be pressure.
• u1tt is used to generically refer to the derivative of u1 that is needed to compute the imaging condition.
• If u0tt is not specified, it may be computed on the fly at potentially high expense.
linear_forward_model_kappa(self, shot, m0, m1, return_parameters=[], dWaveOp0=None)[source]

Applies the forward model to the model for the given solver, in terms of a pertubation of kappa.

Parameters: shot : pysit.Shot Gives the source signal approximation for the right hand side. m0 : solver.ModelParameters The parameters upon where to center the linear approximation. m1 : solver.ModelParameters The parameters upon which to apply the linear forward model to. return_parameters : list of {‘wavefield1’, ‘dWaveOp1’, ‘dWaveOp0’, ‘simdata’} Values to return. u0tt : ndarray Derivative field required for the imaging condition to be used as right hand side. retval : dict Dictionary whose keys are return_parameters that contains the specified data.

Notes

• u1 is used as the target field universally. It could be velocity potential, it could be displacement, it could be pressure.
• u1tt is used to generically refer to the derivative of u1 that is needed to compute the imaging condition.
• If u0tt is not specified, it may be computed on the fly at potentially high expense.
linear_forward_model_rho(self, shot, m0, m1, return_parameters=[], dWaveOp0=None, wavefield=None)[source]

Applies the forward model to the model for the given solver in terms of a pertubation of rho.

Parameters: shot : pysit.Shot Gives the source signal approximation for the right hand side. m0 : solver.ModelParameters The parameters upon where to center the linear approximation. m1 : solver.ModelParameters The parameters upon which to apply the linear forward model to. return_parameters : list of {‘wavefield1’, ‘dWaveOp1’, ‘dWaveOp0’, ‘simdata’} Values to return. u0tt : ndarray Derivative field required for the imaging condition to be used as right hand side. retval : dict Dictionary whose keys are return_parameters that contains the specified data.

Notes

• u1 is used as the target field universally. It could be velocity potential, it could be displacement, it could be pressure.
• u1tt is used to generically refer to the derivative of u1 that is needed to compute the imaging condition.
• If u0tt is not specified, it may be computed on the fly at potentially high expense.
migrate_shot(self, shot, m0, operand_simdata, imaging_period, operand_dWaveOpAdj=None, operand_model=None, dWaveOp=None, adjointfield=None, dWaveOpAdj=None, wavefield=None)[source]

Performs migration on a single shot.

Parameters: shot : pysit.Shot Shot for which to compute migration. operand : darray Operand, i.e., b in (F^*)b. dWaveOp : list Imaging condition components from the forward model for each receiver in the shot. qs : list Optional return list allowing us to retrieve the adjoint field as desired.