seisflows.plugins.preprocess.adjoint
====================================

.. py:module:: seisflows.plugins.preprocess.adjoint

.. autoapi-nested-parse::

   Adjoints used by the 'default' preprocess class use to generate adjoint sources

   All functions defined have four required positional arguments

       :type syn: np.array
       :param syn: synthetic data array
       :type obs: np.array
       :param obs: observed data array
       :type nt: int
       :param nt: number of time steps in the data array
       :type dt: float
       :param dt: time step in sec



Functions
---------

.. autoapisummary::

   seisflows.plugins.preprocess.adjoint.waveform
   seisflows.plugins.preprocess.adjoint.envelope
   seisflows.plugins.preprocess.adjoint.instantaneous_phase
   seisflows.plugins.preprocess.adjoint.traveltime
   seisflows.plugins.preprocess.adjoint.traveltime_inexact
   seisflows.plugins.preprocess.adjoint.amplitude
   seisflows.plugins.preprocess.adjoint.envelope2
   seisflows.plugins.preprocess.adjoint.envelope3
   seisflows.plugins.preprocess.adjoint.instantaneous_phase2
   seisflows.plugins.preprocess.adjoint.displacement
   seisflows.plugins.preprocess.adjoint.velocity
   seisflows.plugins.preprocess.adjoint.acceleration


Module Contents
---------------

.. py:function:: waveform(syn, obs, *args, **kwargs)

   Waveform difference from Tromp et al 2005 Eq 9

   :type syn: np.array
   :param syn: synthetic data array
   :type obs: np.array
   :param obs: observed data array


.. py:function:: envelope(syn, obs, nt, dt, eps=0.05, *args, **kwargs)

   Waveform envelope difference from Yuan et al. 2015 Eq. 16

   :type syn: np.array
   :param syn: synthetic data array
   :type obs: np.array
   :param obs: observed data array
   :type nt: int
   :param nt: number of time steps in the data array
   :type dt: float
   :param dt: time step in sec


.. py:function:: instantaneous_phase(syn, obs, nt, dt, eps=0.05, *args, **kwargs)

   Instantaneous phase difference from Bozdag et al. 2011 Eq. 27

   :type syn: np.array
   :param syn: synthetic data array
   :type obs: np.array
   :param obs: observed data array
   :type nt: int
   :param nt: number of time steps in the data array
   :type dt: float
   :param dt: time step in sec


.. py:function:: traveltime(syn, obs, nt, dt, *args, **kwargs)

   Cross-correlation traveltime from Tromp et al. 2005 Eq. 45

   :type syn: np.array
   :param syn: synthetic data array
   :type obs: np.array
   :param obs: observed data array
   :type nt: int
   :param nt: number of time steps in the data array
   :type dt: float
   :param dt: time step in sec


.. py:function:: traveltime_inexact(syn, obs, nt, dt, *args, **kwargs)

   A faster cc traveltime function but possibly innacurate

   :type syn: np.array
   :param syn: synthetic data array
   :type obs: np.array
   :param obs: observed data array
   :type nt: int
   :param nt: number of time steps in the data array
   :type dt: float
   :param dt: time step in sec


.. py:function:: amplitude(syn, obs, nt, dt, *args, **kwargs)

   Cross-correlation amplitude difference

   :type syn: np.array
   :param syn: synthetic data array
   :type obs: np.array
   :param obs: observed data array
   :type nt: int
   :param nt: number of time steps in the data array
   :type dt: float
   :param dt: time step in sec


.. py:function:: envelope2(syn, obs, nt, dt, eps=0.0, *args, **kwargs)

   Envelope amplitude ratio from Yuan et al. 2015 Eq. B-2

   :type syn: np.array
   :param syn: synthetic data array
   :type obs: np.array
   :param obs: observed data array
   :type nt: int
   :param nt: number of time steps in the data array
   :type dt: float
   :param dt: time step in sec


.. py:function:: envelope3(syn, obs, nt, dt, eps=0.0, *args, **kwargs)

   Envelope lag from Yuan et al. 2015 Eq. B-2, B-5

   :type syn: np.array
   :param syn: synthetic data array
   :type obs: np.array
   :param obs: observed data array
   :type nt: int
   :param nt: number of time steps in the data array
   :type dt: float
   :param dt: time step in sec


.. py:function:: instantaneous_phase2(syn, obs, nt, dt, eps=0.0, *args, **kwargs)

   Alterative instantaneous phase function

   :type syn: np.array
   :param syn: synthetic data array
   :type obs: np.array
   :param obs: observed data array
   :type nt: int
   :param nt: number of time steps in the data array
   :type dt: float
   :param dt: time step in sec


.. py:function:: displacement(syn, obs, nt, dt, *args, **kwargs)

   Displacement waveform for migration


.. py:function:: velocity(syn, obs, nt, dt, *args, **kwargs)

   Velocity waveform for migration, taking derivative of obs


.. py:function:: acceleration(syn, obs, nt, dt, *args, **kwargs)

   Acceleration waveform for migration, second derivative of obs
   Use finite difference to differentiate observatio nwaveform