seisflows.plugins.preprocess.misfit
===================================

.. py:module:: seisflows.plugins.preprocess.misfit

.. autoapi-nested-parse::

   Misfit functions used by the 'default' preprocess class use to quantify 
   differences between data and synthetics. 

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


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

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

   Direct waveform differencing

   :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:: envelope(syn, obs, nt, dt, *args, **kwargs)

   Waveform envelope difference from Yuan et al. 2015 Eq. 9

   :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, *args, **kwargs)

   Instantaneous phase difference from Bozdag et al. 2011

   :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 misfit function that is proportional to the
   squared time shift corresponding to the highest correlation coefficient
   of the cross-correlation between observed and synthetics

   :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, *args, **kwargs)

   Envelope amplitude ratio from Yuan et al. 2015 Eq. B-1

   :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 cross-correlation lag from Yuan et al. 2015, Eq. B-4

   :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(*args, **kwargs)

.. py:function:: velocity(*args, **kwargs)

.. py:function:: acceleration(*args, **kwargs)