diff --git a/tutorials/plot_post_stack_inversion.py b/tutorials/plot_post_stack_inversion.py index fae7a93d..c273f270 100644 --- a/tutorials/plot_post_stack_inversion.py +++ b/tutorials/plot_post_stack_inversion.py @@ -3,7 +3,7 @@ ========================= This tutorial demonstrates the implementation of a distributed 3D Post-stack inversion. It consists of a first part showing how to model a 3D synthetic post-stack seismic data from a 3D model of the -subsurface acoustic impedence in a distributed manner, following by a second part when inversion +subsurface acoustic impedance in a distributed manner, following by a second part when inversion is carried out. This tutorial builds on the :py:func:`pylops.avo.poststack.PoststackLinearModelling` @@ -136,40 +136,40 @@ # * Inversion with spatial regularization using normal equations along all three dimensions (x, y and z). # This requires extending the operator and data in the following manner: # -# .. math:: -# \mathbf{NormEqOp} = -# \begin{bmatrix} -# \mathbf{G}_1 & \mathbf{0} & \ldots & \mathbf{0} \\ -# \mathbf{0} & \mathbf{G}_2 & \ldots & \mathbf{0} \\ -# \vdots & \vdots & \ddots & \vdots \\ -# \mathbf{0} & \mathbf{0} & \ldots & \mathbf{G}_N -# \end{bmatrix} -# \begin{bmatrix} +# .. math:: +# \mathbf{NormEqOp} = +# \begin{bmatrix} # \mathbf{G}_1^H & \mathbf{0} & \ldots & \mathbf{0} \\ # \mathbf{0} & \mathbf{G}_2^H & \ldots & \mathbf{0} \\ # \vdots & \vdots & \ddots & \vdots \\ # \mathbf{0} & \mathbf{0} & \ldots & \mathbf{G}_N^H -# \end{bmatrix} + \epsilon \mathbf{LapOp} \\ +# \end{bmatrix} +# \begin{bmatrix} +# \mathbf{G}_1 & \mathbf{0} & \ldots & \mathbf{0} \\ +# \mathbf{0} & \mathbf{G}_2 & \ldots & \mathbf{0} \\ +# \vdots & \vdots & \ddots & \vdots \\ +# \mathbf{0} & \mathbf{0} & \ldots & \mathbf{G}_N +# \end{bmatrix} + \epsilon \mathbf{LapOp} \\ # # .. math:: -# \begin{bmatrix} +# \begin{bmatrix} # \mathbf{d}_{1}^{Norm} \\ # \mathbf{d}_{2}^{Norm} \\ # \vdots \\ # \mathbf{d}_{N}^{Norm} -# \end{bmatrix} = -# \begin{bmatrix} +# \end{bmatrix} = +# \begin{bmatrix} # \mathbf{G}_1^H & \mathbf{0} & \ldots & \mathbf{0} \\ # \mathbf{0} & \mathbf{G}_2^H & \ldots & \mathbf{0} \\ # \vdots & \vdots & \ddots & \vdots \\ # \mathbf{0} & \mathbf{0} & \ldots & \mathbf{G}_N^H -# \end{bmatrix} -# \begin{bmatrix} +# \end{bmatrix} +# \begin{bmatrix} # \mathbf{d}_{1} \\ # \mathbf{d}_{2} \\ # \vdots \\ # \mathbf{d}_{N} -# \end{bmatrix} +# \end{bmatrix} # # where :math:`\mathbf{LapOp}` is the :py:class:`pylops_mpi.basicoperators.MPILaplacian` operator # which is used to apply second derivative along all three axes, :math:`\mathbf{NormEqOp}` is the regularized operator