diff options
Diffstat (limited to 'docs/source/operations/transformations')
| -rw-r--r-- | docs/source/operations/transformations/deformation.rst | 20 |
1 files changed, 10 insertions, 10 deletions
diff --git a/docs/source/operations/transformations/deformation.rst b/docs/source/operations/transformations/deformation.rst index 87b08453..0a772547 100644 --- a/docs/source/operations/transformations/deformation.rst +++ b/docs/source/operations/transformations/deformation.rst @@ -127,7 +127,7 @@ Mathematically speaking, application of a deformation model is simple. The defor represented as a grid of velocities in three dimensions. Coordinate corrections are applied in cartesian space. For a given coordinate, :math:`(X, Y, Z)`, velocities :math:`(V_X, V_Y, V_Z)` can be interpolated from the gridded model. The time span -between :math:`t_c` and :math:`t_{obs}` determine the magnitude of the coordinate +between :math:`t_{obs}` and :math:`t_c` determine the magnitude of the coordinate correcton as seen in eq. :eq:`apply_velocity` below. .. math:: @@ -144,7 +144,7 @@ correcton as seen in eq. :eq:`apply_velocity` below. Y \\ Z \\ \end{pmatrix}_A + - (t_c - t_{obs}) + (t_{obs} - t_c) \begin{pmatrix} V_X \\ V_Y \\ @@ -154,14 +154,14 @@ correcton as seen in eq. :eq:`apply_velocity` below. Corrections are done in cartesian space. -Coordinates of the gridded model are in ENU (east, north, up) space because it would -otherwise require an enormous 3 dimensional grid to handle the corrections in cartesian -space. Keeping the correction in lat/long space reduces the complexity of the grid -significantly. Consequently though, the input coordinates needs to be converted to -lat/long space when searching for corrections in the grid. This is done with the *cart* -operation. The converted grid corrections can then be applied to the input coordinates -in cartesian space. The conversion from ENU space to cartesian space is done in the -following way: +Coordinates of the gridded model are in ENU (east, north, up) space because it +would otherwise require an enormous 3 dimensional grid to handle the corrections +in cartesian space. Keeping the correction in lat/long space reduces the +complexity of the grid significantly. Consequently though, the input coordinates +needs to be converted to lat/long space when searching for corrections in the +grid. This is done with the :ref:`cart<cart>` operation. The converted grid +corrections can then be applied to the input coordinates in cartesian space. The +conversion from ENU space to cartesian space is done in the following way: .. math:: :label: enu2xyz |