Modify a reconstruction pole

This example:

  • reads a rotation file,
  • modifies a total reconstruction pole such that a reconstructed point coincides with its desired location at a particular reconstruction time, and
  • writes the modifications back to the same rotation file.

The functionality in this example is similar to the Modify Reconstruction Pole tool in GPlates.

Sample code

import pygplates
import sys


# One or more rotation filenames.
rotation_filenames = ['rotations.rot']

# The reconstruction time (Ma) at which the rotation adjustment needs to be applied.
reconstruction_time = pygplates.GeoTimeInstant(60)

# The plate ID of the plate whose rotation we are adjusting.
reconstruction_plate_id = 801

# The present day point position specified using latitude and longitude (in degrees).
present_day_latitude = -20
present_day_longitude = 135
present_day_position = pygplates.PointOnSphere(
    present_day_latitude, present_day_longitude)

# The desired reconstructed point position specified using latitude and longitude (in degrees).
desired_reconstructed_latitude = -45
desired_reconstructed_longitude = 130
desired_reconstructed_position = pygplates.PointOnSphere(
    desired_reconstructed_latitude, desired_reconstructed_longitude)

# Create a point feature so we can reconstruct it using its plate ID.
point_feature = pygplates.Feature()
point_feature.set_reconstruction_plate_id(reconstruction_plate_id)
point_feature.set_geometry(present_day_position)

# Load the rotation features from rotation files.
# Using a 'pygplates.FeaturesFunctionArgument' to make it easier to write changes back out to the files.
rotation_features = pygplates.FeaturesFunctionArgument(rotation_filenames)

# A rotation model using the rotation features before they are modified.
rotation_model_before_adjustment = pygplates.RotationModel(rotation_features.get_features())

# Reconstruct our point feature to obtain the reconstructed point location.
reconstructed_feature_geometries = []
pygplates.reconstruct(point_feature, rotation_model_before_adjustment, reconstructed_feature_geometries, reconstruction_time)
reconstructed_position = reconstructed_feature_geometries[0].get_reconstructed_geometry()

# Print the actual and desired reconstructed point positions to show they are different.
print 'Reconstructed lat/lon position before adjustment (%f, %f)' % reconstructed_position.to_lat_lon()
print 'Desired reconstructed lat/lon position (%f, %f)' % desired_reconstructed_position.to_lat_lon()

# If the actual and desired reconstructed positions are different then adjust rotation feature(s) to make them the same.
if reconstructed_position != desired_reconstructed_position:

    # The rotation that moves the actual reconstructed position to the desired position.
    rotation_adjustment = pygplates.FiniteRotation(reconstructed_position, desired_reconstructed_position)

    # Modify the rotation feature (or features) corresponding to the reconstruction plate ID.
    for rotation_feature in rotation_features.get_features():

        # Get the rotation feature information.
        total_reconstruction_pole = rotation_feature.get_total_reconstruction_pole()
        if not total_reconstruction_pole:
            # Not a rotation feature.
            continue

        fixed_plate_id, moving_plate_id, rotation_sequence = total_reconstruction_pole
        # We're only interested in rotation features whose moving plate ID matches are reconstruction plate ID.
        if moving_plate_id != reconstruction_plate_id:
            continue

        # Get the enabled rotation samples - ignore the disabled samples.
        enabled_rotation_samples = rotation_sequence.get_enabled_time_samples()
        if not enabled_rotation_samples:
            # All time samples are disabled.
            continue

        # Match sure the time span of the rotation feature's enabled samples spans the reconstruction time.
        if not (enabled_rotation_samples[0].get_time() <= reconstruction_time and
                enabled_rotation_samples[-1].get_time() >= reconstruction_time):
            continue

        # Get the finite rotation at the reconstruction time.
        # If the reconstruction time is between rotation samples then it will get interpolated.
        rotation_property_value = rotation_sequence.get_value(reconstruction_time)
        if not rotation_property_value:
            continue
        rotation = rotation_property_value.get_finite_rotation()

        # The rotation adjustment needs to be applied to the rotation feature (total reconstruction pole).
        # Since this is a rotation relative to the fixed plate of the rotation feature, and not the anchored plate,
        # we need to transform the adjustment appropriately before applying it.
        fixed_plate_frame = rotation_model_before_adjustment.get_rotation(reconstruction_time, fixed_plate_id)
        fixed_plate_frame_rotation_adjustment = fixed_plate_frame.get_inverse() * rotation_adjustment * fixed_plate_frame
        adjusted_rotation = fixed_plate_frame_rotation_adjustment * rotation

        # If one of the enabled rotation samples matches the reconstruction time then
        # get its description so we don't clobber it when we write the adjusted rotation.
        rotation_description = None
        for rotation_sample in enabled_rotation_samples:
            if rotation_sample.get_time() == reconstruction_time:
                rotation_description = rotation_sample.get_description()
                break

        # Set the adjusted rotation back into the rotation sequence.
        rotation_sequence.set_value(
            pygplates.GpmlFiniteRotation(adjusted_rotation),
            reconstruction_time,
            rotation_description)

    # Our rotation adjustment may require crossovers to be re-synchronised.
    if not pygplates.synchronise_crossovers(
            rotation_features.get_features(),
            crossover_threshold_degrees = 0.01,
            # Default to 'pygplates.CrossoverType.synch_old_crossover_and_stages' when/if crossover tags
            # are missing in the rotation file...
            crossover_type_function = pygplates.CrossoverTypeFunction.type_from_xo_tags_in_comment_default_xo_ys):
        print >> sys.stderr, 'Unable to synchronise all crossovers.'

    # Get a new rotation model that uses the adjusted rotation features.
    rotation_model_after_adjustment = pygplates.RotationModel(rotation_features.get_features())
    reconstructed_feature_geometries = []
    pygplates.reconstruct(point_feature, rotation_model_after_adjustment, reconstructed_feature_geometries, reconstruction_time)
    reconstructed_position = reconstructed_feature_geometries[0].get_reconstructed_geometry()

    # Print the adjusted reconstructed point position - should now be same as desired position.
    print 'Reconstructed lat/lon position after adjustment (%f, %f)' % reconstructed_position.to_lat_lon()

    # Write the (modified) rotation feature collections back to the files they came from.
    rotation_files = rotation_features.get_files()
    if rotation_files:
        for feature_collection, filename in rotation_files:
            feature_collection.write(filename)

Details

The filenames of one or more rotation files. We’ll be writing modifications back out to these files.

rotation_filenames = ['rotations.rot']
The rotation adjustment will get applied at 60Ma.
We wrap the reconstruction time in a pygplates.GeoTimeInstant purely because its comparison operators (==, !=, <, <=, >, >=) handle numerical tolerance in floating-point comparisons. This is a good idea in general when comparing floating-point numbers even though in our case the sample code would probably still work if we directly compared floating-point numbers (without a comparison threshold) - in other words if we wrote this as reconstruction_time = 60 instead.
reconstruction_time = pygplates.GeoTimeInstant(60)
The desired reconstructed position is the location we want the present day point position to reconstruct to at 60Ma.
We specify point locations by passing a latitude and longitude to pygplates.PointOnSphere.
present_day_latitude = -20
present_day_longitude = 135
present_day_position = pygplates.PointOnSphere(
    present_day_latitude, present_day_longitude)

desired_reconstructed_latitude = -45
desired_reconstructed_longitude = 130
desired_reconstructed_position = pygplates.PointOnSphere(
    desired_reconstructed_latitude, desired_reconstructed_longitude)
Before we can reconstruct the point location we need to create a pygplates.Feature.
This contains the information (plate ID and present day position) needed to reconstruct the point to the reconstruction time.
point_feature = pygplates.Feature()
point_feature.set_reconstruction_plate_id(reconstruction_plate_id)
point_feature.set_geometry(present_day_position)
We use the utility class pygplates.FeaturesFunctionArgument to load our rotation file(s).
This makes it a little easier for us to write changes to the rotation features back out to the same files.
Alternatively we could have loaded each rotation file into its own pygplates.FeatureCollection and then later saved them back to their rotation file(s).
rotation_features = pygplates.FeaturesFunctionArgument(rotation_filenames)
We use the unmodified rotation features to generate a rotation model.
We’ll use this model to reconstruct the point and to help us make an adjustment to the total reconstruction pole.
rotation_model_before_adjustment = pygplates.RotationModel(rotation_features.get_features())
To find the actual reconstructed point location at 60Ma we reconstruct our point feature.
Since our point feature is valid for all time (by default if we don’t set its valid time) we should get one pygplates.ReconstructedFeatureGeometry from which we obtain the reconstructed point position.
reconstructed_feature_geometries = []
pygplates.reconstruct(point_feature, rotation_model_before_adjustment, reconstructed_feature_geometries, reconstruction_time)
reconstructed_position = reconstructed_feature_geometries[0].get_reconstructed_geometry()
If the actual reconstructed position differs from the desired reconstructed position then we need to adjust the appropriate rotation feature(s) so that they match.
The rotation adjustment is the rotation from reconstructed_position to desired_reconstructed_position. The rotation is created using the constructor of pygplates.FiniteRotation.
if reconstructed_position != desired_reconstructed_position:
    rotation_adjustment = pygplates.FiniteRotation(reconstructed_position, desired_reconstructed_position)
Next we iterate over all the rotation features to find those whose moving plate ID matches the plate ID of our point feature. This is because we only want to our rotation adjustment to affect the plate on which our point lies (and all child plates at the reconstruction time).
We obtain the moving/fixed plate IDs and the time-varying total reconstruction poles from the rotation feature using pygplates.Feature.get_total_reconstruction_pole().
for rotation_feature in rotation_features.get_features():
    total_reconstruction_pole = rotation_feature.get_total_reconstruction_pole()
    if not total_reconstruction_pole:
        continue
    fixed_plate_id, moving_plate_id, rotation_sequence = total_reconstruction_pole
    if moving_plate_id != reconstruction_plate_id:
        continue
A rotation sequence is a time sequence of total rotations of a moving plate relative to a fixed plate.
Not all rotation samples in the sequence are necessarily enabled. So we ignore the disabled samples by calling pygplates.GpmlIrregularSampling.get_enabled_time_samples().
We use the enabled rotation samples to determine if the time range of the rotation sequence includes the reconstruction time.
Note that since reconstruction_time is a pygplates.GeoTimeInstant, comparisons with it will handle numerical tolerance (as mentioned above). This ensures that the test will pass if the reconstruction time coincides with the time of the first or last rotation sample.
enabled_rotation_samples = rotation_sequence.get_enabled_time_samples()
if not enabled_rotation_samples:
    continue
if not (enabled_rotation_samples[0].get_time() <= reconstruction_time and
        enabled_rotation_samples[-1].get_time() >= reconstruction_time):
    continue
If one of the enabled rotation samples matches the reconstruction time then get its description so we don’t clobber it when we write the adjusted rotation.
Each rotation sample usually has a comment/description in the rotation file and this enables us to retain them when writing back out to the rotation file.
rotation_description = None
for rotation_sample in enabled_rotation_samples:
    if rotation_sample.get_time() == reconstruction_time:
        rotation_description = rotation_sample.get_description()
        break
We obtain the original rotation (at the reconstruction time) from the rotation feature using pygplates.GpmlIrregularSampling.get_value().
This will interpolate between the two nearest rotation time samples in the rotation sequence if the reconstruction time does not coincide with a rotation sample.
rotation_property_value = rotation_sequence.get_value(reconstruction_time)
if not rotation_property_value:
    continue
rotation = rotation_property_value.get_finite_rotation()

Now that we have the original rotation from the rotation feature we need to calculate a rotation adjustment such that the new rotation will result in the present day position reconstructing to the desired reconstructed position.

The reconstruction of the present day point position is given by the equation for the Equivalent total rotation which shows the equivalent total rotation of moving plate \(P_{M}\) (relative to anchored plate \(P_{A}\)) at time \(t\) (relative to present day) is:

\[\text{reconstructed_position} = R(0 \rightarrow t,P_{A} \rightarrow P_{M}) \times \text{present_day_position}\]

Using the approach in Composing finite rotations we write the desired reconstructed position in terms of the actual reconstructed position:

\[\begin{split}\text{desired_reconstructed_position} &= R(\text{reconstructed_position} \rightarrow \text{desired_reconstructed_position}) \times \text{reconstructed_position} \\ &= R(\text{reconstructed_position} \rightarrow \text{desired_reconstructed_position}) \times R(0 \rightarrow t,P_{A} \rightarrow P_{M}) \times \text{present_day_position}\end{split}\]

...where the rotation adjustment \(R(\text{reconstructed_position} \rightarrow \text{desired_reconstructed_position})\) represents the rotation from \(\text{reconstructed_position}\) to \(\text{desired_reconstructed_position}\) which (in pygplates) is pygplates.FiniteRotation(reconstructed_position, desired_reconstructed_position).

The composed rotation from present day position to desired reconstructed position represents the adjusted equivalent rotation:

\[\begin{split}\text{desired_reconstructed_position} &= R(0 \rightarrow t,P_{A} \rightarrow P_{M})_{adjusted} \times \text{present_day_position} \\ R(0 \rightarrow t,P_{A} \rightarrow P_{M})_{adjusted} &= R(\text{reconstructed_position} \rightarrow \text{desired_reconstructed_position}) \times R(0 \rightarrow t,P_{A} \rightarrow P_{M})\end{split}\]
However we want to adjust a total rotation pole in a rotation feature. But a rotation feature represents a relative rotation between a moving and fixed plate pair.
So we need to rewrite the adjusted equivalent rotation (which is relative to the anchored plate) as an adjusted relative rotation (relative to the fixed plate \(P_{F}\) of the rotation feature/pole) using the result \(R(P_{A} \rightarrow P_{M}) = R(P_{A} \rightarrow P_{F}) \times R(P_{F} \rightarrow P_{M})\) from Plate circuit paths:
\[\begin{split}R(0 \rightarrow t,P_{A} \rightarrow P_{M})_{adjusted} &= R(\text{reconstructed_position} \rightarrow \text{desired_reconstructed_position}) \times R(0 \rightarrow t,P_{A} \rightarrow P_{M}) \\ R(0 \rightarrow t,P_{A} \rightarrow P_{F}) \times R(0 \rightarrow t,P_{F} \rightarrow P_{M})_{adjusted} &= R(\text{reconstructed_position} \rightarrow \text{desired_reconstructed_position}) \times R(0 \rightarrow t,P_{A} \rightarrow P_{F}) \times R(0 \rightarrow t,P_{F} \rightarrow P_{M})\end{split}\]

Pre-multiplying both sides by \(R(0 \rightarrow t,P_{A} \rightarrow P_{F})^{-1}\) gives:

\[\begin{split}R(0 \rightarrow t,P_{F} \rightarrow P_{M})_{adjusted} &= R(0 \rightarrow t,P_{A} \rightarrow P_{F})^{-1} \times R(\text{reconstructed_position} \rightarrow \text{desired_reconstructed_position}) \times R(0 \rightarrow t,P_{A} \rightarrow P_{F}) \times R(0 \rightarrow t,P_{F} \rightarrow P_{M})\end{split}\]

...which represents the adjusted relative rotation \(R(0 \rightarrow t,P_{F} \rightarrow P_{M})_{adjusted}\) in terms of the original relative rotation \(R(0 \rightarrow t,P_{F} \rightarrow P_{M})\).

This is written in pygplates as:

fixed_plate_frame = rotation_model_before_adjustment.get_rotation(reconstruction_time, fixed_plate_id)
adjusted_rotation = fixed_plate_frame.get_inverse() * rotation_adjustment * fixed_plate_frame * rotation

...where fixed_plate_frame represents \(R(0 \rightarrow t,P_{A} \rightarrow P_{F})\).

Now that we have calculated the adjusted relative rotation we need to set it back in the rotation feature.
The process of getting the original rotation, adjusting it and setting the adjusted rotation is essentially the following:
rotation = rotation_sequence.get_value(reconstruction_time).get_finite_rotation()

adjusted_rotation = fixed_plate_frame.get_inverse() * rotation_adjustment * fixed_plate_frame * rotation

rotation_sequence.set_value(
    pygplates.GpmlFiniteRotation(adjusted_rotation),
    reconstruction_time,
    rotation_description)
Our rotation adjustment may require crossovers to be re-synchronised. This can happen when a child plate (a plate that moves relative to the plate we made the adjustment on) crosses over from another plate (or to another plate) at the reconstruction time of the rotation adjustment (60Ma). The two crossover rotations will no longer match resulting in a jump in the reconstruction.
So we call pygplates.synchronise_crossovers() to synchronise all crossover rotations.
How each encountered crossover is synchronised needs to be specified. For example, do we synchronise the younger or older rotation sequence (younger/older relative to the crossover time) ? Here we use the function pygplates.CrossoverTypeFunction.type_from_xo_tags_in_comment_default_xo_ys to determine this for us. It will use @xo_ tags in the rotation file (pole comments/descriptions) to determine this and default to the @xo_ys tag if not present for a particular crossover. See pygplates.synchronise_crossovers() for more details.
Note that this modifies the rotation features in-place.
if not pygplates.synchronise_crossovers(
        rotation_features.get_features(),
        crossover_threshold_degrees = 0.01,
        crossover_type_function = pygplates.CrossoverTypeFunction.type_from_xo_tags_in_comment_default_xo_ys):
    print >> sys.stderr, 'Unable to synchronise all crossovers.'
Now we reconstruct the point feature again, but this time using the modified rotation features.
This time the reconstructed point location should match the desired reconstructed point location.
rotation_model_after_adjustment = pygplates.RotationModel(rotation_features.get_features())
reconstructed_feature_geometries = []
pygplates.reconstruct(point_feature, rotation_model_after_adjustment, reconstructed_feature_geometries, reconstruction_time)
reconstructed_position = reconstructed_feature_geometries[0].get_reconstructed_geometry()

print 'Reconstructed lat/lon position after adjustment (%f, %f)' % reconstructed_position.to_lat_lon()
The last step is to write the (modified) rotation features back to the files they came from.
This is made a little easier for us by using the ability of pygplates.FeaturesFunctionArgument to list those feature collections that came from files as well as their associated filenames.
rotation_files = rotation_features.get_files()
if rotation_files:
    for feature_collection, filename in rotation_files:
        feature_collection.write(filename)

Output

Reconstructed lat/lon position before adjustment (-45.962028, 131.398490)
Desired reconstructed lat/lon position (-45.000000, 130.000000)
Reconstructed lat/lon position after adjustment (-45.000000, 130.000000)

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