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Implementing Crossovers in PaleoGIS
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Implementing Crossovers in PaleoGIS

Rotation table crossovers are used to perform a transition between reference plates for a given plate at a given age.   Each crossover is represented in the table by two poles of rotation: one containing the reference plate for before the transition and one containing the reference plate for after the transition.  

There are two methods (described in detail below) for implementing crossovers in the rotation table that are compatible with PaleoGIS:

Method 1)  Make age values on both sides of the crossover unique.  

Method 2)  Use the same age value for both sides of the crossover.

Crossover Method 1

Making the age values on both sides of the crossover unique is the most robust method for implementing crossovers.  With this method, the age on the younger side of the crossover should be very slightly less than the age on the older side of the crossover, or the age on the older side of the crossover should be very slightly greater than the age on the younger side of the crossover.  The age values can be carried out to up to 15 decimal places in order to minimize the age delta between the two poles.  

This method provides complete control over when the reference plate transition occurs.  For example, for a plate with a crossover at 20 Ma, if the if the age for the pole on the younger side of the crossover is 19.9999 Ma, and the age for the older side is 20 Ma, reconstructions at 19.9999 Ma and younger will use the younger pole (and its reference plate) to calculate the reconstructed location for the plate and reconstructions to 20 Ma and greater will use the older pole.

Note: For consecutive crossovers (i.e., two more crossovers occurring at ages which are not separated by at least one age with a non-crossover pole) this method must be used to ensure that the correct reference plate is being used for reconstructions at or between the consecutive crossover ages.  This is especially important for plates where the reference plate before and after the two crossovers is the same, such as in the example below where the reference plate before 124 Ma and after 132.09999 Ma is 702.

Method 1 for implementing crossovers is illustrated in the figure below where there are three crossovers for plate 501 at 83.5, 124, and 132.1 Ma.  The age value of the first record in each crossover pair has been set to be 0.00001 smaller than the second record.

Crossover Method 2

In this method for handling crossovers, the same age value is used for both poles in the crossover pair.  In this case, reconstructions to ages younger than the crossover will use the younger pole in the calculation of the interpolated reconstruction pole for the plate, and reconstructions to ages older than the crossover will use the older pole.  However, for reconstructions to the exact crossover age, either of the crossover poles might be used for the reconstruction because PaleoGIS uses the first pole it encounters when one or more poles exist for an exact age (i.e., if no pole interpolation is required).   The ID column numbering of the two poles relative to each other in the table does not guarantee which of the two poles will be selected first during reconstructions to the exact crossover age due to the nature of database queries.  As a result, if it is important in your model to have precise control over which pole is used at the exact crossover age, then crossovers should be implemented using Method 1.

Note that crossovers using Method 2 are the only case in PaleoGIS where a plate is allowed to have more than one pole at the same age.

Note: For consecutive crossovers (i.e., two more crossovers occurring at ages which are not separated by at least one age with a non-crossover pole) this Method 1 must be used to ensure that the correct reference plate is being used for reconstructions at or between the consecutive crossover ages.  This is especially important when there are more than two consecutive crossovers and for cases where the reference plate before and after two crossovers is the same, such as in the example shown in Method 1 where the reference plate before 124 Ma and after 132.09999 Ma is 702.

Method 2 for implementing crossovers is illustrated in the figure below where there is a crossover for plate 501 at 83.5 Ma.  

Single Pole Crossovers - A Common Crossover Error

All crossovers in PaleoGIS must be implemented with a pair of poles using either Method 1 or Method 2 described above.  Transitions between reference plates using only a single pole at the crossover age will not work correctly in PaleoGIS.  For example, in the figure below plate 203 changes reference plate from 701 to 926, however, the oldest pole with reference plate 701 is at age 160 Ma, while the youngest pole with reference plate 929 is at age 180 Ma.  Therefore, PaleoGIS cannot determine if the reference plate transition was supposed to occur at 160 Ma or 180 Ma, and as a result, for reconstructions to ages between 160 Ma and 180 Ma the reference frame is ambiguous so the reconstruction pole cannot be correctly interpolated.  In these cases PaleoGIS defaults to no rotation for the plate.