Hardware And Method Of Numerical Integration

A method of implementing a Runge-Kutta integration for generating a travel time half step for a single point defined by X, Y, and Z values along X, Y and Z axes in a travel time data volume comprising:

• at least one memory bank;
• at least one alternate memory bank;
• and at least one decision block interacting with the at least one memory bank and the at least one alternate memory bank comprising the steps of:
• calculating an X-Y plane for each Z for a series of points in the X-Y plane of the travel time data volume and writing the X-Y plane for each Z back to the at least one memory bank and the at least one alternate memory bank;
• calculating an X-Z plane for each Y in one Y direction for a series of points on the X-Z plane of the travel time data volume and writing to the at least one memory bank and the at least one alternate memory bank as Z-X plane for each Y in either Y direction;
• calculating an Z-Y plane for each X in either X direction for a series of points on the Z-Y plane of the travel time data volume and writing the Z-Y plane for each X in either X direction back to the at least one memory bank and the at least one alternate memory bank;
• calculating an Z-X plane for each Y in the other Y direction for a series of points on the Z-X plane of the travel time data volume and writing the X-Z plane for each Y in the other Y direction back to the at least one memory bank and the at least one alternate memory bank;
• if a second half step for single point has not been calculated, return to calculating an X-Y plane for each Z for a series of points in the X-Y plane of the travel time data volume and writing the X-Y plane for each Z back to the at least one memory bank and the at least one alternate memory bank;
• if a second half step for a single point has been calculated, send the travel time data volume to the at least one memory bank.

A system for transforming data through a Rung-Kutta integration of a single point defined by X, Y, and Z values along X, Y and Z axes from a travel time data volume comprising:

• at least one memory bank and at least one alternate memory bank;
• at least one single cycle Runge-Kutta travel time generator in communication with the at least one memory bank and the at least one alternate memory bank;
• wherein the at least one single cycle Runge-Kutta travel time generator reads data from the at least one memory bank, and transforms the data by performing a Runge-Kutta integration on points of a plane defined by X, Y, and Z values along X, Y and Z axes in a travel time data volume and slowness data to generate another plane of values with the integration carried forward by a half step;
• and writes the data back to the at least one alternate memory bank.

A chip implementing a Runge-Kutta integration comprising:

• a first port for accepting an input of travel time data for a current plane;
• a port for accepting an input of slowness data from a velocity model;
• transforming the inputs through a Runge-Kutta integration;
• outputting a plane of travel time data with integration carried forward by a
• calculating an X-Y plane for each Z for a series of points in the X-Y plane of the travel time data;
• swapping X and Z axes in the travel time data volume;
• calculating an Z-Y plane for each X in either X direction for a series of points on the Z-Y plane of the travel time data volume;
• swapping Z and X axes in the travel time data volume;
• calculating an X-Z plane for each Y in either Y direction for a series of points on the X-Z plane of the travel time data volume;
• if a second half step for single point has not been calculated, return to calculating an X-Y plane for each Z for a series of points in the X-Y plane of the travel time data volume.