Migration with dipping acquisition plane system and method

A method of generating a zero-offset trace, at a zero-offset location, for a time sampled recording having a source location and receiver location associated therewith, the method comprising:

• determining a reflecting surface;
• determining a set of normal points on the reflecting surface;
• wherein a line from the zero-offset trace location to the reflecting surface is normal to the tangent of the reflecting surface;
• determining the distance between the zero-offset trace location and a normal point;
• dividing twice the distance by the velocity of the medium, wherein the zero-offset travel time for each normal point is determined;
• and
• assigning an amplitude to each zero-offset travel time;
• wherein a zero-offset trace is generated.

A system of generating a zero-offset trace, at a zero-offset location on a processing plane, for a time sampled recording, the time sampled recording having a source and receiver associated therewith, the time sampled recording having a source coordinate and a receiver coordinate associated therewith, the time sampled recording having an amplitude and a sampled time associated therewith, the system comprising:

• a means for reading the source and receiver coordinates;
• wherein the source and receiver coordinates have a non-zero vertical offset associated therewith;
• a means for computing a source-receiver offset from the source and receiver coordinates;
• a means for determining an ellipsoid dependant upon the source-receiver offset, the sampled time, and the velocity of the medium, the ellipsoid having the source as one focus and the receiver as the other focus;
• a means for determining a set of normal points on the ellipsoid, wherein a line from the zero-offset trace location to the ellipsoid is normal to the tangent of the ellipsoid at each of the normal points;
• a means for determining the distance between each of the normal points and the zero-offset trace location;
• a means for dividing twice the distance by the velocity of the medium, wherein the zero-offset travel time for each normal point is determined;
• and
• a means for assigning an amplitude to each zero-offset travel time;
• wherein a zero-offset trace is generated.

A system of generating a zero-offset trace, at a zero-offset location, for a time sampled recording having a source location and receiver location associated therewith, the system comprising:

• a means for determining a reflecting surface;
• a means for determining a set of normal points on the reflecting surface;
• wherein a line from the zero-offset trace location to the reflecting surface is normal to the tangent of the reflecting surface;
• a means for determining the distance between the zero-offset trace location and a normal point;
• a means for dividing twice the distance by the velocity of the medium, wherein the zero-offset travel time for each normal point is determined;
• and
• a means for assigning an amplitude to each zero-offset travel time;
• wherein a zero-offset trace is generated.