Seismic data processing method and system for migration of seismic signals incorporating azimuthal variations in the velocity

A method of seismic data processing for migration that incorporates variations in velocity with azimuth, the method utilizing a plurality of seismic energy sources and seismic receivers located at known positions at the surface of the earth and a plurality of image points located at predetermined depths beneath the surface, each seismic energy source generating one or more seismic signals that propagate into the earth and return to the surface where the seismic signals are received by the seismic receivers, the method comprising the steps of:

• determining the distance from the energy source to the surface location of the image point;
• determining the fast travel time of the seismic signal from the energy source to the image point;
• determining the slow travel time of the seismic signal from the energy source to the image point;
• determining the azimuth angle between the energy source and the surface location of the image point;
• determining a first azimuth dependent travel time for the seismic signal traveling from the energy source to the image point using the fast travel time, the slow travel time, the azimuth angle of the fast velocity direction, and the azimuth angle of the energy source location to the image point location on the surface;
• determining the distance from the receiver to the surface location of the image point;
• determining the fast travel time of the seismic signal from the receiver to the image point;
• determining the slow travel time of the seismic signal from the receiver to the image point;
• determining the azimuth angle between the receiver and the surface location of the image point;
• and
• determining a second azimuth dependent travel time for the seismic signal traveling from the receiver to the image point using the fast travel time, the slow travel time, the azimuth angle of the fast velocity direction, and the azimuth angle of the receiver location to the image point on the surface, wherein the calculation of the first azimuth dependent travel time for the seismic signal traveling from the energy source to the image point comprises:
• fitting an ellipse to the fast and slow travel times using the slow travel time as the major axis and the fast travel time as the minor axis;
• determining the angle difference between the azimuth angle of the fast axis and the azimuth angle between the energy source and the surface location of the image point;
• determining, using the difference angle in the equation for the ellipse, the travel time from the azimuth of the energy source to the image point.

A method of seismic data processing for migration that incorporates variations in velocity with azimuth, the method utilizing a plurality of seismic energy sources and seismic receivers located at known positions at the surface of the earth and a plurality of image points located at predetermined depths beneath the surface, each seismic energy source generating one or more seismic signals that propagate into the earth and return to the surface where the seismic signals are received by the seismic receivers, the method comprising the steps of:

• determining the distance from the energy source to the surface location of the image point;
• determining the fast travel time of the seismic signal from the energy source to the image point;
• determining the slow travel time of the seismic signal from the energy source to the image point;
• determining the azimuth angle between the energy source and the surface location of the image point;
• determining a first azimuth dependent travel time for the seismic signal traveling from the energy source to the image point using the fast travel time, the slow travel time, the azimuth angle of the fast velocity direction, and the azimuth angle of the energy source location to the image point location on the surface;
• determining the distance from the receiver to the surface location of the image point;
• determining the fast travel time of the seismic signal from the receiver to the image point;
• determining the slow travel time of the seismic signal from the receiver to the image point;
• determining the azimuth angle between the receiver and the surface location of the image point;
• and
• determining a second azimuth dependent travel time for the seismic signal traveling from the receiver to the image point using the fast travel time, the slow travel time, the azimuth angle of the fast velocity direction, and the azimuth angle of the receiver location to the image point on the surface, wherein the determination of the second azimuth dependent travel time for the seismic signal traveling from the receiver to the image point comprises the steps of:
• fitting an ellipse to the fast and slow travel times using the slow travel time as the major axis and the fast travel time as the minor axis;
• computing the angle difference between the azimuth angle of the fast axis and the azimuth angle between the receiver and the surface location of the image point;
• determining, using the difference angle in the equation for the ellipse, the travel time from the azimuth of the receiver to the image point.

A system for seismic data processing by incorporating the azimuthal variations of the velocity of seismic signals, comprising:

• a computer comprising;
• a processor;
• a memory coupled to the processor;
• an input device coupled to the processor and adapted to receive seismic data and to provide the seismic data to the processor,
• a program code stored in the memory and executable by the processor to process the seismic data by performing the following steps:
• determining the distance from an energy source to an image point;
• determining the fast travel time of the seismic signal from an energy source to an image point;
• determining the slow travel time of the seismic signal from the energy source to the image point;
• determining the azimuth angle between the energy source and the surface location of the image point,
• determining a first azimuth dependent travel time of the seismic signal traveling from the energy source to the image point;
• determining the distance from a receiver to an image point;
• determining the fast travel time of the seismic signal from a receiver to an image point;
• determining the slow travel time of the seismic signal from the receiver to the image point;
• determining the azimuth angle between the receiver and the surface location of the image point,
• determining a second azimuth dependent travel time of the seismic signal traveling from the image point to the receiver;
• calculating the total travel time by adding the first and second azimuth dependent travel times;
• summing the amplitudes from the input signals at the total travel time, wherein the signals are phase adjusted according the Kirchhoff imaging criteria and then summed into the output image at the image point;
• and
• repeating the foregoing steps for a plurality of image points beneath the surface of the earth and calculating the total travel time for the plurality of image points, wherein the determination of the azimuth dependent travel times for the seismic signal traveling from the energy source of the receiver to the image point comprises the steps of:
• fitting an ellipse to the fast and slow travel times using the slow travel time as the major axis and the fast travel time as the minor axis;
• computing the angle difference between the azimuth angle of the fast axis and the azimuth angle between the energy source or the receiver and the surface location of the image point;
• determining, using the difference angle in the equation for the ellipse, the travel time at the azimuth of the energy source or the receiver to the image point.