Data processing

Claim 1

A method for determining the phase misalignment between at least a first part of a first sinusoidal waveform and at least a first part of a second sinusoidal waveform, wherein said first sinusoidal waveform and said second sinusoidal waveform are produced in response to the reception of seismic energy from a seismic source by an array of seismic detectors, said method comprising the steps of: (a) selecting a plurality of data points in said first part of said first sinusoidal waveform and said first part of said second sinusoidal waveform, wherein said plurality of data points are equally spaced apart; (b) assigning a quadrant value to each data point selected in step (a) for said first sinusoidal waveform and said second sinusoidal waveform, wherein a first quadrant value is assigned to a data point if the data point has a positive amplitude and a positive slope, wherein a second quadrant value is assigned to a data point if the data point has a positive amplitude and a negative slope, wherein a third quadrant value is assigned to a data point if the data point has a negative amplitude and a negative slope and wherein a fourth quadrant value is assigned to a data point if the data point has a negative amplitude and a positive slope; (c) selecting a first window for said first part of said first sinusoidal waveform and said first part of said second sinusoidal waveform, wherein said window contains a plurality of the data points selected in step (a); (d) shifting said second sinusoidal waveform with respect to said first sinusoidal waveform by a first phase shift; (e) comparing the quadrant value assigned to the first data point in said first window for said first sinusoidal waveform to the quadrant value assigned to the first data point in said first window for said second sinusoidal waveform shifted by said first phase shift to establish a first correlation value, wherein said first correlation value has a first value if the compared quadrant values are equal and has a second value if the compared quadrant values are not equal; (f) repeating step (e) for all data points contained in said first window for said first sinusoidal waveform and said second sinusoidal waveform shifted by said first phase shift, wherein each data point in said first sinusoidal waveform is compared to a corresponding data point in said second sinusoidal waveform; (g) summing all correlation values established in steps (e) and (f) to establish a total correlation value for said first window for said first phase shift; and (h) repeating steps (d)-(g), wherein different phase shifts are applied in step (d) and wherein the total correlation values derived for each phase shift gives the phase misalignment between said first sinusoidal waveform and said second sinusoidal waveform in said first window.

Claim 2

A method for determining the phase misalignment between at least a first part of a first sinusoidal waveform and at least a first part of a second sinusoidal waveform, wherein said first sinusoidal waveform and said second sinusoidal waveform are produced in response to the reception of seismic energy from a seismic source by an array of seismic detectors, said method comprising the steps of: (a) selecting a plurality of data points in said first part of said first sinusoidal waveform and said first part of said second sinusoidal waveform, wherein said plurality of data points are equally spaced apart; (b) assigning a quadrant value to each data point selected in step (a) for said first sinusoidal waveform and said second sinusoidal waveform, wherein a first quadrant value is assigned to a data point if the data point has a positive amplitude and a positive slope, wherein a second quadrant value is assigned to a data point if the data point has a positive amplitude and a negative slope, wherein a third quadrant value is assigned to a data point if the data point has a negative amplitude and a negative slope and wherein a fourth quadrant value is assigned to a data point if the data point has a negative amplitude and a positive slope; (c) selecting a first window for said first part of said first sinusoidal waveform and said first part of said second sinusoidal waveform, wherein said window contains a plurality of the data points selected in step (a); (d) shifting said second sinusoidal waveform with respect to said first sinusoidal waveform by a first phase shift; (e) comparing the quadrant value assigned to the first data point in said first window for said first sinusoidal waveform to the quadrant value assigned to the first data point in said first window for said second sinusoidal waveform shifted by said first phase shift to establish a first correlation value, wherein said first correlation value has a first value if the compared quadrant values are equal and has a second value if the compared quadrant values are not equal; (f) repeating step (e) for all data points contained in said first window for said first sinusoidal waveform and said second sinusoidal waveform shifted by said first phase shift, wherein each data point in said first sinusoidal waveform is compared to a corresponding data point in said second sinusoidal waveform; (g) summing all correlation values established in steps (e) and (f) to establish a total correlation value for said first window for said first phase shift; and (h) repeating steps (d)-(g), wherein different phase shifts are applied in step (d) and wherein the total correlation values derived for each phase shift gives the phase misalignment between said first sinusoidal waveform and said second sinusoidal waveform in said first window.

Claim 11

A method comprising: (a) imparting seismic waves into the earth from a seismic source; (b) receiving reflected seismic waves at an array of seismic detectors so as to generate a first sinusoidal waveform and a second sinusoidal waveform; (c) selecting a plurality of data points in at least a first part of said first sinusoidal waveform and at least a first part of said second sinusoidal waveform, wherein said plurality of data points are equally spaced apart; (d) assigning a quadrant value to each data point selected in step (c) for said first sinusoidal waveform and said second sinusoidal waveform, wherein a first quadrant value is assigned to a data point if the data point has a positive amplitude and a positive slope, wherein a second quadrant value is assigned to a data point if the data point has a positive amplitude and a negative slope, wherein a third quadrant value is assigned to a data point if the data point has a negative amplitude and a negative slope and wherein a fourth quadrant value is assigned to a data point if the data point has a negative amplitude and a positive slope; (e) selecting a first window for said first part of said first sinusoidal waveform and said first part of said second sinusoidal waveform, wherein said window contains a plurality of the data points selected in step (c); (f) shifting said second sinusoidal waveform with respect to said first sinusoidal waveform by a first phase shift; (g) comparing the quadrant value assigned to the first data point in said first window for said first sinusoidal waveform to the quadrant value assigned to the first data point in said first window for said second sinusoidal waveform shifted by said first phase shift to establish a first correlation value, wherein said first correlation value has a first value if the compared quadrant values are equal and has a second value if the compared quadrant values are not equal; (h) repeating step (g) for all data points contained in said first window for said first sinusoidal waveform and said second sinusoidal waveform shifted by said first phase shift, wherein each data point in said first sinusoidal waveform is compared to a corresponding data point in said second sinusoidal waveform; (i) summing all correlation values established in steps (g) and (h) to establish a total correlation value for said first window for said first phase shift; (j) repeating steps (f)-(i), wherein different phase shifts are applied in step (f) and wherein the total correlation values derived for each phase shift gives the phase misalignment between said first sinusoidal waveform and said second sinusoidal waveform in said first window.

Claim 12

A method comprising: (a) imparting seismic waves into the earth from a seismic source; (b) receiving reflected seismic waves at an array of seismic detectors so as to generate a first sinusoidal waveform and a second sinusoidal waveform; (c) selecting a plurality of data points in at least a first part of said first sinusoidal waveform and at least a first part of said second sinusoidal waveform, wherein said plurality of data points are equally spaced apart; (d) assigning a quadrant value to each data point selected in step (c) for said first sinusoidal waveform and said second sinusoidal waveform, wherein a first quadrant value is assigned to a data point if the data point has a positive amplitude and a positive slope, wherein a second quadrant value is assigned to a data point if the data point has a positive amplitude and a negative slope, wherein a third quadrant value is assigned to a data point if the data point has a negative amplitude and a negative slope and wherein a fourth quadrant value is assigned to a data point if the data point has a negative amplitude and a positive slope; (e) selecting a first window for said first part of said first sinusoidal waveform and said first part of said second sinusoidal waveform, wherein said window contains a plurality of the data points selected in step (c); (f) shifting said second sinusoidal waveform with respect to said first sinusoidal waveform by a first phase shift; (g) comparing the quadrant value assigned to the first data point in said first window for said first sinusoidal waveform to the quadrant value assigned to the first data point in said first window for said second sinusoidal waveform shifted by said first phase shift to establish a first correlation value, wherein said first correlation value has a first value if the compared quadrant values are equal and has a second value if the compared quadrant values are not equal; (h) repeating step (g) for all data points contained in said first window for said first sinusoidal waveform and said second sinusoidal waveform shifted by said first phase shift, wherein each data point in said first sinusoidal waveform is compared to a corresponding data point in said second sinusoidal waveform; (i) summing all correlation values established in steps (g) and (h) to establish a total correlation value for said first window for said first phase shift; (j) repeating steps (f)-(i), wherein different phase shifts are applied in step (f) and wherein the total correlation values derived for each phase shift gives the phase misalignment between said first sinusoidal waveform and said second sinusoidal waveform in said first window.

Claim 14

A method for correcting the phase misalignment between at least a first pair of a first sinusoidal waveform and at least a first part of a second sinusoidal waveform, wherein said first and second sinusoidal waveforms are seismic wiggle traces, said method comprising the steps of: (a) selecting a plurality of data points in said first part of said first sinusoidal waveform and said first part of said second sinusoidal waveform, wherein said plurality of data points are equally spaced apart; (b) assigning a quadrant value to each data point selected in step (a) for said first sinusoidal waveform and said second sinusoidal waveform, wherein a first quadrant value is assigned to a data point if the data point has a positive amplitude and a positive slope, wherein a second quadrant value is assigned to a data point if the data point has a positive amplitude and a negative slope, wherein a third quadrant value is assigned to a data point if the data point has a negative amplitude and a negative slope and wherein a fourth quadrant value is assigned to a data point if the data point has a negative amplitude and a positive slope; (c) selecting a window for said first part of said first sinusoidal waveform and said first part of said second sinusoidal waveform, wherein said window contains a plurality of the data points selected in step (a); (d) shifting said second sinusoidal waveform with respect to said first sinusoidal waveform by a first phase shift; (e) comparing the quadrant value assigned to the first data point in said window for said first sinusoidal waveform to the quadrant value assigned to the first data point in said window for said second sinusoidal waveform shifted by said first phase shift to establish a first correlation value, wherein said first correlation value has a first value of 1 if the compared quadrant values are equal and has a second value of 0 if the compared quadrant values are not equal; (f) repeating step (e) for all data points contained in said window for said first sinusoidal waveform and said second sinusoidal waveform shifted by said first phase shift, wherein each data point in said first sinusoidal waveform is compared to a corresponding data point in said second sinusoidal waveform; (g) summing all correlation values established in steps (e) and (f) to establish a total correlation value for said window for said first phase shift; (h) repeating steps (d)-(g), wherein different phase shifts are applied in step (d) and wherein the total correlation values derived for each phase shift gives the phase misalignment between said first sinusoidal waveform and said second sinusoidal waveform in said first window; and (i) shifting said second sinusoidal waveform with respect to said first sinusoidal waveform by the phase shift which results in the highest total correlation value to thereby produce phase aligned first and second sinusoidal waveforms for said window.

Claim 15

A method for correcting the phase misalignment between at least a first pair of a first sinusoidal waveform and at least a first part of a second sinusoidal waveform, wherein said first and second sinusoidal waveforms are seismic wiggle traces, said method comprising the steps of: (a) selecting a plurality of data points in said first part of said first sinusoidal waveform and said first part of said second sinusoidal waveform, wherein said plurality of data points are equally spaced apart; (b) assigning a quadrant value to each data point selected in step (a) for said first sinusoidal waveform and said second sinusoidal waveform, wherein a first quadrant value is assigned to a data point if the data point has a positive amplitude and a positive slope, wherein a second quadrant value is assigned to a data point if the data point has a positive amplitude and a negative slope, wherein a third quadrant value is assigned to a data point if the data point has a negative amplitude and a negative slope and wherein a fourth quadrant value is assigned to a data point if the data point has a negative amplitude and a positive slope; (c) selecting a window for said first part of said first sinusoidal waveform and said first part of said second sinusoidal waveform, wherein said window contains a plurality of the data points selected in step (a); (d) shifting said second sinusoidal waveform with respect to said first sinusoidal waveform by a first phase shift; (e) comparing the quadrant value assigned to the first data point in said window for said first sinusoidal waveform to the quadrant value assigned to the first data point in said window for said second sinusoidal waveform shifted by said first phase shift to establish a first correlation value, wherein said first correlation value has a first value of 1 if the compared quadrant values are equal and has a second value of 0 if the compared quadrant values are not equal; (f) repeating step (e) for all data points contained in said window for said first sinusoidal waveform and said second sinusoidal waveform shifted by said first phase shift, wherein each data point in said first sinusoidal waveform is compared to a corresponding data point in said second sinusoidal waveform; (g) summing all correlation values established in steps (e) and (f) to establish a total correlation value for said window for said first phase shift; (h) repeating steps (d)-(g), wherein different phase shifts are applied in step (d) and wherein the total correlation values derived for each phase shift gives the phase misalignment between said first sinusoidal waveform and said second sinusoidal waveform in said first window; and (i) shifting said second sinusoidal waveform with respect to said first sinusoidal waveform by the phase shift which results in the highest total correlation value to thereby produce phase aligned first and second sinusoidal waveforms for said window.

Claim 16

A method for correcting the phase misalignment between at least a first part of a first sinusoidal waveform and at least a first part of a second sinusoidal waveform, wherein said first and second sinusoidal waveforms are seismic wiggle traces, said method comprising the steps of: (a) selecting a plurality of data points in said first part of said first sinusoidal waveform and said first part of said second sinusoidal waveform, wherein said plurality of data points are equally spaced apart; (b) assigning a quadrant value to each data point selected in step (a) for said first sinusoidal waveform and said second sinusoidal waveform, wherein a first quadrant value is assigned to a data point if the data point has a positive amplitude and a positive slope, wherein a second quadrant value is assigned to a data point if the data point has a positive amplitude and a negative slope, wherein a third quadrant value is assigned to a data point if the data point has a negative amplitude and a negative slope and wherein a fourth quadrant value is assigned to a data point if the data point has a negative amplitude and a positive slope; (c) selecting a window for said first part of said first sinusoidal waveform and said first part of said second sinusoidal waveform, wherein said window contains a plurality of the data points selected in step (a); (d) shifting said second sinusoidal waveform with respect to said first sinusoidal waveform by a first phase shift; (e) comparing the quadrant value assigned to the first data point in said window for said first sinusoidal waveform to the quadrant value assigned to the first data point in said window for said second sinusoidal waveform shifted by said first phase shift to establish a first correlation value, wherein said first correlation value has a first value if the compared quadrant values are equal and has a second value if the compared quadrant values are not equal; (f) repeating step (e) for all data points contained in said window for said first sinusoidal waveform and said second sinusoidal waveform shifted by said first phase shift, wherein each data point in said first sinusoidal waveform is compared to a corresponding data point in said second sinusoidal waveform; (g) summing all correlation values established in steps (e) and (f) to establish a total correlation value for said window for said first phase shift; (h) repeating steps (d)-(g), wherein different phase shifts are applied in step (d) and wherein the total correlation values derived for each phase shift gives the phase misalignment between said first sinusoidal waveform and said second sinusoidal waveform in said window; and (i) shifting said second sinusoidal waveform with respect to said first sinusoidal waveform by the phase shift which results in the total correlation value corresponding to the maximum number of matches between quadrant values for said first sinusoidal waveform and quadrant values for said second sinusoidal waveform, thereby producing phase aligned first and second sinusoidal waveforms for said window.

Claim 17

A method for correcting the phase misalignment between at least a first part of a first sinusoidal waveform and at least a first part of a second sinusoidal waveform, wherein said first and second sinusoidal waveforms are seismic wiggle traces, said method comprising the steps of: (a) selecting a plurality of data points in said first part of said first sinusoidal waveform and said first part of said second sinusoidal waveform, wherein said plurality of data points are equally spaced apart; (b) assigning a quadrant value to each data point selected in step (a) for said first sinusoidal waveform and said second sinusoidal waveform, wherein a first quadrant value is assigned to a data point if the data point has a positive amplitude and a positive slope, wherein a second quadrant value is assigned to a data point if the data point has a positive amplitude and a negative slope, wherein a third quadrant value is assigned to a data point if the data point has a negative amplitude and a negative slope and wherein a fourth quadrant value is assigned to a data point if the data point has a negative amplitude and a positive slope; (c) selecting a window for said first part of said first sinusoidal waveform and said first part of said second sinusoidal waveform, wherein said window contains a plurality of the data points selected in step (a); (d) shifting said second sinusoidal waveform with respect to said first sinusoidal waveform by a first phase shift; (e) comparing the quadrant value assigned to the first data point in said window for said first sinusoidal waveform to the quadrant value assigned to the first data point in said window for said second sinusoidal waveform shifted by said first phase shift to establish a first correlation value, wherein said first correlation value has a first value if the compared quadrant values are equal and has a second value if the compared quadrant values are not equal; (f) repeating step (e) for all data points contained in said window for said first sinusoidal waveform and said second sinusoidal waveform shifted by said first phase shift, wherein each data point in said first sinusoidal waveform is compared to a corresponding data point in said second sinusoidal waveform; (g) summing all correlation values established in steps (e) and (f) to establish a total correlation value for said window for said first phase shift; (h) repeating steps (d)-(g), wherein different phase shifts are applied in step (d) and wherein the total correlation values derived for each phase shift gives the phase misalignment between said first sinusoidal waveform and said second sinusoidal waveform in said window; and (i) shifting said second sinusoidal waveform with respect to said first sinusoidal waveform by the phase shift which results in the total correlation value corresponding to the maximum number of matches between quadrant values for said first sinusoidal waveform and quadrant values for said second sinusoidal waveform, thereby producing phase aligned first and second sinusoidal waveforms for said window.