Seismic source separation

A method of processing geophysical data, the method comprising the acts of:

• emitting a first sweep sequence;
• emitting a second sweep sequence contemporaneous to the first sweep sequence;
• receiving a blended signal that includes components corresponding to the first and second sweep sequences;
• determining a blending operator indicative of a noise contribution of the second sweep sequence in the blended signal;
• and
• determining a first annihilator capable of increasing a rank of the blending operator;
• wherein the blending operator indicative of the noise contribution of the second sweep sequence in the blended signal comprises
• ∑
• i
• =
• 1
• ,
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• ≠
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• n
• ⁢
• ⁢
• E
• j
• ⊗
• s
• j
• ⊗
• s
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• ,
• where sj is the second sweep sequence, Ej refers to a matrix having columns that generally correspond to measurements of the second sweep sequence from an array of receivers, and si is the time reversal of the first sweep sequence si that originates at a location l;
• further wherein at least one of the acts of determining the blending operator and/or determining the first annihilator is performed using a computer system.

A method of processing geophysical data, the method comprising the acts of:

• emitting a first sweep sequence;
• emitting a second sweep sequence contemporaneous to the first sweep sequence;
• receiving a blended signal that includes components corresponding to the first and second sweep sequences;
• determining a blending operator indicative of a noise contribution of the second sweep sequence in the blended signal;
• and
• determining a first annihilator capable of increasing a rank of the blending operator;
• wherein the act of determining the first annihilator comprises determining the coefficients λj,y,ωi such that
• E
• i
• ⁡
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• ≠
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• λ
• j
• ,
• y
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• is minimized for each triple i, y, ω, where Ei(iy)(ω) denotes the impulse response of an array of receivers for a source at location i, with offset y between the source and the array of receivers, and frequency ω;
• further wherein at least one of the acts of determining the blending operator and/or determining the first annihilator is performed using a computer system.

A method of processing geophysical data, the method comprising the acts of:

• emitting a first sweep sequence;
• emitting a second sweep sequence contemporaneous to the first sweep sequence;
• emitting a third sweep sequence;
• receiving a blended signal that includes components corresponding to the first and second sweep sequences;
• determining a blending operator indicative of a noise contribution of the second sweep sequence in the blended signal;
• determining a first annihilator capable of increasing a rank of the blending operator;
• and
• inverting the blending operator and the first annihilator;
• wherein the acts of determining the blending operator, determining the first annihilator, and inverting are performed on the third sweep sequence after being performed on the second sequence;
• further wherein at least one of the acts of determining the blending operator, determining the first annihilator, and/or inverting the blending operator and the first annihilator is performed using a computer system.