Method for attenuating undesirable data, such as multiples, using constrained cross-equalization

A method of cross-equalizing an electrical data trace signal produced by sensing an underwater land formation in an underwater environment and an electrical model trace signal determined from said data trace signal and from parameters of said underwater environment, said method comprising the steps of:

• representing said data trace signal as a sum of:
• a real component of said model trace signal, an imaginary component of said model trace signal, a derivative component of said real component of said model trace signal, and a derivative component of said imaginary component of said model trace signal;
• weighting each of said summed components by a respective weighting factor, said weighting factors embodying amplitude, phase and time differences between said model trace signal and said data trace signal;
• solving for each of said weighting factors to determine said amplitude, phase and time differences;
• designing a constrained filter using said amplitude, phase and time differences;
• and
• filtering said model trace signal with said constrained filter to produce a crossequalized model trace signal.

A method of cross-equalizing an electrical data trace signal produced by sensing an underwater land formation in an underwater environment and an electrical model trace signal determined from said data trace signal and from parameters of said underwater environment, said method comprising the steps of:

• determining a real component of said model trace signal, an imaginary component of said model trace signal, a derivative component of said real component of said model trace signal, and a derivative component of said imaginary component of said model trace signal;
• summing each of said components;
• weighting each of said summed components by a respective weighting factor, said weighting factors embodying amplitude, phase and time differences between said model trace signal and said data trace signal;
• and
• solving for each of said weighting factors to produce a cross-equalized model trace signal.

A method of removing undesirable data from an electrical data trace signal being produced by sensing an underwater land formation and having amplitude, phase and time characteristics, said method comprising the steps of:

• preparing an electrical model trace signal that estimates said undesirable data, said model trace signal having amplitude, phase and time characteristics;
• determining a ratio of said amplitude of said data trace signal and said amplitude of said model trace signal;
• determining a phase difference between said phase of said data trace signal and said phase of said model trace signal;
• determining a time delay between said time characteristic of said data trace signal and said time characteristic of said model trace signal;
• designing a constrained filter using said ratio, phase difference and time delay;
• filtering said model trace signal with said constrained filter to produce a new model trace signal;
• and
• subtracting said new model trace signal from said data trace signal to produce a data trace signal substantially free from said undesirable data.

A method of removing undesirable data from an electrical data trace signal being produced by sensing an underwater land formation and having amplitude, phase and time characteristics, said method comprising the steps of:

• preparing an electrical model trace signal that estimates said undesirable data, said model trace signal having amplitude, phase and time characteristics;
• representing said undesirable data as a sum of:
• a real component of said model trace signal, an imaginary component of said model trace signal, a derivative component of said real component of said model trace signal, and a derivative component of said imaginary component of said model trace signal;
• weighting each of said summed components by a respective weighting factor, said weighting factors embodying amplitude, phase and time differences between said model trace signal and said data trace signal;
• solving for each of said weighting factors to determine said amplitude, phase and time differences;
• designing a constrained filter using said amplitude, phase and time differences;
• filtering said model trace signal with said constrained filter to produce a new model trace signal;
• and
• subtracting said new model trace signal from said data trace signal to produce a data trace signal substantially free from said undesirable data.

A method of removing undesirable data from an electrical data trace signal being produced by sensing an underwater and formation and having amplitude, phase and time characteristics, said method comprising the steps of:

• preparing an electrical model trace signal that estimates said undesirable data, said model trace signal having amplitude, phase and time characteristics;
• determining a real component of said model trace signal, an imaginary component of said model trace signal, a derivative component of said real component of said model trace signal, and a derivative component of said imaginary component of said model trace signal;
• summing each of said components;
• weighting each of said summed components by a respective weighting factor, said weighting factors embodying amplitude, phase and time differences between said model trace signal and said data trace signal;
• solving for each of said weighting factors to produce a cross-equalized model trace signal;
• and
• subtracting said cross-equalized model trace signal from said data trace signal to produce a data trace signal substantially free from said undesirable data.