Method for improving the accuracy of ocean bottom reflectivity estimations using the inverse backus filter

A method for determining ocean bottom reflectivities from dual sensor seismic data, comprising the steps of:

• applying a first time window in which both signal and noise exist to a pressure signal and a velocity signal, generating a first-windowed pressure signal and a first-windowed velocity signal, respectively;
• summing said first-windowed pressure signal and first-windowed velocity signal to generate said first summed signal;
• applying a second time window in which noise dominates to said pressure signal and said velocity signal, generating a second-windowved pressure signal and a second-windowed velocity signal, respectively;
• summing said second-windowed pressure signal and second-windowed velocity signal to generate a second summed signal;
• transforming said first summed signal and said second summed signal from a time domain to a frequency domain, generating a first transformed sum and a second transformed sum, respectively;
• selecting a trial value R for said ocean bottom reflectivity;
• calculating a trial inverse Backus filter (1+RZ).sup.2 for said selected trial ocean bottom reflectivity R, where Z is a Z-transform of two-way travel time delay filter;
• multiplying said first transformed sum and said second transformed sum by said trial inverse Backus filter, generating a first filtered sum and a second filtered sum, respectively;
• calculating a cross spectrum from said first filtered sum and said second filtered sum, generating a trial cross spectrum to substantially remove effects of random noise;
• and
• applying an optimization algorithm to said trial cross spectrum to determine said ocean bottom reflectivity.

A method for determining ocean bottom reflectivities from dual sensor seismic data, comprising the steps of:

• applying a first time window in which both signal and noise exist to a pressure signal and a velocity signal, generating a first-windowed pressure signal and a first-windowed velocity signal, respectively;
• summing said first-windowed pressure signal and first-windowed velocity signal to generate said first summed signal;
• applying a second time window in which noise dominates to said pressure signal and said velocity signal, generating a second-windowed pressure signal and a second-windowed velocity signal, respectively;
• summing said second-windowed pressure signal and second-windowed velocity signal to generate a second summed signal;
• transforming said first summed signal and said second summed signal from a time domain to a frequency domain, generating a first transformed sum and a second transformed sum, respectively;
• selecting a trial value R for said ocean bottom reflectivity;
• calculating a trial inverse Backus filter (1+RZ).sup.2 for said selected trial ocean bottom reflectivity R;
• where Z is a Z-transform of two-way travel time delay filter;
• multiplying said first transformed sum and said second transformed sum by said trial inverse Backus filter, generating a first filtered sum and a second filtered sum, respectively;
• calculating cross spectrums of said first filtered sum and of said second filtered sum, generating a first cross spectrum and a second cross spectrum, respectively;
• subtracting said second cross spectrum from said first cross spectrum, generating said trial cross spectrum;
• and
• applying an optimization algorithm to said trial cross spectrum to determine said ocean bottom reflectivity.

A method for determining ocean bottom reflectivities from dual sensor seismic data, comprising the steps of:

• applying a time window to a first pressure trace and a first velocity trace, generating a windowed first pressure trace and a windowed first velocity trace, respectively;
• summing said windowed first pressure trace and windowed first velocity trace to generate a first summed signal;
• applying said time window to a second pressure trace and a second velocity trace, generating a windowed second pressure trace and a windowed second velocity trace, respectively;
• summing said windowed second pressure trace and windowed second velocity trace to generate a second summed signal;
• transforming said first summed signal and said second summed signal from a time domain to a frequency domain, generating a first transformed sum and a second transformed sum, respectively;
• selecting a trial value R for said ocean bottom reflectivity;
• calculating a trial inverse Backus filter (1+RZ).sup.2 for said selected trial ocean bottom reflectivity R, where Z is a Z-transform of two-way travel time delay filter;
• multiplying said first transformed sum and said second transformed sum by said trial inverse Backus filter, generating a first filtered sum and a second filtered sum, respectively;
• calculating a cross spectrum of said first filtered sum with said second filtered sum, generating a trial cross spectrum;
• and
• applying an optimization algorithm to said trial cross spectrum to determine said ocean bottom reflectivity.