A single-channel seismic reflection method for quantifying lateral ...

30T.M. McGee / Marine Geology 164 (2000) 29–35BSRs are commonly relied upon as indicators of gashydrates in the sea floor. The distribution of propagationspeeds in the vicinity of BSRs, as revealed byseismic reflectivity, has been investigated at severallocations worldwide by applying full-waveforminversion to multi-offset reflection data. Resultsfrom several locations indicate that BSRs characterizedby high reflection amplitudes are underlain by athin layer of free gas (Singh et al., 1993). This hasbeen confirmed by drilling (MacKay et al., 1994;Holbrook et al., 1996).Reflections from BSRs are not always high amplitude,however, and they commonly display stronglateral variability. The reasons for this are not wellunderstood. The use of waveform inversion to investigateBSRs is limited due to the requirement ofrelatively large source/receiver offset distances. Themethod also involves a significant level of effort forprocessing and interpretation.This paper discusses a method for determiningvariations in BSR reflectivity that is fast and applicableto single-channel data. The method was originallydeveloped for environmental and engineeringapplications as part of the European CommunitiesMAST-1 Project GISP (Theilen et al., 1993). Itrequires that the source/receiver offset distance besmall compared to the water depth and that reflectordips not exceed a few degrees; prerequisites which areusually satisfied in the context of BSRs. It alsorequires that the data be recorded digitally untilthe onset of the second water-layer multiple; a prerequisitethat is satisfied less often.The method produces best results if the water isdeep enough that the so-called “primary sequence”,i.e. the water-bottom reflection and the coda thatfollows it (including shallow subsurface reflections,the BSR and attendant interbed multiples) decay toinsignificance prior to the onset of the first waterlayermultiple. Also, results are improved if digitizationis done at a rapid rate, i.e. fast enough to place atleast 10 samples within the dominant wavelength ofthe seismic signal. This improves the coherencebetween the primary sequence and the analogous“first multiple sequence” that begins with the firstwater-layer multiple of the water-bottom reflection.If the coherence is high enough, a deconvolution ofthe first multiple sequence to the primary sequencecompensates for the source pulse and provides, aftercorrection for wave front divergence, a measure of thetrue amplitude of each reflected arrival. These trueamplitudes then yield reflection coefficients whencorrected for transmission losses.2. The single-channel methodIf the signal-to-noise ratio is high, the frequencydomain representation of the primary sequence,P… f †; may be approximated as a multiplication ofthe spectral response of the system, S… f †; with thatof the geologic layering, G… f †; i.e.:P… f †ˆS… f †G… f †…1†Under calm conditions, the surface of the water is anearly perfect (negative) reflector which reflects theupward traveling primary sequence back toward thesea floor to produce what is called a “water-layermultiple”. Each time the sequence of propagatingwavelets is reflected from the water surface, the effectof the sea floor and subbottom layers can be representedin the frequency domain as an additional multiplicationby G… f †; the minus sign accounting for thepolarity reversal that accompanies reflection from theunderside of the water surface. Thus the spectrum ofthe first multiple sequence can be written:M… f †ˆS… f †G… f †G… f †…2†At frequencies for which P… f † is not zero, Eq. (2)may be divided by Eq. (1) to obtain the negative of thespectral response of the geologic layering:M… f †=P… f †ˆG… f †…3†which may be inversely transformed to obtain a timeseries containing the negative of the true amplitudesof primary reflections from the sea floor and subbottominterfaces. This time series also containsmultiple reflections internal to the geologic layers,so some interpretation is required to identify theprimary reflections. After that is done, the reflectioncoefficient of any layer interface may be determinedby dividing the true amplitude of the primaryreflection from that interface by the product of thetransmission coefficients of all interfaces above it.