The resolving power of a seismic array is defined in terms of the array response function and via the classical uncertainty principle. Using the theory of maximum likelihood wavenumber spectra (Capon, 1969), we show for the case of two correlated plane waves that arbitrarily high resolution is achievable in the limit as the background white noise tends to zero. This extends Barnard’s (1969) result to the case of correlated plane waves. The increased resolution arises from the additional assumption that the data are plane waves over all space, and not zero off the array as the classical result assumes. It is found that a sample rate (in time) large compared to the Nyquist rate, is needed in the case of a short time gate at a small array. Cross‐power spectral matrices are estimated at 4 hz from 1 sec of computer generated data consisting of two correlated plane waves in white noise. These spectral matrices are then used to generate maximum likelihood wavenumber spectra. The two plane waves are resolved at various signal‐to‐noise ratios and at correlations up to ρ=0.8. The need for using a high sampling rate is demonstrated. Results are compared with conventional wavenumber spectra, where the classical resolution results hold. The use of a 1‐sec window provides improved resolution of the wavenumber structure as it changes in time, resulting in better separation of any time‐overlapping phases and multipathed waves that arise from one event.
Using the 100% relative-humidity technique for controlling the mole fraction of water vapor, the Napier (relaxation) frequency of oxygen has been measured as a function of the mole fraction of various water vapors, consisting of pure H20, pure D20, and three mixtures thereof. Pure H20 gives, as is well known, a quadratic in H, the mole fraction; pure D•O gives a linear relation down to 0.7X 10 -a. The mixtures show a linear relation above 1.5 X 10-a and a curvilinear approach to zero below that. Calculation indicates that the heterogeneous molecule HDO is far more effective as a thermal equilibrator for oxygen than either of its homogeneous parents. Quantitatively, with (f/p),,, in cps per atm and h in mole fraction X 10 a, the results are-100% H•O' (f/p),,,= 7 q-183hq-132h•-; 50% D•O' (f/p),•=--664q-llOOh; 80% D20' (f/p),•= --490q-908h; 92% D20' (f/p),,,= --250q-585h (above h= 1.3); 92% D•O' (f/p),•= 7q-275hq-100h•(below h= 1.3); 99.8% D•.O' (f/p),•=--85q-385h.
There is a fundamental error in the article “Estimation of Seismic Noise Structure Using Arrays” by Lacoss et al which appeared in the February 1969 issue of Geophysics. The fundamental error is that the authors are attempting to resolve the horizontal phase velocity v into two components [Formula: see text] and [Formula: see text] where it is implied that [Formula: see text] and [Formula: see text]. This is incorrect as can be seen from Figure 1 in which d is the distance of the plane wavefront from the origin, [Formula: see text] and [Formula: see text] are the x and y components, and t is the corresponding time.
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