The H + 3 ion plays a key role in the chemistry of dense interstellar gas clouds where stars and planets are forming. The low temperatures and high extinctions of such clouds make direct observations of H + ratio as well as the para-D 2 H + /ortho-H 2 D + ratio from a non-local thermodynamic equilibrium analysis. The comparison between our chemical modeling and the observations suggests that the CO depletion must be high (larger than 100), with a density between 5 × 10 5 and 10 6 cm −3 . Also the upper limit on the ortho-D 2 H + line is consistent with a low gas temperature (∼11 K) with a ortho-to-para ratio of 6 to 9, i.e. 2 to 3 times higher than the value estimated from the chemical modeling, making it impossible to detect this high frequency transition with the present state of the art receivers.

The intrinsic seismic quality factor [Formula: see text] is known from poroelastic rock-physics theory to be frequency dependent, even within typical bandwidths of individual surface- and borehole-based surveys in which measurement methods usually deliver frequency-independent [Formula: see text]. Thus, measuring frequency-dependent [Formula: see text] instead offers better characterization of seismic properties and moreover a potential step toward estimating permeability directly from seismic data. Therefore, we have introduced a method to measure frequency-dependent [Formula: see text] from pairs of reflections in prestack [Formula: see text]-[Formula: see text] domain surface seismic data — a data type that, unlike a vertical seismic profile, offers useful areal coverage. Although, in principle, any analytic form with a manageable number of parameters could be prescribed, the frequency dependence of [Formula: see text] is modeled as a power law, [Formula: see text]. Inversion is done with a simple grid search over coefficient ([Formula: see text]) and exponent [Formula: see text], seeking a minimum [Formula: see text]-norm. We have found, using a numerical experiment and a synthetic data set, that it is robust and also accurate down to a signal-to-noise ratio of approximately 0.65. Then, [Formula: see text] is estimated for some 955 [Formula: see text] superbins of a 3D prestack ocean bottom cable data set over the Kinnoull field, central North Sea. All combinations of eight prominent reflections between Top Miocene and Base Cretaceous were treated together to give some 21,000 frequency-dependent and (for comparison) constant-[Formula: see text] results. The median coefficient ([Formula: see text]) and exponent [Formula: see text] were 0.0074 and 0.06, respectively, with sharply peaked distributions (excess kurtosis [Formula: see text]). Outlier, strongly frequency-dependent results, given by [Formula: see text], coincide with low-frequency “shadows” under amplitude anomalies, adversely affecting the spectra of reflections. The inferred frequency-dependent [Formula: see text] at 32.5 Hz, the center of the available bandwidth, is not statistically different from the frequency-independent [Formula: see text], 181 with a standard error from the distribution of one, derived from the same data. Hence for this data set, a constant-[Formula: see text] assumption would in fact be adequate. However, our method has the ability to measure stable estimates of [Formula: see text].

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We introduce the signal dependent time–frequency distribution, which is a time–frequency distribution that allows the user to optimize the tradeoff between joint time–frequency resolution and suppression of transform artefacts. The signal‐dependent time–frequency distribution, as well as the short‐time Fourier transform, Stockwell transform, and the Fourier transform are analysed for their ability to estimate the spectrum of a known wavelet used in a tuning wedge model. Next, the signal‐dependent time–frequency distribution, and fixed‐ and variable‐window transforms are used to estimate spectra from a zero‐offset synthetic seismogram. Attenuation is estimated from the associated spectral ratio curves, and the accuracy of the results is compared. The synthetic consisted of six pairs of strong reflections, based on real well‐log data, with a modeled intrinsic attenuation value of 1000/Q = 20. The signal‐dependent time–frequency distribution was the only time–frequency transform found to produce spectra that estimated consistent attenuation values, with an average of 1000/Q = 26±2; results from the fixed‐ and variable‐window transforms were 24±17 and 39±10, respectively. Finally, all three time–frequency transforms were used in a pre‐stack attenuation estimation method (the pre‐stack Q inversion algorithm) applied to a gather from a North Sea seismic dataset, to estimate attenuation between nine different strong reflections. In this case, the signal‐dependent time‐frequency distribution produced spectra more consistent with the constant‐Q model of attenuation assumed in the pre‐stack attenuation estimation algorithm: the average L1 residuals of the spectral ratio surfaces from the theoretical constant‐Q expectation for the signal‐dependent time‐frequency distribution, short‐time Fourier transform, and Stockwell transform were 0.12, 0.21, and 0.33, respectively. Based on the results shown, the signal‐dependent time‐frequency distribution is a time–frequency distribution that can provide more accurate and precise estimations of the amplitude spectrum of a reflection, due to a higher attainable time–frequency resolution.

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