Transmission-based near-surface deconvolution

We have developed a new framework for performing surface-consistent amplitude balancing and deconvolution of the near-surface attenuation response. Both approaches rely on the early arrival waveform of a seismic recording, which corresponds to the refracted or, more generally speaking, to the transmitted energy from a seismic source. The method adapts standard surface-consistent amplitude compensation and deconvolution to the domain of refracted/transmitted waves. A sorting domain specific for refracted energy is extended to the analysis of amplitude ratios of each trace versus a reference average trace to identify amplitude residuals that are inverted for surface consistency. The residual values are either calculated as a single scalar value for each trace or as a function of frequency to build a surface-consistent deconvolution operator. The derived operators are then applied to the data to obtain scalar amplitude balancing or amplitude balancing with spectral shaping. The derivation of the operators around the transmitted early arrival waveforms allows for deterministically decoupling the near-surface attenuation response from the remaining seismic data. The developed method is fully automatic and does not require preprocessing of the data. As such, it qualifies as a standard preprocessing tool to be applied at the early stages of seismic processing. Applications of the developed method are provided for a case in a complex, structure-controlled wadi, for a seismic time-lapse [Formula: see text] land monitoring case, and for an exploration area with high dunes and sabkhas producing large frequency-dependent anomalous amplitude responses. The new development provides an effective tool to enable better reservoir characterization and monitoring with land seismic data.

The phase-functions method and scalar amplitude of nucleon–nucleon scattering

A known phase-functions method (PFM) has been considered for calculation of a single-channel nucleon–nucleon scattering. The following partial waves of a nucleon–nucleon scattering have been considered using the phase shifts by PFM: 1S0-, 3P0-, 3P1-, 1D2-, 3F3-states for nn-scattering, 1S0-, 3P0-, 3P1-, 1D2-states for pp-scattering and 1S0-, 1P1-, 3P0-, 3P1-, 1D2-, 3D2-states for np-scattering. The calculations have been carried out using phenomenological nucleon–nucleon Nijmegen group potentials (NijmI, NijmII, Nijm93 and Reid93) and Argonne v18 potential. The scalar scattering amplitude has been calculated using the obtained phase shifts. Our results are not much different from those obtained by using the known phase shifts published in other papers. The difference between calculations depending on a computational method of phase shifts makes: for real (imaginary) parts 0.14–4.36% (0.16–4.05%) for NijmI. 0.02–4.79% (0.08–3.88%) for NijmII. 0.01–5.49% (0.01–4.14%) for Reid93 and 0.01–5.11% (0.01–2.40%) for Argonne v18 potentials.

A BACK-REACTION INDUCED LOWER BOUND ON THE TENSOR-TO-SCALAR RATIO

There are large classes of inflationary models, particularly popular in the context of string theory and braneworld approaches to inflation, in which the ratio of linearized tensor-to-scalar metric fluctuations is very small. In such models, however, gravitational waves produced by scalar modes cannot be neglected. We derive the lower bound on the tensor-to-scalar ratio by considering the back-reaction of the scalar perturbations as a source of gravitational waves. These results show that no cosmological model that is compatible with a metric scalar amplitude of ≈10-5 can have a ratio of the tensor-to-scalar power spectra less than ≈10-8 at recombination and that higher-order terms leads to logarithmic growth for r during radiation domination. Our lower bound also applies to non-inflationary models which produce an almost scale-invariant spectrum of coherent super-Hubble scale metric fluctuations.

Non-Gaussian scalar statistics in homogeneous turbulence

Results are presented of numerical simulations of passive scalar mixing in homogeneous, incompressible turbulent flows. These results are generated via the Linear Eddy Model (LEM) and Direct Numerical Simulation (DNS) of turbulent flows under a variety of different conditions. The nature of mixing and its response to the turbulence field is examined and the single-point probability density function (p.d.f.) of the scalar amplitude and the p.d.f.s of the scalar spatial-derivatives are constructed. It is shown that both Gaussian and exponential scalar p.d.f.s emerge depending on the parameters of the simulations and the initial conditions of the scalar field. Aided by the analyses of data, several reasons are identified for the non-Gaussian behaviour of the scalar amplitude. In particular, two mechanisms are identified for causing exponential p.d.f.s: (i) a non-uniform action of advection on the large and the small scalar scales, (ii) the nonlinear interaction of the scalar and the velocity fluctuations at small scales. In the absence of a constant non-zero mean scalar gradient, the behaviour of the scalar p.d.f. is very sensitive to the initial conditions. In the presence of this gradient, an exponential p.d.f. is not sustained regardless of initial conditions. The numerical results pertaining to the small-scale intermittency (non-Gaussian scalar derivatives) are in accord with laboratory experimental results. The statistics of the scalar derivatives and those of the velocity-scalar fluctuations are also in accord with laboratory measured results.

Variability of responses to sinusoidal modulation

Many studies of visual neurons make use of stimuli that are sinusoidally modulated in time, and take as the response the fundamental Fourier component of the firing. This is a study of the variability of the fundamental sinusoidal components.A theoretical analysis shows that the variance of sinusoidal components should be nearly independent of their amplitudes; this is expected despite the observation that variance of firing rate increases with increasing firing rate. However, this result applies only to the variance of the complex amplitude, defined as the complex Fourier amplitude in response to each stimulus cycle. This variance is called the complex variance. The variance of the scalar amplitude, which is simply the amplitude in response to each stimulus cycle disregarding phase (scalar variance) is expected to shrink by a factor of up to 2⅓ as the response magnitude approaches zero.If the relationship between variance of rate and rate is linear, complex variance should be independent of amplitude. If the relationship between variance of rate and rate is characterized by a compressive nonlinearity (as has been observed), the complex variance should very slightly decrease with increased amplitude, despite the main trend of increased variance of rate with increased rate.Data from cat ganglion cells stimulated with sinusoidally modulated lights of various contrasts agree with the theory, although some individual cases show trends that may be indicative of nonlinearity in the relationship between variance of rate and rate.