David E. Norris

Wavetable audio synthesizer with low frequency oscillators for tremolo and vibrato effects

A digital wavetable audio synthesizer with an LFO generator is described. The synthesizer can generate up to 32 high-quality audio digital signals or voices, including delay-based effects. The synthesizer includes an address generator which has several modes of addressing wavetable data. The address generators addressing rate controls the pitch of the synthesizers output signal. A synthesizer volume generator, which has several modes of controlling the volume, adds envelope, right offset, left offset, and effects volume to the data. The synthesizer LFO generator can add LFO variation to: (i) the wavetable data addressing rate, for creating a vibrato effect; and (ii) a voices volume, for creating a tremolo effect. The LFO generator assigns two triangular-wave LFOs to each of the 32 possible voices. One LFO is dedicated to vibrato (frequency modulation) effects and the other to tremolo (amplitude modulation) effects. It is possible to ramp the depth of each LFO into and out of a programmable maximum. The parameters for each LFO are stored in local memory. When creating delay-based effects, data is stored in one of several effects accumulators. This data is then written to a wavetable. The difference between the wavetable write and read addresses for this data provides a delay for echo and reverb effects. LFO variations can be added to the read address to create chorus and flange effects.

Atmospheric scattering for varying degrees of saturation and turbulent intermittency

Atmospheric turbulence is inherently inhomogeneous and intermittent. Short periods of high activity are embedded in longer periods of relative calm. Local spatial and temporal changes in sound speed associated with this intermittency increase the likelihood of measuring large values of scattered acoustic signals. Previous work successfully predicted the probability density functions (pdfs) of fully saturated, scattered signals measured within an acoustic shadow zone [Wilson et al., J. Acoust. Soc. Am. 99, 3393-3400 (1996)]. The more general case of incompletely saturated scattering is considered in this paper; using the Rice-Nagakami distribution a theory is developed. The predicted intensity pdf has two free parameters: one to describe the degree of intermittency and a second for the degree of saturation. For validation purposes, outdoor propagation measurements were made over a flat, hard ground at ranges of 146-283 m and at frequencies of 50-540 Hz. The saturation parameter was determined from the acoustic data and also estimated from the turbulence conditions. The degree of saturation increased with frequency, and measured intensity pdfs were found to be in excellent agreement with the theory.

Comparison of basin-scale acoustic transmissions with rays and further evidence for a structured thermal field in the northeast Pacific

From May to September of 1987, 250-Hz, 16-ms resolution acoustic signals were transmitted between four sources and nine receivers in the northeast Pacific. This paper examines the acoustic transmissions across nine of the sections within this group, with path lengths ranging from approximately 1700 to 3300 km. Acoustic multipaths are tracked in the data, and ray theory is successfully used to identify the multipaths, where the spring and summer Levitus’ climatological databases are used to determine the sound speeds. The observed multipaths arrive on the order of 1 s later than the predicted rays. Travel time differences greater than 0.15 s are due to temperature errors in Levitus’ climatology within the ocean’s upper 1 km. The resulting corrections to Levitus’ spring and summer oceans are −0.2 and −0.3 °C, respectively. The upper turning depths for all rays are found to vary by less than 50 m from spring to summer. Variations in the measured travel times over the four month period are about 0.5 s. Some s...

Long‐range infrasound propagation modeling using updated atmospheric characterizations

Infrasonic waves can propagate thousands of kilometers in range and sample regions of the atmosphere from the ground up to and including the thermosphere. Conventional infrasound propagation modeling techniques rely on climatological models of mean temperatures and winds to characterize the environment. However, temperature and wind vary over temporal and spatial scales that are not captured by climatological models. Recent work addresses the integration of infrasound propagation models, such as three‐dimensional ray tracing, with numerical weather prediction models, such as the Navy Operational Global Atmospheric Prediction System (NOGAPS). Propagation results are computed using both climatological and updated atmospheric characterizations, and comparisons are presented. Implications for global infrasound monitoring are discussed. [Work supported by the Defense Threat Reduction Agency.]

Infrasonic scattering studies using time‐domain parabolic equation (TDPE) and gravity wave models

The time‐domain parabolic equation (TDPE) model is useful in predicting infrasonic waveforms, as it can account for diffraction and scattering mechanisms. In this study, a split‐step Fourier (SSF) implementation of the TDPE is used to study infrasonic propagation. Scattering is modeled using a spectral gravity wave model, and multiple gravity wave realizations are used to quantify the uncertainty in waveform properties introduced by scattering from the gravity wave inhomogeneities. TDPE predictions are compared to specific infrasonic events and conclusions regarding the dominant propagation mechanisms are presented.

Parabolic equation (PE) model approximations and implications for infrasound

The continuous‐wave parabolic equation (PE) model is widely used in the prediction of atmospheric propagation. In this study, the effects of several PE approximations are evaluated in the context of long‐range infrasonic propagation. Specifically, the focus is on quantifying: phase errors resulting from different split‐step Fourier (SSF) implementations, solution stability with respect to step size, and prediction sensitivity to the choice of reference sound speed. The tradeoff between improved performance gain and increased computational loading will also be considered. The study will include comparison of PE waveform predictions with measurements from infrasonic events. These comparisons are of interest in assessing the PE modeling performance, applicability, and limitations. Waveform predictions are made by integrating the continuous‐wave PE model into a Fourier‐synthesis Time‐domain PE (TDPE).

The effects of turbulent intermittency on scattering and estimates for the degree of saturation

Turbulent fluctuations in atmospheric wind and temperature fields are observed to be erratic in time; strong activity is typically interspersed with periods of relative calm. This property, referred to as turbulent intermittency, has an observable effect on the statistics of scattered acoustic signals. For fully saturated scattering, large intensity deviations about the mean result in a divergence from log‐normal intensity probability density functions (pdfs) typically used to describe such statistics. Previous studies have developed the theory to predict the intensity pdf’s that account for both turbulent intermittency and the degree of saturation [Norris et al., J. Acoust. Soc. Am. 109, 1871–1880 (2001); Wilson et al., J. Acoust. Soc. Am. 99, 3393–3400 (1996)]. The new formulation with intermittency is compared to the generalized gamma pdf previously proposed for propagation in random media. It is also compared to data collected over a 140 m line‐of‐sight path at 110 to 525 Hz. Experimental characteriza...

Propagation variability and localization accuracy of infrasonic networks

Prediction of propagation variability induced by the environment is used to evaluate the localization performance of infrasonic networks. The dominant source of variability affecting infrasonic propagation is believed to result from gravity waves. A gravity wave spectral model based on scale‐independent diffusive filtering is used to generate multiple wind perturbation realizations. A Monte Carlo simulation is executed where rays are traced through the perturbed environmental fields, and uncertainty in ray travel time and azimuthal deviation is calculated. The propagation uncertainties, along with uncertainty in infrasonic measurements, are then used to compute 90 percent confidence bounds of multi‐station event localizations. Infrasonic data from the April 2001 Pacific bolide event are used to compute the performance of a five station network, and the network localization is compared to that found from satellites. [Work sponsored by Defense Threat Reduction Agency, Contract No. DTRA01‐00‐C‐0063.]

Seasonal variability in the atmosphere and its effect on infrasonic propagation

Infrasonic waves can propagate thousands of kilometers in range and sample regions of the atmosphere from the ground up to and including the thermosphere. In this study, seasonal changes in the atmosphere and their effect on infrasonic propagation are characterized. The NASA/NRL empirically based models HWM‐93 (for winds) and MSIS‐90 (for temperature) are used. Three‐dimensional ray traces are computed through the modeled atmosphere for several representative scenarios. Seasonal trends in both ray arrival times and ray azimuth bias are computed, and limited comparisons with data are made where possible. [Sponsored by Defense Threat Reduction Agency, Contract No. DSWA01‐97‐C‐0160.]

The effects of atmospheric turbulence on the cross correlation between wind and travel time fluctuations

Previous measurements over flat, hard ground showed strong coherence in received acoustic phases across frequencies from 90 to 660 Hz [D. E. Norris and D. W. Thomson, J. Acoust. Soc. Am. 101, 3102(A) (1996)]. A recent test program was conducted at the same site in which concurrent acoustic and wind data were recorded. Similar coherences in the phase and travel time fluctuations were observed, and cross correlations between wind and travel time fluctuations were calculated. A theory was developed to predict the cross correlations by considering the effects of the two‐dimensional horizontal wind spectrum on the direct source–receiver path. The theoretical parameters include the horizontal separation between the acoustic and wind sensor positions, and the bearing offset between the wind and propagation directions. Calculated and predicted cross correlations were compared and found to be in good agreement. The bearing offset was found to significantly influence both the magnitude and shape of the cross correl...