Linear Propagation Model Research Articles

On the stability of the effective apodization of the nonlinearly generated second harmonic with respect to range

The concept of an effective apodization was introduced to describe the field pattern for the nonlinearly generated second harmonic (2f) within the focal zone using a linear propagation model. Our objective in this study was to investigate the validity of the concept of an effective apodization at 2f as an approach to approximating the field of the second harmonic over a wide range of depths. Two experimental setups were employed: a vascular imaging array with a water path and an adult cardiac imaging array with an attenuating liver path. In both cases the spatial dependencies of the ultrasonic fields were mapped by scanning a point-like hydrophone within a series of planes orthogonal to the propagation direction. The sampling distances were located before, within, and beyond the focal zone. The signals were Fourier transformed and the complex values at 2f were linearly backpropagated to the transmit plane in order to obtain an effective apodization. The measured results demonstrated a relatively constant effective apodization at 2f as a function of propagation distance. Finite amplitude computer simulations were found to be in agreement with these measurements. Thus the measure of the effective apodization at 2f provides an approximation to the second harmonic field outside the focal zone.

Demonstration of Adaptive Extended Kalman Filter for Low-Earth-Orbit Formation Estimation Using CDGPS

ABSTRACT: Carrier-phase differential GPS is an ideal sensor for formation flying missions in low earth orbit since it provides a direct measure of the relative positions and velocities of the vehicles in the fleet. This paper presents results for a relative navigation filter that achieves centimeter-level precision using a customized GPS receiver. A precise, robust extended Kalman filter estimates the relative states based on simple measurement models and a linear Keplerian propagation model. To increase the filter robustness in the face of environment uncertainty, adaptive method of maximum likelihood estimation (MMLE) algorithms are implemented. The adaptive filter accurately identifies the process and sensor noise covariances for the system. Despite the simplicity of the filter, hardware-in-the-loop simulations performed on the Formation Flying Testbed at Goddard Space Flight Center demonstrated that this filter can achieve ≅2 cm relative position accuracy and <0.5 mm/s relative velocity accuracy for a range of low-earth-orbit formation.

A New Approach to Measuring Financial Contagion

This paper proposes a new approach to evaluate contagion in financial markets. Our measure of contagion captures the co-incidence of extreme return shocks across countries within a region and across regions that cannot be explained by linear propagation models of shocks. We characterize the extent of contagion, its economic significance, and its determinants using a multinomial logistic regression model. Applying our approach to daily returns of emerging markets during the 1990s, we find that contagion, when measured by the co-incidence within and across regions of extreme return shocks, is predictable and depends on regional interest rates, exchange rate changes, and conditional stock return volatility. Evidence that contagion is stronger for extreme negative returns than for extreme positive returns is mixed.

The intensity dependence of lesion position shift during focused ultrasound surgery

Knowledge of the spatial distribution of intensity loss from an ultrasonic beam is critical for predicting lesion formation in focused ultrasound (US) surgery (FUS). To date, most models have used linear propagation models to predict intensity profiles required to compute the temporally varying temperature distributions used to compute thermal dose contours. These are used to predict the extent of thermal damage. However, these simulations fail to describe adequately the abnormal lesion formation behaviour observed during ex vivo experiments in cases for which the transducer drive levels are varied over a wide range. In such experiments, the extent of thermal damage has been observed to move significantly closer to the transducer with increased transducer drive levels than would be predicted using linear-propagation models. The first set of simulations described herein use the KZK (Khokhlov–Zabolotskaya–Kuznetsov) nonlinear propagation model with the parabolic approximation for highly focused US waves to demonstrate that both the peak intensity and the lesion positions do, indeed, move closer to the transducer. This illustrates that, for accurate modelling of heating during FUS, nonlinear effects should be considered. Additionally, a first order approximation has been employed that attempts to account for the abnormal heat deposition distributions that accompany high transducer drive level FUS exposures where cavitation and boiling may be present. The results of these simulations are presented. It is suggested that this type of approach may be a useful tool in understanding thermal damage mechanisms.

Acoustic source calculations for nuclear bursts

Research has been conducted on the source term for long-range underwater propagation of signals from nuclear explosions in and above the ocean, in support of CTB monitoring objectives. A suite of source-region simulations is reviewed to study the variation of wave properties and source-region energy partition as a function of height or depth of burst. The multistep calculation combines LLNL’s CALE hydrodynamics code in the strong shock region with NRL’s weak shock code, NPE, at intermediate ranges. The source term calculations are intended as a starter field for long-range linear propagation models to obtain signature estimates at normal observational ranges. Calculations are presented to examine the effect of sea ice below an air burst on acoustic coupling into the water column. The ice was modeled as a continuous elastic layer 5-m thick at the water surface, and the source as a 1-Kt explosion 50 m above the ice. Calculations with and without the ice layer predict a moderate, but noticeable reduction in coupled acoustic energy in signals observed at the 10&amp;lt;th&amp;gt;000-m range. [Work performed under the auspices of the U. S. Department of Energy by the Lawrence Livermore National Laboratory under Contract No. W-7405-ENG-48.]

Numerical modeling of borehole pressurization

This paper presents a method for obtaining the complete pressure versus time curve generated during pressurization of a wellbore considering the pumping rate as input. The rock formation is treated as a poroelasto-plastic material and the pressurization fluid is considered to have the same properties of the rock pore fluid. A fracture initiation criterion (maximum tensile stress) and a non linear fracture propagation model are used in order to handle the wellbore post failure behavior. The finite element method was used to formulate the solution for this coupled hydromechanical problem. It is shown that fracture energy, pumping rate and fluid viscosity affect both the maximum pressure on the borehole wall and the post failure pressure versus time curve. Result of a pressurization test carried out in a small diameter borehole is compared to the one predicted by the computer program and there is very good agreement. The paper investigates the fracture closure process upon shut in and shows the relationship between wellbore pressure and fracture closing pressure.

Pulse shape evolution and noise estimates in concatenated fiber links using analog optoelectronical repeaters

The pulse shape evolution in a chain consisting of dispersive fiber segments concatenated by analog optoelectronical repeaters is investigated. Analytical results based on a linear propagation model and Gaussian pulse shape with linear chirp as well as more realistic simulations, taking into account different pulse shapes and fiber nonlinearities, show that analog optoelectronical repeaters allow a significant improvement in the dispersion accumulation along the chain compared with all-optical amplification. To transmit data sequences, return-to-zero modulation has to be applied and simulations show that 10 Gb/s data can be transmitted at least over a distance of 1000 km with an power penalty caused by dispersion of 0.7 dB only. However, the noise accumulation reduces this length. For sufficiently large number of fiber segments with realistic parameters, the all-optical amplification performs better from a noise point of view.

Nonlinear wave energy modelling in the surf zone

Abstract. Breaking wave energy in the surf zone is modelled through the incorporation of the time dependent energy balance equation in a non linear dispersive wave propagation model. The energy equations solved simultaneously with the momentum and continuity equation. Turbulence effects and the non uniform horizontal velocity distribution due to breaking is introduced in both the energy and momentum equations. The dissipation term is a function of the velocity defect derived from a turbulent analysis. The resulting system predicts both wave characteristics (surface elevation and velocity) and the energy distribution inside surf zone. The model is validated against experimental data and analytical expressions.

Modeling the seismic source and tsunami generation of the December 12, 1992 Flores Island, Indonesia, earthquake

On December 12, 1992 a large earthquake (M s 7.5) occurred just north of Flores Island, Indonesia which, along with the tsunami it generated, killed more than 2,000 people. In this study, teleseismic P and SH waves, as well as PP waves from distances up to 123°, are inverted for the orientations and time histories of multiple point sources. By repeating the inversion for reasonable values of depth, time separation and spatial separation, a 2-fault model is developed. Next, the vertical deformation of the seafloor is estimated from this fault model. Using a detailed bathymetric model, linear and nonlinear tsunami propagation models are tested. The data consist of a single tide gauge record at Palopo (650 km to the north), as well as tsunami runup height measurements from Flores Island and nearby islands. Assuming a tsunami runup amplification factor of two, the two-fault model explains the tide gauge record and the tsunami runup heights on most of Flores Island. It cannot, however, explain the large tsunami runup heights observed near Leworahang (on Hading Bay) and Riangkroko (on the northeast peninsula). Massive coastal slumping was observed at both of these locations. A final model, which in addition to the two faults, includes point sources of large vertical displacement at these two locations explains the observations quite well.

A linear propagation model adapted to the study of fast perturbations in arterial hemodynamics

The hemodynamic effect of rapid body accelerations is studied in this work using two different models of wave propagation in blood vessels. Simulation curves have been obtained with both models and compared with those measured in vivo on a dog's carotid artery. Results of the first model demonstrate that classic linear theories, based on linearization of the Navier-Stokes and continuity equations, provide a good explanation of the initial effect of body acceleration on pressure. However, the same models significantly underestimate the subsequent pressure perturbation damping. Modified empirical expressions for wave propagation, able to furnish a more accurate description of pressure energy losses occurring during fast hemodynamic phenomena, are thus utilized in the second model and their biophysical significance discussed.

Prediction of in situ exposure to ultrasound: An improved method

The acoustic output of medical ultrasonic equipment is usually measured in water but to determine the safety (or performance) of a machine it is necessary to know the in situ acoustic pressure levels inside a patient. At present, when estimates of these levels are made, a linear propagation model is used although in practice the propagation is nonlinear. This paper shows that such a model can lead to large errors (80% or more in pressure) and in particular that in situ predictions of the peak-negative acoustic pressure are too low. To describe the field in water and in tissue it is necessary to take account of diffraction, attenuation, and dispersion as well as nonlinear propagation. It is difficult to use acoustic output levels in water to predict in situ values because the amplitude in water approaches a limit, an effect known as saturation. Nevertheless, a method of making such predictions is presented in this paper and is validated by comparison with experiment. The method is relatively time-consuming to implement and has not yet been applied to pulsed fields, so there is a need for more complete and simpler methods.

Verification of a parabolic equation for propagation of weakly-nonlinear waves

Verification tests of linear wave propagation models for cases of waves propagating through a refractive focus typically overpredict peak amplitudes in the vicinity of the focus. Using a parabolic equation model for the combined refraction-diffraction of weakly-nonlinear waves [valid for Ursell number U r < O(1)], we show that, in a particular experiment, much of the discrepancy between laboratory measurements and linear wave model predictions can be accounted for by including the effect of nonlinearity, which is important in the region of the focus.

Normal-Mode Approach to Wave Propagation in the Turbulent Atmosphere

Recent studies have used the superposition principle (extended Huygens-Fresnel principle) to characterize completely the statistics of a field that has propagated through a thick slab of turbulent air in terms of the statistics for spherical-wave sources. In this paper, we consider the normal-mode decomposition associated with this linear system propagation model. In particular, we use the statistics of the atmospheric impulse response (Green's function) to show that the atmospheric mode decomposition exhibits far-field and near-field regimes very similar to those of free-space propagation. The significance of these results for optical communication through the atmosphere is briefly discussed.