hypothesis testing for geoacoustic environmental models using likelihood ratio a generalized likelihood ratio test is developed for testing acoustic environmental models with an application to parameter inversion using an acoustic propagation code the signal to noise ratio in acoustic measurements proves to limit the details on geoacoustic environments that can be determined by matched field processing methods a hypothesis test serves in monte carlo simulations as a tool to determine minimal signal levels for the bottom parameter inversion the term hierarchy of models is used for denoting a sequence of models in which each particular model contains all previous ones for determining the model order and its parameters a combined parameter estimation and multiple sequential test is proposed given the observed data how many parameters should be included in the model the last question is important for the order selection in hierarchies of models with an increasing number of parameters multiple sequential hypotheses testing provides a procedure to determine the model order in a statistically justified way monte carlo simulations show the behavior of the test for selecting a model order as a function of the signal to noise snr ratio the test is applied to broadband data measured using a vertical array near the island of elba in the mediterranean sea and compared with akaike s information criterion

efficient navigation of parameter landscapes optimization techniques can have difficulty navigating long valleys that are oriented obliquely to the parameter axes efficiency may be improved by rotating coordinates so that the most prominent valleys are optimally aligned with the parameter axes the rotated axes are parallel to the eigenvectors of the covariance matrix of the gradient of the cost function which may be estimated efficiently by monte carlo integration the information in the covariance matrix may also be used to obtain an improved parametrization which corresponds to the rotated coordinates associated with the largest eigenvalues the approach is illustrated for the inverse problem of estimating ocean bottom parameters from acoustic data using simulated annealing for multifrequency inverse problems the resolution for each frequency is optimized

an iterative implementation of rotated coordinates for inverse problems a generalized inversion method is presented that uses a rotated coordinates technique collins and fishman j acoust soc am 98 1637 1644 1995 in simulated annealing to invert for both the location of an acoustic source and parameters that describe the ocean seabed the rotated coordinates technique not only aids in the inversion process but also indicates the coupling of the source and environmental parameters and the relative sensitivities of the cost function to changes in the various parameters the information obtained from the rotated coordinates provides insights into how the inversion problem can be effectively decoupled an iterative process consisting of multiple simulated annealing runs that each use a different set of rotated coordinates is demonstrated this multistep algorithm is called systematic decoupling using rotated coordinates and is especially helpful when inverting for a large number of unknown parameters the cost function minimized in the inversion algorithm is model data cross hydrophone spectra summed coherently over frequency and receiver pairs the results of applying this inversion method to simulated data are presented in this paper

metastate approach to thermodynamic chaos in realistic disordered systems such as the edwards anderson ea spin glass no order parameter such as the parisi overlap distribution can be both translation invariant and non self averaging the standard mean field picture of the ea spin glass phase can therefore not be valid in any dimension and at any temperature further analysis shows that in general when systems have many competing pure thermodynamic states a single state which is a mixture of many of them as in the standard mean field picture contains insufficient information to reveal the full thermodynamic structure we propose a different approach in which an appropriate thermodynamic description of such a system is instead based on a metastate which is an ensemble of possibly mixed thermodynamic states this approach modeled on chaotic dynamical systems is needed when chaotic size dependence of finite volume correlations is present here replicas arise in a natural way when a metastate is specified by its meta correlations the metastate approach explains connects and unifies such concepts as replica symmetry breaking chaotic size dependence and replica nonindependence furthermore it replaces the older idea of non self averaging as dependence on the bulk couplings with the concept of dependence on the state within the metastate at fixed coupling realization we use these ideas to classify possible metastates for the ea model and discuss two scenarios introduced by us earlier char22 a nonstandard mean field picture and a picture intermediate between that and the usual scaling droplet picture

sound speed estimation and source localization with linearization and particle filtering a method is developed for the estimation of source location and sound speed in the water column relying on linearization the jacobian matrix necessary for the proposed linearization approach includes derivatives with respect to empirical orthogonal function coefficients instead of sound speed directly first the inversion technique is tested on synthetic arrival times using gaussian distributions for the errors in the considered arrival times the approach is efficient requiring a few iterations and produces accurate results probability densities of the estimates are calculated for different levels of noise in the arrival times subsequently particle filtering is employed for the estimation of arrival times from signals recorded during the shallow water 06 experiment it has been shown in the past that particle filtering can be employed for the successful estimation of multipath arrival times from short range data and consequently in geometry bathymetry and sound speed inversion here probability density functions of arrival times computed via particle filtering are propagated backward through the proposed inversion process inversion estimates are consistent with values reported in the literature for the same quantities last it is shown that results are consistent with estimates resulting from fast simulated annealing applied to the same data

how should one define a weak crystal we compare two proposals for the study of positional long range order one in terms of the spectrum of the translation operator the other in terms of the fourier spectrum we point out that only the first one allows for the consideration of molecular as opposed to atomic weakly periodic structures we illustrate this point on the thue morse system

ocean acoustic inversion with estimation of a posteriori probability distributions inversion methods are applied in ocean acoustics to infer parameters which characterize the environment the objective of this paper is to provide such estimates and means of evaluating the inherent uncertainty of the parameter estimates in a bayesian approach the result of inversion is the a posteriori probability density for the estimated parameters from which all information such as mean higher moments and marginal distributions can be extracted these are multidimensional integrals of the a posteriori probability density which are complicated to evaluate for many parameters various sampling options are examined and it is suggested that importance sampling based on a directed monte carlo method such as genetic algorithms is the preferred method the formulation of likelihood functions and maximum likelihood objective functions for multifrequency data on a vertical array is discussed a priori information about the parameters may be used in the formulation shallow water acoustic data obtain

nonlinear multiparameter optimization using genetic algorithms inversion of plane wave seismograms seismic waveform inversion is one of many geophysical problems which can be identified as a nonlinear multiparameter optimization problem methods based on local linearization fail if the starting model is too far from the true model we have investigated the applicability of genetic algorithms ga to the inversion of plane wave seismograms like simulated annealing genetic algorithms use a random walk in model space and a transition probability rule to help guide their search however unlike a single simulated annealing run the genetic algorithms search from a randomly chosen population of models strings and work with a binary coding of the model parameter set unlike a pure random search such as in a monte carlo method the search used in genetic algorithms is not directionless genetic algorithms essentially consist of three operations selection crossover and mutation which involve random number generation string copies and some partial string exchanges the choice of the initial popul

matched field inversion of broadband data using the freeze bath method this paper presents a statistical freeze bath method for geoacoustic inversion that emphasizes the search for a distribution of models that fit the data well contrary to simulated annealing optimization the freeze bath samples the multidimensional model parameter space at constant freeze probability corresponding to fixed temperatures for each parameter the sampling process uses a heat bath algorithm as a boltzmann sampling tool to carry out a global search over the model parameter space the conventional heat bath algorithm is modified to sample on a fuzzy grid in order to access the entire range of parameter values the inversion provides a set of good models that indicates how well the model parameters are constrained by the data and reveals the degree of correlation between parameters the efficiency of the search process is improved by reparameterizing the original model parameters to a new set based on the eigenvectors of the model covariance matrix the inversion performance of the freeze bath

range dependent matched field inversion of swellex 96 data using the downhill simplex algorithm matched field inversion mfi techniques have been applied for effective and efficient estimation of geoacoustic parameters of the ocean bottom this paper presents a new tomographic mfi method for use in range dependent environments the mfi correlates modeled data with measured data and uses a search algorithm to determine model parameter values that maximize the correlator in the present method a parabolic equation propagation model is used to compute replica fields to account for mode coupling in the environment the search algorithm is a two stage hybrid method that combines an initial global component and a final local component the first stage employs a random search to determine n 1 parameter sets with the best correlations where n is the number of parameters being determined in the next stage the n 1 sets are used as inputs to the local downhill simplex algorithm the algorithm is shown to perform well for simulated vertical line array data for an environment representative of the swellex 96 experimental site the inversion technique is then applied to measured data obtained from a radial track in swellex 96 the geometric parameters of the experiment and dominant geoacoustic parameters were successfully recovered for data with relatively low signal to noise ratio

matrix fitting approach to direction of arrival estimation with imperfect spatial coherence of wavefronts the performance of high resolution direction of arrival doa estimation methods significantly degrades in several practical situations where the wavefronts have imperfect spatial coherence the original solution to this problem was proposed by paulraj and kailath 1988 but their technique requires a priori knowledge of the matrix characterizing the loss of wavefront coherence along the array aperture a novel solution to this problem is proposed which does not require a priori knowledge of the spatial coherence matrix

localization using bartlett matched field processor sidelobes ambiguity surface sidelobes generated by the bartlett matched field processor mfp shift location with frequency this sidelobe shift can be viewed as a continuous trajectory in a range frequency plane at a fixed depth where the trajectories converge to the correct source range for a perfectly matched surface in isovelocity or bottom interacting environments the sidelobe trajectories are straight lines that converge to the true range at zero frequency while environments with upward refracting sound speed profiles have trajectories that asymptotically converge as the frequency approaches infinity this behavior can be explained by the theory of waveguide invariants which predict the local behavior of interference maxima minima of acoustic intensity in the frequency range plane as the ambiguity surface of the bartlett matched field processor has a physical interpretation in terms of a time reversed acoustic field with the sidelobes analogous to local interference maxima these invariant concepts can be reformulated for application to mfp these interference trajectories are demonstrated to exist in simulations broadband source tows and a type a blue whale vocalization sidelobe trajectories also exist in the range depth plane but they contain no information about the correct source depth an appendix demonstrates how these sidelobe properties can be exploited when combining ambiguity surfaces through use of gradient and radon transform information the resulting range estimators demonstrate better peak to sidelobe ratios than a simple incoherent average

inversion of acoustic data using a combination of genetic algorithms and the gauss newton approach an inversion procedure for obtaining speeds attenuation densities and thicknesses for a layered medium is described the inversion is carried out using the least squares technique and the forward modeling is based on safari the optimization is a hybrid method combining the global genetic algorithms and the local gauss newton method this is done by taking several gradient steps between each update of the object function for each individual in the population the gradients for the gauss newton method are computed analytically this makes the computation faster and more stable than computing the gradients by numerical differentiation the combination of a global and a local method makes the hybrid method faster and it gets closer to the global minimum than a pure global method examples based on both real and synthetic data in wave number frequency and range frequency domains show that the method works well

estimation of radio refractivity from radar clutter using bayesian monte carlo analysis this paper describes a markov chain monte carlo mcmc sampling approach for the estimation of not only the radio refractivity profiles from radar clutter but also the uncertainties in these estimates this is done by treating the refractivity from clutter rfc problem in a bayesian framework it uses unbiased mcmc sampling techniques such as metropolis and gibbs sampling algorithms to gather more accurate information about the uncertainties application of these sampling techniques using an electromagnetic split step fast fourier transform parabolic equation propagation model within a bayesian inversion framework can provide accurate posterior probability distributions of the estimated refractivity parameters then these distributions can be used to estimate the uncertainties in the parameters of interest two different mcmc samplers metropolis and gibbs are analyzed and the results compared not only with the exhaustive search results but also with the genetic algorithm results and helicopter refractivity profile measurements although it is slower than global optimizers the probability densities obtained by this method are closer to the true distributions

bayesian focalization quantifying source localization with environmental uncertainty this paper applies a bayesian formulation to study ocean acoustic source localization as a function of uncertainty in environmental properties water column and seabed and of data information content signal to noise ratio snr and number of frequencies the approach follows that of the optimum uncertain field processor a m richardson and l w nolte j acoust soc am 89 2280 2284 1991 in that localization uncertainty is quantified by joint marginal probability distributions for source range and depth integrated over uncertain environmental properties the integration is carried out here using metropolis gibbs sampling for environmental parameters and heat bath gibbs sampling for source location to provide efficient sampling over complicated parameter spaces the approach is applied to acoustic data from a shallow water site in the mediterranean sea where previous geoacoustic studies have been carried out it is found that reliable localization requires a sufficient combination of prior e

invariant differential operators and the range of the matrix radon transform in this paper we characterize the range of the matrix radon transform by invariant differential operators this generalizes analogous results for the d plane transform in rn

markov chain monte carlo identification of favorable design choices with application to anechoic coatings global optimization methods can be used to numerically determine optimal design parameters for an object however this does not by itself give a good appreciation of other parameter choices that may be almost as good and even preferable from other points of view in the present paper markov chain monte carlo methods are used to go beyond the optimal solution and create an ensemble of object models in parameter space that covers a set of favorable models uniformly in direct analogy with applications to bayesian inversion with determination of an unknown posterior probability density projections of the model ensemble onto parameter axes and planes are used to exhibit parameter sensitivities and dependencies design of anechoic rubber coatings with cylinder cavities having axes in a lateral direction is considered as a particular application the anechoic effect is evaluated by the efficient layer multiple scattering method which is extended to handle cylinder scatterers of noncircular cross sections and mixed types as anticipated by computed scattering and absorption cross sections for an isolated cavity the favorable coatings have oblate cavity cross section shapes which is useful to achieve good low frequency reflection reduction with a thin coating

focalization environmental focusing and source localization conventional matched field processing mfp requires accurate knowledge of the ocean acoustic environment focalization which simultaneously focuses and localizes eliminates this stringent requirement by including the environment in the parameter search space this generalization of mfp involves defining an appropriate high resolution cost function parametrizing the search space of the environment and source constructing solutions of the wave equation and utilizing a nonlinear optimization method to search the parameter landscape for the global minimum of the cost function focalization is implemented using cost functions based on ray theory and wave theory empirical orthogonal functions for the environmental description and simulated annealing for optimization numerical simulations are presented to demonstrate the feasibility of focalization

a hybrid global optimization method the multi dimensional case we extend the hybrid global optimization method proposed by xu j comput appl math 147 2002 301 314 for the one dimensional case to the multi dimensional case the method consists of two basic components local optimizers and feasible point finders local optimizers guarantee efficiency and speed of producing a local optimal solution in the neighbourhood of a feasible point feasible point finders provide the theoretical guarantee for the new method to always produce the global optimal solution s correctly if a nonlinear nonconvex inverse problem has multiple global optimal solutions our algorithm is capable of finding all of them correctly three synthetic examples which have failed simulated annealing and genetic algorithms are used to demonstrate the proposed method

extraction of acoustic normal mode depth functions using vertical line array data a method for extracting the normal modes of acoustic propagation in the shallow ocean from sound recorded on a vertical line array vla of hydrophones as a source travels nearby is presented the mode extraction is accomplished by performing a singular value decomposition svd of individual frequency components of the signal s temporally averaged spatial cross spectral density matrix the svd produces a matrix containing a mutually orthogonal set of basis functions which are proportional to the depth dependent normal modes and a diagonal matrix containing the singular values which are proportional to the modal source excitations and mode eigenvalues the conditions under which the method is expected to work are found to be 1 sufficient depth sampling of the propagating modes by the vla receivers 2 sufficient source vla range sampling and 3 sufficient range interval traversed by the source the mode extraction method is applied to data from the area characterization test ii conducted in september 1993 in the hudson canyon area off the new jersey coast modes are successfully extracted from cw tones recorded while 1 the source traveled along a range independent track with constant bathymetry and 2 the source traveled up slope with gradual changes in bathymetry in addition modes are successfully extracted at multiple frequencies from ambient noise

parametric sensor array calibration using measured steering vectors of uncertain locations we consider the problem of sensor array calibration using a set of unique measured steering vectors of uncertain locations to estimate the unknown deterministic array perturbation parameters in a maximum likelihood framework the array perturbations are parameterized by the sensor locations mutual coupling coefficients and receiver channel mismatch we introduce a hybrid optimizer based on the amalgamation of gradient based algorithms and the genetic algorithm this optimizer is capable of coping with the problem of local extrema attractors particularly initial estimates with large deviations from their true values numerical examples are provided to demonstrate the effectiveness and behavior of the proposed algorithms

estimating parameter uncertainties in matched field inversion by a neighborhood approximation algorithm in bayesian inversion the solution is characterized by its posterior probability density ppd a fast gibbs sampler fgs has been developed to estimate the multi dimensional integrals of the ppd which requires solving the forward models many times and leads to intensive computation for multi frequency or range dependent inversion cases this paper presents an alternative approach based on a neighborhood approximation bayes nab algorithm for lower dimension geoacoustic inversion the nab can approximate the ppd very well for higher dimensional problems and sensitive parameters however the nab algorithm has difficulty estimating the ppd accurately with limited model samples according to the preliminary ppd estimation from the nab this paper developed a multi step inversion scheme which adjusts the parameter search intervals flexibly in order to improve the approximation accuracy of the nab and obtain more complete parameter uncertainties the prominent feature of the nab is to approximate the ppd by incorporating all models for which the forward problem has been solved into the appraisal stage comparison of the fgs and nab for noisy synthetic benchmark test cases and mediterranean real data indicates that the nab provides reasonable estimates of the ppd moments while requiring significantly less computation time

perturbative inversion methods for obtaining bottom geoacoustic parameters in shallow water three perturbative inverse methods for obtaining bottom geoacoustic parameters as a function of depth in shallow water are described the required input data are the trapped mode eigenvalues for one or more frequencies the group velocity dispersion curves for one or more modes or the cw pressure field versus range in each case a fredholm integral equation arises that can be solved using linear inverse theory and for which resolution and variance estimates of the solution can be readily made attention is focused primarily on the modal eigenvalue inverse problem for which the theory for determining the compressional wave speed compressional wave attenuation and density is developed in detail properties of this technique are studied using synthetic data and include investigations of the dependence of the results on acoustic frequency number of modes excited and partial a priori knowledge of the bottom the method is demonstrated on experimental data obtained in nantucket sound at 140 and 220 hz d

an ultrametric state space with a dense discrete overlap distribution paperfolding sequences we compute the parisi overlap distribution for paperfolding sequences it turns out to be discrete and to live on the dyadic rationals hence it is a pure point measure whose support as a closed set is the full interval 1 1 the space of paperfolding sequences has an ultrametric structure our example provides an illustration of some properties which were suggested to occur for pure states in spin glass models

inversion of seismoacoustic data using genetic algorithms and a posteriori probability distributions the goal of many underwater acoustic modeling problems is to find the physical parameters of the environment with the increase in computer power and the development of advanced numerical models it is now feasible to carry out multiparameter inversion the inversion is posed as an optimization problem which is solved by a directed monte carlo search using genetic algorithms the genetic algorithm presented in this paper is formulated by steady state reproduction without duplicates for the selection of parents the object function is scaled according to a boltzmann distribution with a temperature equal to the fitness of one of the members in the population the inversion would be incomplete if not followed by an analysis of the uncertainties of the result when using genetic algorithms the response from many environmental parameter sets has to be computed in order to estimate the solution the many samples of the models are used to estimate the a posteriori probabilities of the model parameters t

global optimization of statistical functions with simulated annealing abstract many statistical methods rely on numerical optimization to estimate a model s parameters unfortunately conventional algorithms sometimes fail even when they do converge there is no assurance that they have found the global rather than a local optimum we test a new optimization algorithm simulated annealing on four econometric problems and compare it to three common conventional algorithms not only can simulated annealing find the global optimum it is also less likely to fail on difficult functions because it is a very robust algorithm the promise of simulated annealing is demonstrated on the four econometric problems

adjoint modeling for acoustic inversion the use of adjoint modeling for acoustic inversion is investigated an adjoint model is derived from a linearized forward propagation model to propagate data model misfit at the observation points back through the medium to the medium perturbations not being accounted for in the model this adjoint model can be used to aid in inverting for these unaccounted medium perturbations adjoint methods are being applied to a variety of inversion problems but have not drawn much attention from the underwater acoustic community this paper presents an application of adjoint methods to acoustic inversion inversions are demonstrated in simulation for both range independent and range dependent sound speed profiles using the adjoint of a parabolic equation model sensitivity and error analyses are discussed showing how the adjoint model enables calculations to be performed in the space of observations rather than the often much larger space of model parameters using an adjoint model enables directions of steepest descent in the model parameters what we invert for to be calculated using far fewer modeling runs than if a forward model only were used

evaluation of decay times in coupled spaces reliability analysis of bayeisan decay time estimation this paper discusses quantitative tools to evaluate the reliability of decay time estimates and inter relationships between multiple decay times for estimates made within a bayesian framework previous works xiang and goggans j acoust soc am 110 1415 1424 2001 113 2685 2697 2003 have applied bayesian framework to cope with the demanding tasks in estimating multiple decay times from schroeder decay functions measured in acoustically coupled spaces a parametric model of schroeder decay function xiang j acoust soc am 98 2112 2121 1995 has been used for the bayesian model based analysis the relevance of this work is that architectural acousticians need to know how well determined are the estimated decay times calculated within bayesian framework using schroeder decay function data this paper will first address the estimation of global variance of the residual errors between the schroeder function data and its model moreover this paper discusses how the landscape shape of the posterior probability density function over the decay parameter space influences the individual decay time estimates their associated variances and their inter relationships this paper uses experimental results from measured room impulse responses in real halls to describe a model based sampling method for an efficient estimation of decay times and their individual variances these parameters along with decay times are relevant decay parameters for evaluation and understanding of acoustically coupled spaces

limit quasi periodic point sets as quasicrystals with p adic internal spaces model sets or cut and project sets provide a familiar and commonly used method of constructing and studying nonperiodic point sets here we extend this method to situations where the internal spaces are no longer euclidean but instead spaces with p adic topologies or even with mixed euclidean p adic topologies we show that a number of well known tilings precisely fit this form including the chair tiling and the robinson square tilings thus the scope of the cut and project formalism is considerably larger than is usually supposed applying the powerful consequences of model sets we derive the diffractive nature of these tilings

quantifying uncertainty in geoacoustic inversion i a fast gibbs sampler approach this paper develops a new approach to estimating seabed geoacoustic properties and their uncertainties based on a bayesian formulation of matched field inversion in bayesian inversion the solution is characterized by its posterior probability density ppd which combines prior information about the model with information from an observed data set to interpret the multi dimensional ppd requires calculation of its moments such as the mean covariance and marginal distributions which provide parameter estimates and uncertainties computation of these moments involves estimating multi dimensional integrals of the ppd which is typically carried out using a sampling procedure important goals for an effective bayesian algorithm are to obtain efficient unbiased sampling of these moments and to verify convergence of the sample this is accomplished here using a gibbs sampler gs approach based on the metropolis algorithm which also forms the basis for simulated annealing sa although gs can be computationally slow in its basic form just as modifications to sa have produced much faster optimization algorithms the gs is modified here to produce an efficient algorithm referred to as the fast gibbs sampler fgs an automated convergence criterion is employed based on monitoring the difference between two independent fgs samples collected in parallel comparison of fgs gs and monte carlo integration for noisy synthetic benchmark test cases indicates that fgs provides rigorous estimates of ppd moments while requiring orders of magnitude less computation time

construction of sturmian sequences it is well known that a sturmian sequence can be regarded as a rotation sequence or a balanced sequence in this paper by a rotation sequence we first construct a series of sequences with complexity kn 1 then from these sequences we reconstruct other sturmian sequences and discuss their relationships

validation of statistical estimation of transmission loss in the presence of geoacoustic inversion uncertainty often the ocean acoustic environment is not well known and sonar performance prediction will be affected by this uncertainty here a method for estimating transmission loss tl is proposed which incorporates these environmental uncertainties specifically we derive an approach for the statistical estimation of tl based on the posterior probability density of environmental parameters obtained from the geoacoustic inversion process first a markov chain monte carlo procedure is employed in the inversion process to sample the posterior probability density of the geoacoustic parameters then these sampled parameters are mapped to the transmission loss domain where a full multidimensional probability distribution of tl as a function of range and depth is obtained in addition tl is also characterized by its summary statistics including the median percentiles and correlation coefficients the approach is illustrated using a data set obtained from the asiaex 2001 east china sea experiment based on the geoacoustic inversion results the predicted tl and its variability are estimated and then compared with the measured tl in general there is a good agreement with the percentage of observed number of data points inside the credibility interval

an efficient parabolic equation solution based on the method of undetermined coefficients an implementation of the self starter based on the method of undetermined coefficients is described and tested for many problems this parabolic equation technique for solving short range propagation problems provides an efficiency gain of an order of magnitude or more over the finite difference solution with this forward model it is possible to solve geoacoustic inverse problems in seconds on the current generation of desktop computers the approach can be implemented for the inverse problem so that efficiency is essentially independent of the depth of the water column

overlap distributions for deterministic systems with many pure states we discuss the parisi overlap distribution function for various deterministic systems with uncountably many pure ground states we show examples of trivial countably discrete and continuous distributions

data error covariance in matched field geoacoustic inversion many approaches to geoacoustic inversion are based implicitly on the assumptions that data errors are gaussian distributed and spatially uncorrelated i e have a diagonal covariance matrix however the latter assumption is often not valid due to theory errors and can lead to reduced accuracy for geoacoustic parameter estimates and underestimation of parameter uncertainties this paper examines the effects of data error residual covariance in matched field geoacoustic inversion an inversion approach is developed based on a nonparametric method of estimating the full covariance matrix including off diagonal terms from the data residuals and explicitly including this covariance in the misfit function qualitative and quantitative statistical tests for gaussianity and for correlations in complex residuals are considered to validate the inversion results the approach is illustrated for bayesian geoacoustic inversion of broadband vertical array acoustic data measured in the mediterranean sea

a novel mutation operator based on the immunity operation this paper presents a novel mutation operator based on the immunity operation also the selection is integrated into both crossover and mutation operation experiments with our approach on many test functions resulted in near optimal solutions in all cases in comparison with several other algorithms our approach achieved improved accuracy

weighted dirac combs with pure point diffraction a class of translation bounded complex measures which have the form of weighted dirac combs on locally compact abelian groups is investigated given such a dirac comb we are interested in its diffraction spectrum which emerges as the fourier transform of the autocorrelation measure we present a sufficient set of conditions to ensure that the diffraction measure is a pure point measure simultaneously we establish a natural link to the cut and project formalism and to the theory of almost periodic measures our conditions are general enough to cover the known theory of model sets but also to include examples such as the visible lattice points

frequency wavenumber inversion of acoustic data we describe an inversion procedure for obtaining velocities densities and layer thicknesses from multioffset reflection seismograms generated by a point source excitation in a stratified acoustic medium the reference seismograms are decomposed into cylindrical waves in the frequency wavenumber domain where the inversion is performed by minimizing the difference between the reference data and modeled data using a least squares technique the modeling algorithm is based on the classical reflectivity method we include the effects of limited temporal and spatial apertures by applying a frequency and wavenumber dependent filter in the modeling process this inversion is suited for jacobian matrix methods where the first derivatives of the model generated data with respect to the model parameters are calculated from analytical expressions together with the modeling the numerical examples show that the inversion algorithm recovers with reasonable accuracy the parameters used to generate the reference data the low frequency trends of both the velocity and the density are restored the convergence of the iterative minimization algorithm is fast

parallel tempering for strongly nonlinear geoacoustic inversion this paper applies parallel tempering within a bayesian formulation for strongly nonlinear geoacoustic inverse problems bayesian geoacoustic inversion consists of sampling the posterior probability density ppd of seabed parameters to estimate integral properties such as marginal probability distributions based on ocean acoustic data and prior information this sampling is usually carried out using the markov chain monte carlo method of metropolis hastings sampling however standard sampling methods can be very inefficient for strongly nonlinear problems involving multi modal ppds with the potential to miss important regions of the parameter space and to significantly underestimate parameter uncertainties parallel tempering achieves efficient effective sampling of challenging parameter spaces with the ability to transition freely between multiple ppd modes by running parallel markov chains at a series of increasing sampling temperatures with probabilistic interchanges between chains the approach is illustrated for inversion of simulated acoustic reverberation data for which the ppd is highly multi modal while metropolis hastings sampling gives poor results even with very large sample sizes parallel tempering provides efficient convergent sampling of the ppd methods to enhance the efficiency of parallel tempering are also considered

multiple order derivatives of a waveguide acoustic field with respect to sound speed density and frequency an adjoint perturbative method is used to derive expressions for the first through third order derivatives of a pressure field with respect to sound speed density and frequency for the restricted case of a laterally homogenous waveguide in which environmental parameters are only a function of depth by using a normal mode green s function the three dimensional spatial correlation required by the standard acoustic adjoint equation can be reduced to a set of one dimensional depth integrals the resulting expressions for the first order derivative are similar to those obtained by previous perturbative approaches based on the depth separated wave equation but the approach followed here permits straightforward extension to higher order derivatives explicit evaluations of the expressions for a representative shallow water waveguide model are in excellent agreement with numerical finite difference computations an analysis of the expressions as a function of source receiver range finds the contributions t

an intelligent genetic algorithm designed for global optimization of multi minima functions many practical problems often lead to large non convex non linear programming problems that have multi minima the global optimization algorithms of these problems have received much attention over the last few years generally stochastic algorithms are suitable for these problems but not efficient when there are too many minima genetic algorithms are stochastic search approaches based on randomized operators such as selection crossover and mutation inspired by the natural reproduction and evolution of the living creatures however the existing genetic algorithms cannot solve global optimization of multi minima functions effectively a new algorithm called intelligent genetic algorithm iga is proposed for the global optimization of multi minima functions iga integrates many cross operator mutation operator and reattempt operation it can select the appropriate cross operator mutation operator or reattempt operation according to the current optimization result it converges to the global optimization solution without the influence of random searching process at first this paper introduces the foundation for designing intelligent genetic algorithm secondly this paper reports on the development of an intelligent genetic algorithm approach for global optimization problems thirdly the proposed method is illustrated by means of some numerical examples finally the conclusions of this study are drawn with possible directions for subsequent studies the feasibility the efficiency and the effectiveness of iga are tested in detail through a set of benchmark multi modal functions of which global and local minima are known the experimental results suggest that results from iga are better than results from other methods in conclusion the performance of iga is better than that of other methods iga results are satisfactory for all the functions

quantifying uncertainty in geoacoustic inversion ii application to broadband shallow water data this paper applies the new method of fast gibbs sampling fgs to estimate the uncertainties of seabed geoacoustic parameters in a broadband shallow water acoustic survey with the goal of interpreting the survey results and validating the method for experimental data fgs applies a bayesian approach to geoacoustic inversion based on sampling the posterior probability density to estimate marginal probability distributions and parameter covariances this requires knowledge of the statistical distribution of the data errors including both measurement and theory errors which is generally not available invoking the simplifying assumption of independent identically distributed gaussian errors allows a maximum likelihood estimate of the data variance and leads to a practical inversion algorithm however it is necessary to validate these assumptions i e to verify that the parameter uncertainties obtained represent meaningful estimates to this end fgs is applied to a geoacoustic experiment carried out at a site off the west coast of italy where previous acoustic and geophysical studies have been performed the parameter uncertainties estimated via fgs are validated by comparison with i the variability in the results of inverting multiple independent data sets collected during the experiment ii the results of fgs inversion of synthetic test cases designed to simulate the experiment and data errors and iii the available geophysical ground truth comparisons are carried out for a number of different source bandwidths ranges and levels of prior information and indicate that fgs provides reliable and stable uncertainty estimates for the geoacoustic inverse problem