Matthias Meyer

Adjoint-based acoustic inversion for the physical characterization of a shallow water environmenta)

Recently the concept of adjoint modeling has been introduced in shallow water acoustics for solving inverse problems. Analytical adjoints have been derived for normal modes and for both the standard parabolic equation and Claerbout’s wide-angle approximation (WAPE). This paper proposes the application of a semiautomatic adjoint approach that has been successfully applied in the past for multidimensional variational data assimilation in meteorological and climate modeling. Starting from a modular graph representation of the underlying forward model, a programming tool facilitates the generation and coding of both the tangent linear and the adjoint models. The potential of this numerical adjoint approach for the physical characterization of a shallow water environment is illustrated with two applications for geoacoustic inversion and ocean acoustic tomography using Claerbout’s WAPE in combination with nonlocal boundary conditions. Furthermore, the adjoint optimization is extended to multiple frequencies and...

Optimal nonlocal boundary control of the wide-angle parabolic equation for inversion of a waveguide acoustic field.

This paper applies the concept of optimal boundary control for solving inverse problems in shallow water acoustics. To treat the controllability problem, a continuous analytic adjoint model is derived for the Claerbout wide-angle parabolic equation (PE) using a generalized nonlocal impedance boundary condition at the water-bottom interface. While the potential of adjoint methodology has been recently demonstrated for ocean acoustic tomography, this approach combines the advantages of exact transparent boundary conditions for the wide-angle PE with the concept of adjoint-based optimal control. In contrast to meta-heuristic approaches the inversion procedure itself is directly controlled by the waveguide physics and, in a numerical implementation based on conjugate gradient optimization, many fewer iterations are required for assessment of an environment that is supported by the underlying subbottom model. Furthermore, since regularization schemes are particularly important to enhance the performance of full-field acoustic inversion, special attention is devoted to the application of penalization methods to the adjoint optimization formalism. Regularization incorporates additional information about the desired solution in order to stabilize ill-posed inverse problems and identify useful solutions, a feature that is of particular importance for inversion of field data sampled on a vertical receiver array in the presence of measurement noise and modeling uncertainty. Results with test data show that the acoustic field and the bottom properties embedded in the control parameters can be efficiently retrieved.

Dynamic Estimation of the Sound-Speed Profile from Broadband Acoustic Measurements

Global search and more recently adjoint-based inversion methods used in ocean acoustics showed their effectiveness in the estimation of the sound-speed profile (SSP) in water columns of several environments. In the framework of the European Seas Observatory Network (ESONET) an essential part of the research and technology focuses on continuous and long term observations to characterize dynamic ocean processes and monitor the global state of the ocean. Therefore, the development of high performance integrated tools for acoustic inversion is one of the attractive components in this network. For the purpose of efficient data assimilation this paper investigates sequential methods that are able to update sound-speed profile parameters, typically the coefficients of empirical orthogonal functions (EOF), with respect to new incoming acoustic or hydrographic measurements and take into account the seafloor and sub-seafloor acoustic properties in a shallow water environment. A formulation using Kalman filters is suitable for a sequential treatment. This paper investigates the application of two different extensions of the Kalman filter, the extended Kalman filter and the more recent unscented Kalman filter for comparison.

Backpropagation techniques in ocean acoustic inversion: time reversal, retrogation and adjoint model – A review

In light of recent interest in adjoint modelling in underwater acoustics, we present a selective review which is mainly focused on the underlying concept of backpropagation. The different implementations of that concept to date are compared and discussed in the framework of experimental acoustic inversion in shallow water with application to source localisation, ocean acoustic tomography, geoacoustic inversion and underwater communications. Well established inversion or focalisation methods based on matched field processing, model-based matched filter and time reversal mirror are related to less popular ones such as acoustic retrogation and other variants of backpropagation. In contrast to the latter, adjoint-based, variational inversion approaches make use of the adjoint of a forward model to backpropagate the model-data mismatch at the receiver toward the source. The paper describes in greater detail adjoint methods and applications in underwater acoustics. We also present results using environmental data obtained during a geoacoustic inversion experiment in the Mediterranean.

High‐frequency multibeam echosounder classification for rapid environmental assessment

For shallow‐water naval operations, obtaining rapidly an accurate picture of the environmental circumstances often is of high importance. Hereto a multi‐sensor approach is required. In this context, the MREA/BP07 experiment has been carried out south of Elba (Mediterranean Sea), where several techniques of environmental characterization covering the fields of underwater acoustics, physical oceanography and geophysics have been combined [Le Gac&Hermand, 2007]. The required information typically concerns water‐column properties, sea surface roughness, and sediment geo‐acoustic properties. Estimating these geo‐acoustic parameters from inversion of acoustic data received on drifting sparse arrays has proved to be a promising approach. Part of MREA/BP07 was therefore dedicated to this type of measurement. For validating the resulting geo‐acoustic estimates sediment samples were collected. Additionally, measurements were carried out using a multibeam‐echosounder. This system provides depth information, but al...

SEMI-AUTOMATIC ADJOINT PE MODELING FOR GEOACOUSTIC INVERSION ∗

Recently, an analytic adjoint-based method of optimal nonlocal boundary control has been proposed for inversion of a waveguide acoustic field using the wide-angle parabolic equation [Meyer and Hermand, J. Acoust. Soc. Am. 117, 2937-2948 (2005)]. In this paper a numerical extension of this approach is presented that allows the direct inversion for the geoacoustic parameters which are embedded in a discrete representation of the nonlocal boundary condition. The adjoint model is generated numerically and the inversion is carried out jointly across multiple frequencies. To demonstrate the effectiveness of the implemented numerical adjoint, an illustrative example is presented for the geoacoustic characterization of a Mediterranean shallow water environment using realistic experimental conditions.

On the use of acoustic particle velocity fields in adjoint‐based inversion

Following the recent interest in the use of combined pressure and particle motion sensors in underwater acoustics and signal processing, some general aspects regarding the modeling and multipath phenomenology of acoustic particle velocity fields in shallow water environments have been studied. In this paper we will address a number of issues associated with the incorporation of vector sensor data (pressure and particle velocity) into adjoint‐based inversion schemes. Specifically, we will discuss the ability of a semi‐automatic adjoint approach to compute the necessary gradient information without the need for an analytic model of the adjoint particle velocity field. Solutions to the forward propagation of acoustic pressure are computed using an implicit finite‐difference parabolic equation solver while the particle velocity is calculated locally at each grid point. Some numerical examples of vector sensor inversion results are provided. [Work supported by Royal Netherlands Navy.]

Adjoint-based shallow water tomography with partially known bottom geoacoustic properties

Recently, a numerical extension of the wide-angle PE (WAPE) adjoint-based inversion method has been presented that allows direct inversion of the geoacoustic parameters that are embedded in a discrete representation of nonlocal boundary conditions at the water-sediment interface [Hermand et al., ICTCA 2005]. In contrast to conventional ocean acoustic tomography (OAT), correct modeling of sound interaction with the bottom is particularly important for shallow water acoustic tomography (SWAT). Uncertainty or partial knowledge of the bottom acoustic parameters can significantly degrade SWAT performance. In this context the paper discusses an adjoint-based tomography approach that includes the geoacoustic parameters as additional unknowns in the parameter space. A priori information about the bottom characteristics, e.g., the approximate thickness and composition of sediment layers and hard rock basement are often available from site surveys with sub-bottom profiling systems or in the form of previously archived in situ data. This information can be used as an initial solution to start the inversion process or be included in an augmented cost function through the use of regularization. By means of adjoint modeling exact gradient information can be obtained to determine the sound speed profile of the water column and concomitantly adjust the partially known sediment and bottom halfspace parameters. A case study based on environmental data obtained in Mediterranean shallow waters is used to present first results.

Analytic derivation of adjoint nonlocal boundary conditions for a stratified ocean bottom in parabolic approximation

In underwater acoustics various types of nonlocal boundary conditions have been developed to handle the semi‐infinite bottom in parabolic approximations and to efficiently reduce the computational domain. This paper proposes new exact nonlocal boundary conditions suitable for a layered ocean bottom and presents an analytic derivation of the corresponding adjoint equations. The new boundary condition has the form of a Neumann‐to‐Dirichlet map (NtD) that explicitly contains the geoacoustic parameters of the stratified bottom, i.e., thickness, density, sound speed, and attenuation of each layer. By means of the analytic adjoint, exact gradient information can be obtained which in turn allows a direct inversion of these parameters using a gradient‐based optimization scheme. [Work supported by Royal Netherlands Navy.]

Geoacoustic Adjoint‐Based Inversion via the Parabolic Equation

In this paper an analytic method is exhibited for recovering the acoustic parameters of the sub‐bottom region in the ocean. The acoustic propagation problem is modeled via the wide angle parabolic equation and the bottom boundary condition used is in the form of a Neumann to Dirichlet or Dirichlet to Neumann map. The sub‐bottom region is assumed homogeneous or horizontally stratified with homogeneous layers. The inversion is modeled as an optimal control problem, and the solution is based on the adjoint method. Several cost functions are introduced which make use of the relative amplitude of the observed complex field. The method is applied to several test cases and satisfactory convergence of the inversion scheme is exhibited.