Efficient Forward Model Research Articles

Forward modeling of space-borne gravitational wave detectors

Planning is underway for several space-borne gravitational wave observatories to be built in the next ten to twenty years. Realistic and efficient forward modeling will play a key role in the design and operation of these observatories. Space-borne interferometric gravitational wave detectors operate very differently from their ground based counterparts. Complex orbital motion, virtual interferometry, and finite size effects complicate the description of space-based systems, while nonlinear control systems complicate the description of ground based systems. Here we explore the forward modeling of space-based gravitational wave detectors and introduce an adiabatic approximation to the detector response that significantly extends the range of the standard low frequency approximation. The adiabatic approximation will aid in the development of data analysis techniques, and improve the modeling of astrophysical parameter extraction.

FDTD‐SUPML‐ADE simulation for Ground‐Penetrating Radar modeling

GPR data simulations require above all an efficient forward modeling algorithm. A Finite Difference Time Domain code is presented with Simplified Unsplit Perfect Matched Layer that leads to insignificant reflections on border with few modifications of the core algorithm. In addition, the Auxiliary Differential Equation method allows GPR simulations including dispersive phenomena that could not be neglected at radar frequencies. The numerical validation is done in a classic way for amplitude/time wave propagation and SUPML, and using the nonconventional Dispersion Analysis technique for physical dispersion behavior. Full 3‐D and 2‐D forward modeling results are finally presented for lossy, dispersive and random media in GPR conditions.

Fast inversion of large-scale magnetic data using wavelet transforms and a logarithmic barrier method

SUMMARY In this paper wavelet transforms and a logarithmic barrier method are applied to the inversion of large-scale magnetic data to recover a 3-D distribution of magnetic susceptibility. The fast wavelet transform is used, along with thresholding the small wavelet coefficients, to form a sparse representation of the sensitivity matrix. The reduced size of the resultant matrix allows the solution of large problems that are otherwise intractable. The compressed matrix is used to carry out fast forward modelling by performing matrix-vector multiplications in the wavelet domain. The reduction in CPU time is directly proportional to the compression ratio of the matrix. A second important feature of the algorithm used here is the use of an interior-point method of optimization to enforce positivity constraints. In this approach, the positivity is incorporated into the inversion by a sequence of non-linear optimizations approximated by truncated Newton steps. At the heart of the algorithm, a linear system of equations is solved. The conjugate gradient technique has been used as the basic solver to take the advantage of the efficient forward modelling offered by the sparse matrix representation. Overall, the combination of wavelet transforms, interior point optimization and conjugate gradient solutions readily allows us to solve magnetic inverse problems that have a few hundred thousand parameters and tens of thousands of data.

Beam-tracing-based inverse scattering for general aperture antennas

Iterative techniques are presented for two-dimensional inverse scattering from electrically large regions. The region is illuminated by transmitters with arbitrary profiles; this is an escalation in complexity from the line-source and the plane-wave excitations considered in many previous inverse-scattering studies. Imaging algorithms require an accurate and efficient forward model. Here a Gaussian-beam algorithm is utilized as a forward solver and is incorporated into an iterative-Born inversion scheme. General antenna profiles are incorporated into the algorithm by use of the matched-pursuits technique, by which the aperture fields are matched to the beam-tracing algorithm. Results are presented for several cases in which the simple Born approximation fails. Issues addressed include the types of profiles that can be successfully imaged, suitable antenna distributions, and the range of parameters over which the scheme is effective. Performance of the algorithm in the presence of noisy data is also tested.

Application of an improved self-starter to geoacoustic inversion

The self-starter is improved using the operator of the split-step Pade solution. In addition to providing greater stability and being applicable closer to the source, the improved self-starter is an efficient forward model for geoacoustic inversion. It is necessary to solve only O(10) tridiagonal systems of equations to obtain the acoustic field on a vertical array located O(10) wavelengths from a source. This experimental configuration is effective for geoacoustic inverse problems involving unknown parameters deep in the ocean bottom. For problems involving depth-dependent acoustic parameters, the improved self-starter can be used to solve nonlinear inverse problems involving O(10) unknown sediment parameters in less than a minute on the current generation of workstations.

A rapid forward model for matched‐field inversion

The forward model is an important component of a matched‐field inversion algorithm. The forward model must be efficient because it is often necessary to compute a large number of replica fields during the parameter search. An efficient forward model will be described for an experimental configuration involving a source and a vertical array separated by up to several tens of wavelengths in range. The operators of the self‐starter and the split‐step Pade solution are combined into a single operator that acts on a delta function to give the field on the array. On a parallel‐processing computer, this approach provides the replica field in the computation time it takes to solve a single tridiagonal system in a conventional parabolic equation algorithm. This efficiency gain is not achieved by sacrificing accuracy. The approach typically involves the solution of about ten tridiagonal systems. Finite‐difference based separation of variables solutions typically require the solution of hundreds or thousands of simi...

Surface-wave mode coupling for efficient forward modelling and inversion of body-wave phases

SUMMARY The importance of surface-wave mode coupling in the modelling of body-wave phases by surface-wave mode summation is studied by means of sensitivity kernels obtained with the Born approximation and exact solutions of the Invariant Imbedding Technique. It is shown that, independent of the character of the lateral heterogeneity, surface-wave mode coupling is required to model body-wave phase perturbations and that neglecting intermode coupling, as in the WKBJ method for surface waves, can lead to large biases. Because methods which describe surfacewave mode coupling in an exact fashion are computationally too expensive to use in inversion schemes, the Scalar Exponent Approximation (SEA) is presented, which is a computationally efficient method and takes mode coupling into account. Since, instead of Earth normal modes, surface-wave modes are used, the summation over the angular order l is carried out analytically. This means that the number of modes and mode interactions needed is significantly reduced which assures an efficient manner of modelling. It is shown that the SEA is accurate in modelling body-wave phase perturbations for geophysically realistic configurations. Because, in contrast to the WKBJ sensitivity kernels, mode coupling introduces sensitivity kernels which also depend on the position along the source-receiver path, the SEA requires a larger model parameter set in inversions. A procedure is presented which reorganizes the model parameter set and leads to a reduced set of physically relevant model parameters. The combination of the SEA and the reorganization of the model parameters can be used efficiently in large-scale 3-D inversions which incorporate the important effects of surface-wave mode coupling.

Lattice‐gas automata for modeling acoustic wave propagation in inhomogeneous media

We report recent developments in using lattice‐gas automata to simulate acoustic wave propagation in inhomogeneous media, and give experimental results that include transmitted and reflected waves. Two sets of rules are adopted to govern the evolution of particles in the lattice; one applicable to lattice sites on the interface, the other to interior sites. Both sets of rules are simple and deterministic, thereby preserving the computational advantages of lattice‐gas automata. Further investigation bears long‐term promise of yielding a novel and efficient forward modeling tool for geologically realistic models.

A solution for TM‐mode plane waves incident on a two‐dimensional inhomogeneity

Quantitative interpretation of magnetotelluric (MT) surveys depends at present on the availability of an efficient forward modeling algorithm. To date, two major numerical techniques have been used to obtain the scattered fields from buried inhomogeneities in plane‐wave fields: methods solving the governing differential equation which generally uses a finite‐element or finite‐difference approach, and methods which solve an integral‐equation formulation of the problem. For two‐dimensional (2-D) inhomogeneities a solution for incident fields with the electric field parallel to the strike of the inhomogeneity (TE mode solution) was developed by Hohmann (1971) using the integral‐equation approach. For a perfect conductor an integral formulation, for surface scattering currents, for the TM mode (magnetic field parallel to the strike of the inhomogeneity) was developed by Parry (1969). General 2-D solutions in the presence of an arbitrary mode plane wave (mixed TE-TM) were obtained by Ryu (1970), Swift (1971), and Rijo (1977) using either a finite‐element or finite‐difference technique.