Sven Ivansson

A study of methods for tomographic velocity estimation in the presence of low‐velocity zones

This paper deals with the problem of seismic velocity estimation from first‐arrival traveltimes in a two‐dimensional (2-D) cross‐hole geometry where explosions are detonated in one borehole while recordings are made in another borehole and on the surface. Standard tomographic procedures are based on decomposition of the cross‐hole area into a number of cells and a simplifying assumption of straight raypaths. In the presence of significant low‐velocity zones, the resulting images may be contaminated. Different ways of performing tomographic inversion are tested on a number of synthetic examples. Images obtained by direct, unrestricted least‐squares inversion are often seriously distorted. However, methods using more cells and some kind of damping often give more satisfactory results. Because the risk of distorted images is always present in inversion procedures, comparison with synthetic data (forward modeling) is a valuable tool in the interpretation process. With a reasonably good initial solution, impro...

Sound absorption by viscoelastic coatings with periodically distributed cavities

Thin rubber layers with air-filled cavities can be used as anechoic submarine coatings. Normally incident sonar energy is redistributed in the lateral direction and absorbed. In this paper, the anechoic effect is studied theoretically and numerically by adapting techniques used in electron scattering and band-gap computations for photonic and phononic crystals. Reflection and transmission matrices are computed recursively, from basic ones for layers containing periodic arrays of spherical cavities. A method to locate zeroes of analytical functions is applied to prove the existence of, and to specify, thin coatings with vanishing reflectance at isolated frequencies. Coatings much thinner than quarter-wavelength ones are found. Most of the absorption loss takes place close to the cavities and scattering of compressional spherically symmetric waves is important. The viscoelastic shear-wave properties of the rubber are crucial for generating this loss. The requirements for vanishing reflectance are specified ...

Numerical design of Alberich anechoic coatings with superellipsoidal cavities of mixed sizes

Thin rubber coatings with cavities in a doubly periodic lattice are able to reduce reflections of underwater sound by redistributing normally incident energy such that absorption in the surrounding rubber is enhanced. For spherical scatterers, the anechoic effect can be studied numerically by the layer-multiple-scattering (LMS) method. In comparison to more flexible but also more computer intensive methods, such as finite-element method modeling, there are two important advantages. An improved physical understanding of the anechoic effect can be achieved by simplified semianalytical analysis, and the high computational speed allows modern global optimization techniques to be applied for coating design. In this paper, the flexibility of the LMS method is improved by combination with an efficient algorithm for numerical computation of transition matrices for superellipsoidal scatterers. (A superellipsoid is a generalization of an ellipsoid, allowing more box-filling shapes, for example.) Extensions to mixtures of nonspherical scatterers of different types are also considered, in order to enhance the broadband performance. Symmetry properties are used to reduce the size of the pertinent equation systems. Examples of numerical coating design for underwater acoustic applications are presented, using differential evolution algorithms for the optimization.

A high‐order adaptive integration method for wave propagation in range‐independent fluid–solid media

Efficient computation of the Hankel‐transform integral for the wave field in a laterally homogeneous fluid–solid medium is nontrivial, since the integrand may be both oscillating and irregularly peaked. We propose a high‐order, adaptive integration method suitable for integrands with these characteristics. The method combines trapezoidal or Filon sums, obtained with several step sizes, with polynomial or Bulirsch–Stoer rational extrapolation to increase the order of convergence and to obtain error estimates. This technique is combined with adaptive interval halving, maintaining a hierarchy of subintervals, meshes, and function values in a stack to eliminate duplicate function evaluations. Computational results from an underwater acoustics application are presented. At any level of accuracy, the proposed method requires less computational work than nonadaptive trapezoidal or Filon quadrature, the difference growing to orders of magnitude as the accuracy increases.

Numerical investigation of out-of-plane sound propagation in a shallow water experiment

In an experiment in the Florida Straits, broadband pulses were transmitted over a range of 10 km and received by a vertical hydrophone array. For pulses with center frequency below 400 Hz, the received signal consisted of a dominant arrival followed by a secondary one delayed by about 0.4 s. A hypothesis that the secondary arrival was caused by 3D out-of-plane propagation is investigated here numerically with a 3D parabolic equation model (3DWAPE) and a 3D ray model (MOC3D). Both models clearly predict a secondary arrival caused by 3D horizontal refraction from the sloping bottom in the shoreward direction.

An experiment with the seismic crosshole method in an iron mine

Seismic techniques have so far been only sparsely employed by the mining industry for ore prospecting. In the last few years, however, growing attention has been paid to the seismic reflection method which is the most powerful geophysical tool in terms of resolution and depth penetration for hydrocarbon exploration. At least in Sweden there is an increasing interest in geophysical techniques for ore prospecting which allow depth penetration of 1 km or more. The known bodies in Sweden usually dip, however, very steeply, and the standard seismic reflection method will probably have to be modified substantially in order to perform well for such formations.

Anechoic coatings obtained from two- and three-dimensional monopole resonance diffraction gratings

Underwater sound reflections can be reduced in magnitude by a rubber coating including three-dimensional (3-D) cavities forming a doubly periodic diffraction grating. A monopole resonance for sphere-like cavities enhances absorption in the surrounding rubber solid. A corresponding resonance for an infinite cylinder is studied in the present paper. Appearing at a considerably lower frequency than for a sphere with the same radius, it suggests the possibility of much thinner anechoic coatings including cylindrical cavities, with axes in a lateral direction, forming a diffraction grating with a single period. This is effectively a 2-D case, because of invariance in the axial direction. Subsequent coating design computations, using the layer-multiple-scattering method and including cavities of different sizes, show improved reflection reduction with coatings only about one third as thick. Still accounting for multiple scattering among the cavities and capturing the essential physics, the monopole approximation is applied to advance the analytic study of the reflection reduction. An energy decomposition relation is derived and used to quantify the absorption of the incident sound energy by cavities of different sizes. Coatings based on filled inclusions and other resonance effects are briefly considered. Again, the 2-D alternative with cylinders of mixed sizes gives thinner coatings.

Low-frequency slow-wave dispersion computations by compound-matrix propagation

Slow P-SV modes whose horizontal slowness tends to infinity while the horizontal wave number tends to zero, as the frequency tends to zero, exist in certain laterally homogeneous fluid-solid media. These modes can be characterized by an asymptotic analysis of the dispersion function. Only certain powers of frequency are possible for the asymptotic increase of the horizontal slowness as the frequency tends to zero: −1/3, −1/2, −3/5, and −2/3. In order to investigate the accuracy of the asymptotic predictions, dispersion-curve computations by propagator techniques are attempted for media composed of homogeneous fluid and solid layers. However, numerical precision is lost by cancellation effects for the elements of the solid-layer compound-matrix propagators that are involved. Guided by the asymptotic growth of these compound-matrix elements, cancellation-free expressions are derived for applications to the slow modes at very low frequencies. The harmful contributions causing loss of numerical precision are ...

The Compound Matrix Method for Multi‐Point Boundary‐Value Problems Depending on a Parameter

Boundary-value problems for ordinary differential-equation (ODE) systems often depend on a parameter. It is shown how derivatives of the solution with respect to the parameter can be computed using compound matrices in the linear multi-point case. In the applications, such derivatives are useful e.g. in inversion theory when the parameter is to be estimated. When the dependence on the parameter is analytic, an integral of boundary-problem solutions with respect to the parameter can typically be expanded as a sum of residues. Such integrals and expansions have theoretical as well as practical interest, and an explicit formula is derived for the residue contributions. It is given in terms of eigensolutions to the original problem and an appropriately defined adjoint problem. It is shown how the quantities involved can be computed in a stable way using compound matrices. For the application case with wave-propagation in a range-independent multi-region fluid-solid medium, a solution to the adjoint problem is obtained directly from a solution to the original problem, and the well-known formula for modal excitation coefficients is extended to leaky modes. Modal depth functions can be computed reliably without experimentation with a cut-off depth for an artificial homogeneous half-space.

Shear‐wave induced transmission loss in a fluid–solid medium

Formulas are derived for decomposition of power and energy within a wave field, a modal wave field in particular, into bulk and shear parts. It is noted that the complex bulk and shear moduli must be restricted to the fourth quadrant if a harmonic time dependence e−iωt with ω≳0 is assumed. An example case with frequency‐dependent transmission loss is studied. The power decomposition results turn out to be very useful for demonstrating that shear losses in the sediment form the major cause of the narrow stop bands that occur. Furthermore, these losses have a resonance character which is illustrated very clearly by showing how the bulk and shear losses are distributed within the sediment layer.