Effects of elastic heterogeneities and anisotropy on mode coupling and signals in shallow water

The rotated parabolic equation [J. Acoust. Soc. Am. 87, 1035-1037 (1990)] is generalized to problems involving ocean-sediment interfaces of variable slope. The approach is based on approximating a variable slope in terms of a series of constant slope regions. The original rotated parabolic equation algorithm is used to march the field through each region. An interpolation-extrapolation approach is used to generate a starting field at the beginning of each region beyond the one containing the source. For the elastic case, a series of operators is applied to rotate the dependent variable vector along with the coordinate system. The variable rotated parabolic equation should provide accurate solutions to a large class of range-dependent seismo-acoustics problems. For the fluid case, the accuracy of the approach is confirmed through comparisons with reference solutions. For the elastic case, variable rotated parabolic equation solutions are compared with energy-conserving and mapping solutions.

show abstract

“…Since the bottom slope is constant, this problem can be solved by the method of complex rays. 7 Solutions for example B appear in Fig. 3.…”

Section: Variable Slopesmentioning

confidence: 99%

Generalization of the rotated parabolic equation to variable slopes

Outing

Siegmann

Collins

et al. 2006

The Journal of the Acoustical Society of America

View full text Add to dashboard Cite

show abstract

“…For numerical integration of coupled Riccati equations, the coe¤cient matrix must be computed frequently because B ab is rapidly varying. The phase term will greatly decrease the e¤ciency and the stability of the computation (Park & Odom 1997), especially when we use many sets of local modes for a strongly varying structure. In this section, we remove the phase factor and apply the product integral method of Gilbert & Backus (1966).…”

Section: Coupled -Mode Propagator Representationsmentioning

confidence: 99%

The effect of stochastic rough interfaces on coupled-mode elastic waves

Park

Odom

1999

Geophysical Journal International

View full text Add to dashboard Cite

Summary The effect of stochastic fluctuations of the interface boundaries has been incorporated into the elastic coupled‐mode equations for 2‐D range‐dependent media. We assume the medium to be characterized by some deterministic range‐dependent layered structure superposed by stochastic boundary fluctuations. The deterministic range‐dependent structure defines the reference structure, and the reference structure with superposed stochastic fluctuations defines the true layer boundaries in the medium. The boundary conditions on the true boundary are expanded about the reference boundary, and first‐order perturbation theory is applied to the boundary conditions, as well as to the equation of motion. The calO(1) system and the calO(ɛ) system represent wave propagation in the deterministic model and in the stochastic model, respectively, with a first‐order perturbation of roughness. The solution of the calO(1) system is referred to as the primary field. The solutions to the calO(ɛ) system relate the coherent field and the scattered field, which are represented as the superposition of local modes multiplied by the stochastic modal amplitudes. Propagation of coupled‐mode elastic waves in a 2‐D deterministic range‐dependent medium is represented by a unitary coupled‐mode propagator. The evolution equation for the stochastic medium and the stochastic coupling matrices, which acts to convert the coherent field to the scattered field, is derived. Enforcing energy conservation on the calO(ɛ) system leads to the requirement that the propagator for the stochastic medium must satisfy a Lippmann–Schwinger‐type integral equation, whose solution can be represented by a formal perturbation series for the multiply scattered wavefields. The integral equations for the mean field and the covariance of the field are also presented. These formal theoretical results are valid to all orders of multiple scattering. In the second part of the paper the Born approximation to the Lippmann–Schwinger integral equation is used to extract information about attenuation due to rough surface scattering and in the design of an inverse problem for the boundary roughness variance and correlation length. By defining the modal scattering cross‐section, the formula for the scattering Q− 1s from the Born approximation for the scattered field is derived. The modal scattering cross‐section and scattering Qs for a range‐dependent model with stochastic roughness are computed for both exponential and Gaussian correlation functions. Finally, a formula for the power spectrum of the coherent field is derived from the Born approximation, and an inversion for the roughness variance and correlation length is designed by power spectrum fitting.

show abstract

“…To avoid issues with numerical stability, the two-point boundary-value problem can be recast as an initial-value problem for generalized modal R / T (reflection/transmission) matrices using invariant embedding. For the continuous coupled-mode variant, this has been done, involving differential equations of Riccati type, for reference modes [ 7 ] as well as local modes [ 12 ]. There are other ways to achieve numerical stability, e.g.…”

Section: Introductionmentioning

confidence: 99%

Coupled-mode separation of multiply scattered wavefield components in two-dimensional waveguides

Ivansson

2023

R. Soc. open sci.

View full text Add to dashboard Cite

For a waveguide that is invariant in one of the horizontal directions, this paper presents a mathematically exact partial-wave decomposition of the wavefield for assessment of multiple scattering by horizontally displaced medium anomalies. The decomposition is based on discrete coupled-mode theory and combination of reflection/transmission matrices. In particular, there is no high-frequency ray approximation. Full details are presented for the scalar case with plane-wave incidence from below. An application of interest concerns ground motion induced by seismic waves, which may be severely amplified by local medium anomalies such as alluvial valleys. Global optimization techniques are used to design an artificial medium termination at depth for a normal-mode representation of the field. A derivation of a horizontal source array to produce an incident plane wave gives, as a by-product, an extension of a previous Fourier-transform relation involving Bessel functions. Like purely numerical methods, such as finite differences and finite elements, the method can handle all kinds of (two-dimensional) anomaly shapes.

show abstract

Effects of elastic heterogeneities and anisotropy on mode coupling and signals in shallow water

Cited by 7 publications

References 15 publications

Generalization of the rotated parabolic equation to variable slopes

Generalization of the rotated parabolic equation to variable slopes

The effect of stochastic rough interfaces on coupled-mode elastic waves

Coupled-mode separation of multiply scattered wavefield components in two-dimensional waveguides

Contact Info

Product

Resources

About