Arne Reitan

Decomposition of multicomponent sea‐floor data into upgoing and downgoing P‐ and S‐waves

A method for decomposing multicomponent sea‐floor measurements into upgoing and downgoing P‐ and S‐waves is presented. We assume that a marine survey employing a marine source in the water layer is conducted over a plane‐layered medium. From recordings of the pressure just above the sea floor and the particle velocity vector just below the sea floor, decomposition filters can be determined by plane‐wave analysis. The decomposition filter coefficients depend on the P‐ and S‐wave velocities and the density at the sea bottom. We show how to decompose the multicomponent measurements into upgoing and downgoing P‐ and S‐vertical traction components, vertical‐particle velocity components, and horizontal particle velocity components. The decomposition filters are applied with good results to synthetic data modeled in a plane‐layered medium.

Wave-power absorption by an oscillating water column in a reflecting wall

The wave-power absorption by an oscillating water column in a reflecting wall is studied within linear theory. We give numerical examples demonstrating how the performance depends on the geometry of the system as well as on the frequency and direction of the incident waves.

Estimation of sea-floor wave velocities and density from pressure and particle velocity by AVO analysis

Sea‐bottom properties play an important role in fields as diverse as underwater acoustics, earthquake and geotechnical engineering, and marine geophysics. Water‐column acousticians study shear and interface waves in the nearbottom sediments with the aim of inferring sea‐bed geoacoustic parameters for predicting reflection and absorption of waves at the sea floor. On the other hand, geotechnical engineers working on design and siting of offshore structures focus on these waves to characterize soil and rock properties. In the field of geophysics, sea‐bottom parameters are of interest for several reasons. In conventional marine acquisition, these parameters determine the partitioning of the incident P‐wave energy from the source into transmitted P‐waves and mode‐converted S‐waves (Tatham and Goolsbee, 1984; Kim and Seriff, 1992). The sea‐floor P‐ and S‐wave velocities and density are also necessary inputs for decomposing multicomponent sea‐floor data into P‐ and S‐waves (Amundsen and Reitan, 1995a and b), as...

Short Note: Transformation from 2-D to 3-D wave propagation for horizontally layered media

The relationship between 2-D and 3-D wave propagation in horizontally layered media was first investigated by Dampney (1971). In the last few years the usefulness and feasibility of transforming point‐source responses with 3-D geometric spreading to equivalent line‐source responses with 2-D geometric spreading have been thoroughly discussed (see Helgesen, 1990; Wapenaar et al., 1990, 1992; Herrmann, 1992; Helgesen and Kolb, 1993; Amundsen, 1993). In the case of cylindrical symmetry this transformation constitutes a required preprocessing step for several seismic processing algorithms based on 2-D wave propagation. The work of Dampney (1971) has apparently been missed by the authors discussing the 3-D to 2-D geometric spreading transform.

Wave-power absorption by a finite row of oscillating water columns in a reflecting wall*

The wave-power absorption by a finite row of oscillating water columns in a reflecting wall is studied within linear theory. Comparisons are made with our previus results for an infinite row and for a single column.

Toward optimal spatial filters for demultiple and wavefield splitting of ocean‐bottom seismic data

Suppressing the receiver‐side sea‐surface ghost with its accompanying water‐layer reverberations in multicomponent sea‐floor data can be performed in both the frequency–wavenumber and the frequency–space domains. Similarly, separation of ocean‐bottom seismic (OBS) data into upgoing P‐ and S‐mode responses can be formulated in both domains. The frequency–space domain algorithms can be attractive when the sea‐floor medium has lateral velocity variations or the data are irregularly sampled along the sea floor, which requires that the data be processed with local, compact decomposition filters having optimal angular (wavenumber) response.By deriving the frequency–space domain formulas, we find an exact representation for the demultipled pressure response. This formula involves filter convolutions over the data, with filters having a long spatial impulse response. The filtering can be approximated in the wavenumber domain by, for example, power series, Chebyshev polynonomial fitting, Pade approximants, or cont...

Multicomponent ocean bottom and vertical cable seismic acquisition for wavefield reconstruction

In ocean-bottom seismic and vertical-cable surveying, receiver stations are stationary on the sea floor while a source vessel shoots on a predetermined x-y grid on the sea surface. To reduce exploration cost, the shot point interval often is so coarse that the data recorded at a given receiver station are undersampled and thus irrecoverably aliased. However, when the pressure field and its x - and y -derivatives are measured in the water column, the nonaliased pressure field can be reconstructed by interpolation. Likewise, if the vertical component of the particle velocity (or acceleration) and its x - and y -derivatives are measured, then this component can also be reconstructed by interpolation. The interpolation scheme can be any scheme that reconstructs the field from its sampled values and sampled derivatives. In the case that the two fields’ first-order derivatives are recorded, the total number of components is six. When also their second-order derivatives are measured, the number of components is ...

Wave equation depth migration—a new method of solution

We present a wave propagation method rigorous in one-way and two-way wave theory for complex velocity varying media with new solutions. In the horizontal wavenumber domain, the first-order differential system that governs acoustic wave propagation can be written in terms of field vectors that are coupled in the wavenumber variables through convolutions between the medium and the fields. The differential system can be uncoupled by introducing a reference system with reference velocity equal to the reciprocal of the rms slowness. The uncoupled system of equations has propagator solutions that are coupled in the wavenumber variables. These solutions can be decoupled by introducing simple approximations. This scheme can be exploited for wave equation depth migration. It then is convenient to introduce new field variables that relate to upgoing and downgoing waves in the reference medium. One-way and various two-way wave equations for the laterally varying medium then can be derived by introducing the down-up wave interaction (DUWI) model. The differential equation for the downgoing (incident) field is derived in the zero-order DUWI model, which neglects the interactions with the upgoing field, resulting in a pure one-way wave equation for the downgoing field. Similarly, the zero-order DUWI model yields a one-way wave equation for the upgoing field. In the first-order DUWI model, the downgoing field from the zero-order DUWI model is used as a source for the upgoing field. This solution gives a quasi two-way wave equation which may be used to migrate overturning waves. Noteworthy, the differential equations we derive have analytical solutions for migration in the wavenumber domain. Simple approximations lead to numerically fast migration schemes that can be implemented in a manner like the split-step Fourier migration schemes.

The relationship between 2-D and 3-D wave propagation

Recently, attention has been paid to the problem of transforming three-dimensional, cylindrically-symmetric wave propagation to two-dimensional wave propagation for horizontally layered media. The opposite transform from two-dimensional to three-dimensional wave propagation, however, appears to have received little attention. To establish the pair of transformations is of interest for several reasons: apart from its intrinsic interest, the transformations may be used as amplitude pre- or postprocessing for some multistep seismic processing schemes, as well as to transform some two-dimensional wave propagation phenomena to their three-dimensional counterpart. The authors derive simple integral relationships between the two types of wave propagation for horizontally layered media with an exploding point source or a point force. The transformations of pressure, vertical component of traction and vertical component of particle velocity for a point source, and vertical component of particle velocity for a vertical force, are recognized as pairs of Abel integral equations. The transforms of the other field components can be considered as generalizations of the Abel integral equations. Abel type equations are often encountered in problems where circularly symmetric distributions in two dimensions are projected into one dimension.

Potential and Glauber Scattering of Electrons by Complex Atoms

Some simple models for scattering of electrons in the 1 keV energy region by complex atoms are considered. For a static potential consisting of a sum of Yukawa functions approximate solutions to the scattering problem are compared with the results obtained by a numerical solution of the radial wave equation. The effects due to the separate scatterers in the target are introduced in a non-relativistic Glauber model where the target electrons are taken to be in a common spherically symmetric state. The resulting scattering amplitude is then used to generate an optical potential, which is modified by a method based on the eikonal-Born series and used to calculate differential and total cross sections for scattering on rare gases.