Roger Sollie

Source signature determination by inversion

A new method for estimating the pressure wavefield generated by a marine air‐gun array is presented. It is assumed that data is acquired at a ministreamer located below the source array. Effective source signatures for each air gun are estimated by an inversion algorithm. The forward modeling scheme used in the inversion algorithm is based upon a physical modeling of the air bubble generated by each air gun. This means that typical inversion parameters are: gun depths, empirical damping coefficients, and reflection coefficient of the sea surface. Variations in streamer depth are also taken into account by the inversion scheme. The algorithm has been successfully tested on examples with unknown streamer positions, gun parameters, reflection coefficient of sea surface, and ministreamer data contaminated with white noise.

Using Mindlin theory to model friction-dependent shear modulus in granular media

An explicit expression for the effective shear modulus of a random packing of identical spheres is derived as a function of Mindlin’s tangential stiffness with interparticle contact friction. The motivation behind the approach is to incorporate the effect of intergrain friction to predict velocities in unconsolidated sands. The Mindlin friction term, allowing partial slip across the contact area between pairs of spheres, can be viewed as a parameter accounting for the growing macroscopic intergrain friction in sands as burial progresses. Hence, both moduli and velocities will gradually increase as the compressional- to shear-wave velocity ratioVP /VS or Poisson’s ratio decreases. An estimate of effective elastic constants in particular shear modulus can be obtained for a spherical grain pack with an arbitrary frictional behavior ranging between two special contact boundary conditions representing infinite friction and zero friction. The proposed model predicts a nonlinear transition between the two special grain-contact conditions when compared to previously published linear relationships. Comparison of elastic properties, i.e., dynamic shear-modulus predictions assuming zero contact friction with experimental data on loose glass bead and sand samples undergoing hydrostatic compression, appears to match reasonably well at low confining stressless than 5 MPa but deviates gradually as stress increases. It is advocated that the increasing effective internal frictional resistance of the experimental core samples control both the frictional attenuation mechanism in loose grain packs under low confining stress for strain amplitudes typical of seismic wavesless than 106 and the higher stress-velocity sensitivity. Circumstantial evidence of this is found in publications describing both laboratory attenuation analysis and consolidation experiments on granular materials with different degrees of competence or static shear strength.

3D surface-related multiple elimination using parabolic sparse inversion

The basic theory of surface-related multiple elimination (SRME) can be formulated easily for 3D seismic data. However, because standard 3D seismic acquisition geometries violate the requirements of the method, the practical implementation for 3D seismic data is far from trivial. A major problem is to perform the crossline-summation step of 3D SRME, which becomes aliased because of the large separation between receiver cables and between source lines. A solution to this problem, based on hyperbolic sparse inversion, has been presented previously. This method is an alternative to extensive interpolation and extrapolation of data. The hyperbolic sparse inversion is formulated in the time domain and leads to few, but large, systems of equations. In this paper, we propose an alternative formulation using parabolic sparse inversion based on an efficient weighted minimum-norm solution that can be computed in the angular frequency domain. The main advantage of the new method is numerical efficiency because solving many small systems of equations often is faster than solving a few big ones. The method is demonstrated on 3D synthetic and real data with reflected and diffracted multiples. Numerical results show that the proposed method gives improved results compared to 2D SRME. For typical seismic acquisition geometries, the numerical cost running on 50 processors is 0.05 s per output trace. This makes production-scale processing of 3D seismic data feasible on current Linux clusters.

Nonlinear deformations of liquid-liquid interfaces induced by electromagnetic radiation pressure

The idea of working with a near-critical phase-separated liquid mixture whereby the surface tension becomes weak, has recently made the field of laser manipulation of liquid interfaces a much more convenient tool in practice. The deformation of interfaces may become as large as several tenths of micrometers, even with the use of conventional laser power. This circumstance necessitates the use of nonlinear geometrical theory for the description of surface deformations. The present paper works out such a theory, for the surface deformation under conditions of axial symmetry and stationarity. Good agreement is found with the experimental results of Casner and Delville [A. Casner and J. P. Delville, Phys. Rev. Lett. 87, 054503 (2001); Opt. Lett. 26, 1418 (2001); Phys. Rev. Lett. 90, 144503 (2003)], in the case of moderate power or a broad laser beam. In the case of large power and a narrow beam, corresponding to surface deformations of about 50 micrometers or higher, the theory is found to over-predict the deformation. Possible explanations of this discrepancy are discussed.

Source signature determination from ministreamer data

Two methods for estimating the pressure wavefield generated by a marine airp‐gun array are tested. Data have been acquired at a ministreamer located below the source array. Effective source signatures for each air gun are estimated. In the first method a nonlinear inversion algorithm is used, where the forward modeling scheme is based upon a physical modeling of the air bubble generated by each air gun. In the second method a linear inversion method is used, with the assumption that the physics in the problem can be described by the acoustic wave equation with explosive point sources as the driving term. From the estimated effective source signatures, far‐field signatures have been calculated for both methods and compared with measured far‐field signatures. The error energy between the measured and estimated far‐field signatures was approximately 8 percent for both methods.

Casimir force on a spherical shell when ε(ω)μ(ω)=1

The Casimir surface force on a spherical shell is calculated, assuming the material to be satisfying the condition e(ω)μ(ω)=1, e(ω) being the spectral permittivity and μ(ω) the spectral permeability. The basic formula for the force is given under general conditions, without any restrictive assumption on the thickness of the shell or on the specific dispersion relation. When it comes to numerical evaluations, it is assumed that the shell is of small thickness, and also that the simple form μ(ω)=μs (ω≤ω0), μ(ω)=1 (ω>ω0), for the dispersion relation. The special case when μs →∞ or 0 is given particular attention, since this case appears to be of main physical interest and also since it implies mathematical simplifications. The force F may then be written as the sum of two terms: one ‘‘normal’’ term F(0) containing an attractive dispersion‐induced part as well as a repulsive, nondispersive finite part, and one ‘‘abnormal’’ term F(1) that becomes divergent when summed over all angular momenta. This particular ...

Horizontal resolution of 3‐D VSP data

In this paper we study the horizontal resolution of 3-D VSP data and compare it to the resolution of surface seismic data for various acquisition configurations. The Kirchhoff migration formula is calculated analytically for a point diffractor, and several measures of horizontal resolution are estimated from the migration images. We have performed full 3-D finite-difference modeling for two acquisition configurations, 1) 3-D VSP in a horizontal well, and 2) 3-D surface seismics. A simplified model with well defined reflectors was used, and the data were migrated using a Krichhoff migration scheme. The results shows that the horizontal resolution of both 3-D VSP and 3-D surface seismic data is in agreement with Beylkin’s classical formula.

Finite-difference Modeling of Viscoelastic Wave Propagation in Core Samples

Summary We present a numerical study of wave propagation in a core sample, using viscoelastic finite-difference modeling. The rheological model is a standard linear solid. P- and S-wave source transducers are simulated by single couple body force equivalents. Viscoelastic P- and S- wave velocities computed from simulated pulse transmission experiments using the traditional pulse arrival definitions are neither phase nor group velocity, but typically lie between these values. First break times give results closer to the group velocity and zero crossing and peak amplitude times closer to the phase velocity.

Lithology identification by AVO inversion

A stratigraphic elastic inversion scheme has been applied The main assumptions in the present scheme are: (i) The to two data sets from the ‘Troll East field. The objective of model is locally close to horizontally layered (i.e. the model the present work is to obtain estimates of Pand Swave layers exhibit small dips and small lateral velocity variavelocities and densities in a multilayered model containing tions on a length equal to the streamer length), (ii) only reservoir rocks. Furthermore, we use the estimated paramPP reflections are evident in the data, and (iii) anisotropy eters to distinguish the lithology of the various layers. effects may be neglected. The forward modeling is performed by convolving a wavelet with the reflectivity which includes water bottom multiples, transmission effects, absorption and array filter effects. A damped Gauss-Newton algorithm is used to minimize a least squares misfit function. The inversion is carried out on transformed CMP gathers. The results from the inversion show good correlation D A T A P R O C E S S I N G

3-D Surface-related Multiple Elimination Using Parabolic Sparse Inversion

The basic theory of surface-related multiple elimination SRME can be formulated easily for 3D seismic data. However,becausestandard3Dseismicacquisitiongeometriesviolate the requirements of the method, the practical implementation for 3D seismic data is far from trivial. A major problem is to perform the crossline-summation step of 3D SRME, which becomes aliased because of the large separation between receiver cables and between source lines.Asolution to this problem, based on hyperbolic sparse inversion, has been presented previously. This method is an alternative to extensive interpolation and extrapolation of data. The hyperbolic sparse inversion is formulated in the time domain and leads to few, but large, systems of equations. In this paper, we propose an alternative formulation using parabolic sparse inversion based on an efficient weighted minimumnorm solution that can be computed in the angular frequency domain.Themainadvantageofthenewmethodisnumerical efficiency because solving many small systems of equations often is faster than solving a few big ones. The method is demonstratedon3Dsyntheticandrealdatawithreflectedand diffracted multiples. Numerical results show that the proposed method gives improved results compared to 2D SRME. For typical seismic acquisition geometries, the numerical cost running on 50 processors is 0.05 s per output trace.This makes production-scale processing of 3D seismic datafeasibleoncurrentLinuxclusters.