摘要:

AbstractAlekseev and Mikhailenko have developed a wavenumber‐summation method which combines a finite integral transformation with a finite‐difference calculation and involves no approximations other than numerical ones. However, numerical anisotropy causes velocity errors for shear waves which are unacceptable if Poisson's ratios are larger than 0.4 and unless the number of grid points per wavelength is chosen considerably higher than the value generally regarded as sufficient in finite‐difference computations. To overcome this limitation in the applicability of the otherwise very powerful modelling scheme, the method is applied to the elastodynamic equations for the velocity vector. Thus, instead of solving a second‐order hyperbolic system as in the case of the wave equation, solutions to a first‐order hyperbolic system are computed. The finite‐difference iteration is performed in a staggered grid. In addition to mastering the numerical difficulties in cases where the Poisson's ratio is unusually high, this approach results in a code which can be used for the modelling of liquid layers.With the new scheme, water reverberations are investigated in terms of normal modes. It is found that for realistic sea‐bottom velocities the critical and supercritical cases exist only for P‐waves. It means that compressional waves are trapped within the water layer but energy leaks into the substratum through converted shear waves. These leaky compressional normal modes attain properties similar to those of shear normal modes or Pseudo‐Love waves. Due to their origin from conversion of dispersed multi‐modal compressional waves the shear waves generated at the sea‐bottom form a long complex wavetrain. They were found to mask the reflections from the target horizon in an off

ISSN:0016-8025    

DOI:10.1111/j.1365-2478.1990.tb01839.x

出版商:Blackwell Publishing Ltd    

年代:1990

数据来源: WILEY

摘要:

AbstractA multichannel lattice filter structure is utilized to represent seismic waves propagating in adjacent layers in an elastic medium. Using this model, an explicit time‐domain solution for arbitrary source and receiver locations is obtained as an ARMA (AutoRegressive and Moving‐Average) process. The lattice and ARMA structures have given rise to an effective algorithm for the calculation of offset/downhole synthetic seismograms.A large range of recently developed offset/downhole seismic survey geometries, such as the ‘Yo‐Yo’ arrangement, can thus be simulated. In addition, the explicit solutions for upgoing and downgoing waves provide new insight into the properties of general downhole seismic signals, including wave‐mode conversion effects and multiple reflections. Furthermore, offset/downhole seismograms generated by a line source (i.e. 2D point source) can also be constructed by superposition of plane waves with different incidence angles.Synthetic seismograms generated using a different source‐receiver arrangement indicate that the properties especially associated with offset/downhole seismic signals can be predicted by this modelling method. These properties include arrival times, amplitude attenuation and wave‐mode conversion effects. Finally, utilizing this numerical modelling method to a real downhole survey with Yo‐Yo geometry may lead to a proper data acquisition and processing procedure, and improves the interpretation confidence of

ISSN:0016-8025    

DOI:10.1111/j.1365-2478.1990.tb01840.x

出版商:Blackwell Publishing Ltd    

年代:1990

数据来源: WILEY

摘要:

AbstractThis paper describes a field evaluation of an algebraic reconstruction technique for the tomographic imaging of sub‐surface velocity anomalies. We describe the construction of a three‐dimensional concrete model and the acquisition and processing of seismic traveltime data through the model. Image reconstructions of the data sets, using an algebraic reconstruction technique and incorporating prior knowledge are presented and these are compared with the actual model. Reconstructions show that it is essential that accurate data are obtained as we demonstrate that relatively small errors in the traveltime data can seriously degrade the reconstruction. We also show that raypath effects are very important limiting factors to the analy

ISSN:0016-8025    

DOI:10.1111/j.1365-2478.1990.tb01841.x

出版商:Blackwell Publishing Ltd    

年代:1990

数据来源: WILEY

摘要:

AbstractWavefront charts in anisotropic gradient media are a useful tool in ray geometric constructions, particular in shear‐wave exploration. They can be constructed by: (i) a family of wavefronts that contains a vertical plane as member ‐ it is convenient to choose constant time increments; (ii) tracing one ray that makes everywhere the angle with the normal to the wavefront that is required by the anisotropy of the medium; (iii) scaling this ray to obtain a set of rays with different ray parameters; (iv) shifting these rays (with wavefront elements attached) so that they pass through a common source point; (v) interpolating the wavefronts between the elements.The construction is particularly simple inlinear‐gradient media, since here all members of the family of wavefronts are planes. Since the ray makes everywhere the angle prescribed by the anisotropy with the normal of the (plane) wavefronts, the ray has the shape of the slowness curve rotated by −π/2.For isotropic media the slowness curve is a circle, and thus rays are circular arcs. The circles themselves intersect in the source point and in a second point above the surface of the earth. This provides a simple proof that wavefronts emanating from a point source in an isotropic linear‐gradient medium are spheres: inversion of the set of circular rays with the source as centre maps the pencil of circular rays into a pencil of straight lines passing through a point. A pencil of concentric spheres around this point is perpendicular to the pencil of straight lines. On inverting back the pencil of spheres is mapped into another pencil of spheres that is perpendicular to the cir

ISSN:0016-8025    

DOI:10.1111/j.1365-2478.1990.tb01842.x

出版商:Blackwell Publishing Ltd    

年代:1990

数据来源: WILEY