Synthetic vertical seismic profiles for nonnormal incidence plane waves

Geophysics ◽  
1985 ◽  
Vol 50 (1) ◽  
pp. 127-141 ◽  
Author(s):  
F. Aminzadeh ◽  
J. M. Mendel
Keyword(s):  
Simple Procedure ◽  
Plane Waves ◽  
Space Representation ◽  
Elastic Model ◽  
S Wave ◽  
Seismic Profiles ◽  
Vertical Seismic Profiles ◽  
State Space Representation ◽  
Wave Velocities ◽  
Incidence Plane

Vertical seismic profiles (VSPs) are, by definition, recordings of seismic signals (total upgoing and downgoing seismic wave fields) at different depth points, usually at equally spaced intervals [Formula: see text], i = 1, 2, …, I. In a nonnormal incidence (NNI) elastic model, where each layer is described by thickness, density, and P- and S-wave velocities, the mapping between time and depth needed to generate synthetic VSPs is not usually straightforward. In this paper we develop a relatively simple procedure for generating synthetic vertical and horizontal direction plane wave NNI VSPs. No spatial discretization is necessary. We (1) compute two surface seismograms, one vertical and the other horizontal, exactly as described in Aminzadeh and Mendel (1982); and (2) downward continue the surface seismograms to fixed VSP depth points. This paper demonstrates an algorithm for downward continuation of an elastic wave field using state‐space representation and gives simulations which illustrate both z- and x-direction primaries and complete VSPs for different geologic models and different incident angles.

Vertical open fractures and shear‐wave velocities derived from VSPs, full waveform acoustic logs, and televiewer data

Geophysics ◽  
1993 ◽  
Vol 58 (6) ◽  
pp. 818-834 ◽  
Author(s):  
Frédéric Lefeuvre ◽  
Roger Turpening ◽  
Carol Caravana ◽  
Andrea Born ◽  
Laurence Nicoletis
Keyword(s):  
Shear Wave ◽  
Azimuthal Anisotropy ◽  
Stoneley Wave ◽  
Correlation Technique ◽  
Seismic Profiles ◽  
Vertical Seismic Profiles ◽  
Wave Velocities ◽  
Shear Wave Velocities ◽  
Full Waveform ◽  
Zero Offset

Fracture or stress‐related shear‐wave birefringence (or azimuthal anisotropy) from vertical seismic profiles (VSPs) is commonly observed today, but no attempt is made to fit the observations with observed in‐situ fractures and velocities. With data from a hard rock (limestones, dolomites, and anhydrites) region of Michigan, fast and slow shear‐wave velocities have been derived from a nine‐component zero offset VSP and compared to shear‐wave velocities from two full waveform acoustic logs. To represent the shear‐wave birefringence that affects the shear wave’s vertical propagation, a propagator matrix technique is used allowing a local measurement independent of the overburden layers. The picked times obtained by using a correlation technique have been corrected in the birefringent regions before we compute the fast and slow velocities. Although there are some differences between the three velocity sets, there is a good fit between the velocities from the shear‐wave VSP and those from the two logs. We suspect the formations showing birefringence to be vertically fractured. To support this, we examine the behavior of the Stoneley wave on the full waveform acoustic logs in the formations. In addition, we analyze the borehole televiewer data from a nearby well. There is a good fit between the fractures seen from the VSP data and those seen from the borehole.

Twelve years of vertical birefringence in nine‐component VSP data

Geophysics ◽  
2001 ◽  
Vol 66 (2) ◽  
pp. 582-597 ◽  
Author(s):  
Donald F. Winterstein ◽  
Gopa S. De ◽  
Mark A. Meadows
Keyword(s):  
Seismic Data ◽  
Azimuthal Anisotropy ◽  
Vertical Shear ◽  
S Wave ◽  
Seismic Profiles ◽  
Surface Reflection ◽  
Vertical Seismic Profiles ◽  
Reflection Seismic ◽  
San Andreas ◽  
Vsp Data

Since 1986, when industry scientists first publicly showed data supporting the presence of azimuthal anisotropy in sedimentary rock, we have studied vertical shear‐wave (S-wave) birefringence in 23 different wells in western North America. The data were from nine‐component vertical seismic profiles (VSPs) supplemented in recent years with data from wireline crossed‐dipole logs. This paper summarizes our results, including birefringence results in tabular form for 54 depth intervals in 19 of those 23 wells. In the Appendix we present our conclusions about how to record VSP data optimally for study of vertical birefringence. We arrived at four principal conclusions about vertical S-wave birefringence. First, birefringence was common but not universal. Second, birefringence ranged from 0–21%, but values larger than 4% occurred only in shallow formations (<1200 m) within 40 km of California’s San Andreas fault. Third, at large scales birefringence tended to be blocky. That is, both the birefringence magnitude and the S-wave polarization azimuth were often consistent over depth intervals of several tens to hundreds of meters but then changed abruptly, sometimes by large amounts. Birefringence in some instances diminished with depth and in others increased with depth, but in almost every case a layer near the surface was more birefringent than the layer immediately below it. Fourth, observed birefringence patterns generally do not encourage use of multicomponent surface reflection seismic data for finding fractured hydrocarbon reservoirs, but they do encourage use of crossed‐dipole logs to examine them. That is, most reservoirs were birefringent, but none we studied showed increased birefringence confined to the reservoir.

Elastic model low- to intermediate-wavenumber inversion using reflection traveltime and waveform of multicomponent seismic data

Geophysics ◽  
2019 ◽  
Vol 84 (1) ◽  
pp. R109-R123 ◽  
Author(s):  
Wencai Xu ◽  
Tengfei Wang ◽  
Jiubing Cheng
Keyword(s):  
Waveform Inversion ◽  
Elastic Model ◽  
S Wave ◽  
Reflected Waves ◽  
Wave Velocities ◽  
Reflection Data ◽  
Model Background ◽  
Mode Decomposition ◽  
Model Components ◽  
Two Stages

Low-, intermediate-, and high-wavenumber components of P- and S-wave velocities jointly influence the elastic wave propagation and scattering in an isotropic medium. By taking advantage of all information in the data, elastic full-waveform inversion (E-FWI) has the potential to recover these model components. However, if the transmitted wave data are insufficient to illuminate the deeper part of the subsurface, we should rely on the solutions using reflection data. To reduce the nonlinearity of waveform inversion, we choose to decouple the effects of the model background and perturbation on the reflected waves within a linearized inversion framework. This resorts to three stages aiming to gradually fit the traveltimes and waveforms of the reflected PP and PS waves based on data or gradient preconditioning through P/S mode decomposition. For the first two stages, once the multicomponent seismograms have been separated into PP and PS reflection recordings, reflection traveltime inversion using an acoustic wave propagator (A-RTI) can successively recover the low-wavenumber components of P- and S-wave velocities. In the last stage, starting from the models having reliable low-wavenumber components, elastic reflection waveform inversion (E-RWI) can easily get out of the local minima and continue to retrieve the increasing wavenumber features sensitive to the waveform and amplitude variations. This is supported by gradient preconditioning through P/S mode decomposition of the extrapolated normal and adjoint wavefields, and alternately updating model background and high-wavenumber components in terms of linearized least-squares inversion. Numerical examples have demonstrated the performance of our E-RWI approach and the validity of the three-stage inversion workflow.

Efficient FDTD algorithm for plane-wave simulation for vertically heterogeneous attenuative media

Geophysics ◽  
2007 ◽  
Vol 72 (4) ◽  
pp. H43-H53 ◽  
Author(s):  
Arash JafarGandomi ◽  
Hiroshi Takenaka
Keyword(s):  
Wave Equation ◽  
Finite Difference ◽  
Plane Wave ◽  
Wave Equations ◽  
Plane Waves ◽  
Computation Time ◽  
Staggered Grid ◽  
Seismic Profiles ◽  
Vertical Seismic Profiles ◽  
Incident Waves

We propose an efficient algorithm for modeling seismic plane-wave propagation in vertically heterogeneous viscoelastic media using a finite-difference time-domain (FDTD) technique. In the algorithm, the wave equation is rewritten for plane waves by applying a Radon transform to the 2D general wave equation. Arbitrary values of the quality factor for [Formula: see text]- and [Formula: see text]-waves ([Formula: see text] and [Formula: see text]) are incorporated into the wave equation via a generalized Zener body rheological model. An FDTD staggered-grid technique is used to numerically solve the derived plane-wave equations. The scheme uses a 1D grid that reduces computation time and memory requirements significantly more than corresponding 2D or 3D computations. Comparing the finite-difference solutions to their corresponding analytical results, we find that the methods are sufficiently accurate. The proposed algorithm is able to calculate synthetic waveforms efficiently and represent viscoelastic attenuation even in very attenuative media. The technique is then used to estimate the plane-wave responses of a sedimentary system to normal and inclined incident waves in the Kanto area of Japan via synthetic vertical seismic profiles.

Propagation and Reflection of Plane Waves in a Rotating Magneto-Elastic Fibre-Reinforced Semi Space with Surface Stress

2020 ◽  
Vol 22 (4) ◽  
pp. 939-958
Author(s):  
Indrajit Roy ◽  
D. P. Acharya ◽  
Sourav Acharya
Keyword(s):  
Surface Stress ◽  
Incident Angle ◽  
Plane Waves ◽  
Three Dimensional ◽  
Elastic Fibre ◽  
Amplitude Ratios ◽  
Governing Equations ◽  
Rotation Surface ◽  
Wave Velocities ◽  
Magnetic Field Rotation

AbstractThe present paper investigates the propagation of quasi longitudinal (qLD) and quasi transverse (qTD) waves in a magneto elastic fibre-reinforced rotating semi-infinite medium. Reflections of waves from the flat boundary with surface stress have been studied in details. The governing equations have been used to obtain the polynomial characteristic equation from which qLD and qTD wave velocities are found. It is observed that both the wave velocities depend upon the incident angle. After imposing the appropriate boundary conditions including surface stress the resultant amplitude ratios for the total displacements have been obtained. Numerically simulated results have been depicted graphically by displaying two and three dimensional graphs to highlight the influence of magnetic field, rotation, surface stress and fibre-reinforcing nature of the material medium on the propagation and reflection of plane waves.

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