Wave‐field transformations of vertical seismic profiles

Geophysics ◽  
1987 ◽  
Vol 52 (3) ◽  
pp. 307-321 ◽  
Author(s):  
Liang‐Zie Hu ◽  
George A. McMechan
Keyword(s):  
Fourier Transform ◽  
Wave Field ◽  
Seismic Profile ◽  
Seismic Profiles ◽  
P Waves ◽  
S Waves ◽  
Vertical Seismic Profiles ◽  
Slice Theorem ◽  
Vsp Data ◽  
T Domain

Vertical seismic profile (VSP) data may be partitioned in a variety of ways by application of wave‐field transformations. These transformations provide insights into the nature of the data and aid in the design of processing operations. Transformations are implemented in a reversible sequence that takes the observed VSP data from the depth‐time (z-t) domain through the slowness‐time intercept (p-τ) domain (by a slant stack), to the slowness‐frequency (p-ω) domain (by a 1-D Fourier transform over τ), to the wavenumber‐frequency (k-ω) domain (by resampling using the Fourier central‐slice theorem), and finally back to the z-t domain (by an inverse 2-D Fourier transform). Multidimensional wave‐field transformations, combined with k-ω, p-ω, and p-τ filtering, can be applied to wave‐field resampling, interpolation, and extrapolation; separation of P-waves and S-waves; separation of upgoing and downgoing waves; and wave‐field decomposition for isolation, identification, and analysis of arrivals.

Multichannel Wiener deconvolution of vertical seismic profiles

Geophysics ◽  
1994 ◽  
Vol 59 (10) ◽  
pp. 1500-1511 ◽  
Author(s):  
Jakob B. U. Haldorsen ◽  
Douglas E. Miller ◽  
John J. Walsh
Keyword(s):  
Least Squares ◽  
Amplitude Spectrum ◽  
Seismic Source ◽  
Seismic Profile ◽  
Signal Spectrum ◽  
Seismic Profiles ◽  
Vertical Seismic Profiles ◽  
Vsp Data ◽  
Zero Offset ◽  
Noise Signature

We describe a technique for performing optimal, least‐squares deconvolution of vertical seismic profile (VSP) data. The method is a two‐step process that involves (1) estimating the source signature and (2) applying a least‐squares optimum deconvolution operator that minimizes the noise not coherent with the source signature estimate. The optimum inverse problem, formulated in the frequency domain, gives as a solution an operator that can be interpreted as a simple inverse to the estimated aligned signature multiplied by semblance across the array. An application to a zero‐offset VSP acquired with a dynamite source shows the effectiveness of the operator in attaining the two conflicting goals of adaptively spiking the effective source signature and minimizing the noise. Signature design for seismic surveys could benefit from observing that the optimum deconvolution operator gives a flat signal spectrum if and only if the seismic source has the same amplitude spectrum as the noise.

Synthetic finite‐offset vertical seismic profiles for laterally varying media

Geophysics ◽  
1985 ◽  
Vol 50 (4) ◽  
pp. 627-636 ◽  
Author(s):  
George A. McMechan
Keyword(s):  
Drill Hole ◽  
Seismic Profile ◽  
Rock Properties ◽  
Seismic Profiles ◽  
One Dimensional ◽  
Vertical Seismic Profiles ◽  
Vsp Data ◽  
Lateral Variations ◽  
Lateral Structure

The analysis of vertical seismic profile (VSP) data is generally directed toward determination of rock properties (such as velocity, impedance, attenuation, and anisotropy) as functions of depth (that is, in a one‐dimensional model). If VSPs are extended to include observations from sources at multiple, finite offsets, then lateral variation in structure near the drill hole can be studied. Synthetic offset VSPs are computed by an acoustic finite‐difference algorithm for two‐dimensional models that include the main types of structural traps. These show that diagnostic lateral variations can be detected and interpreted in VSPs. In a VSP, lateral structure variations may produce changes in the type and number of arrivals, in amplitudes, in time and phase shifts, in interference patterns, in curvature of arrival branches, and in the focusing and defocusing of energy. All of these effects are functions of the positions of the source(s) and receiver(s); numerical modeling is a potentially useful tool for interpretation of VSP data from laterally varying structure.

An analytical solution to separate P‐waves and S‐waves in VSP wavefields

Geophysics ◽  
1995 ◽  
Vol 60 (4) ◽  
pp. 955-967 ◽  
Author(s):  
Hiroshi Amano
Keyword(s):  
Analytical Solution ◽  
Formal Solution ◽  
Seismic Profile ◽  
Synthetic Seismograms ◽  
Third Order ◽  
P Waves ◽  
Practical Applications ◽  
S Waves ◽  
The Third ◽  
Z Domain

An analytical solution to separate P‐waves and S‐waves in vertical seismic profile (VSP) wavefields is derived using combinations of certain terms of the formal solution for forward VSP modeling. Some practical applications of this method to synthetic seismograms and field data are investigated and evaluated. Little wave distortion is recognized, and the weak wavefield masked by dominant wavetrains can be extracted with this method. The decomposed wavefield is expressed in the frequency‐depth (f-z) domain as a linear combination of up to the third‐order differential of traces, which is approximated by trace differences in the practical separation process. In general, five traces with single‐component data are required in this process, but the same process is implemented with only three traces in the acoustic case. Two‐trace extrapolation is applied to each edge of the data gather to enhance the accuracy of trace difference. Since the formulas are developed in the f-z domain, the influence of anelasticity can be taken into account, and the calculation is carried out fast enough with the benefit of the fast Fourier transform (FFT).

Vertical seismic profile migration using the Kirchhoff integral

Geophysics ◽  
1988 ◽  
Vol 53 (6) ◽  
pp. 786-799 ◽  
Author(s):  
P. B. Dillon
Keyword(s):  
Wave Equation ◽  
Wave Field ◽  
Near Field ◽  
Synthetic Data ◽  
Real Data ◽  
Seismic Profile ◽  
Processing Strategies ◽  
Receiver Array ◽  
Vsp Data ◽  
Kirchhoff Integral

Wave‐equation migration can form an accurate image of the subsurface from suitable VSP data. The image’s extent and resolution are determined by the receiver array dimensions and the source location(s). Experiments with synthetic and real data show that the region of reliable image extent is defined by the specular “zone of illumination.” Migration is achieved through wave‐field extrapolation, subject to an imaging procedure. Wave‐field extrapolation is based upon the scalar wave equation and, for VSP data, is conveniently handled by the Kirchhoff integral. The migration of VSP data calls for imaging very close to the borehole, as well as imaging in the far field. This dual requirement is met by retaining the near‐field term of the integral. The complete integral solution is readily controlled by various weighting devices and processing strategies, whose worth is demonstrated on real and synthetic data.

Traveltime inversion of offset vertical seismic profiles—A feasibility study

Geophysics ◽  
1984 ◽  
Vol 49 (3) ◽  
pp. 250-264 ◽  
Author(s):  
L. R. Lines ◽  
A. Bourgeois ◽  
J. D. Covey
Keyword(s):  
Inverse Method ◽  
Synthetic Data ◽  
Real Data ◽  
Seismic Profile ◽  
Inversion Method ◽  
Earth Model ◽  
Seismic Profiles ◽  
Traveltime Inversion ◽  
Vertical Seismic Profiles ◽  
Inversion Techniques

Traveltimes from an offset vertical seismic profile (VSP) are used to estimate subsurface two‐dimensional dip by applying an iterative least‐squares inverse method. Tests on synthetic data demonstrate that inversion techniques are capable of estimating dips in the vicinity of a wellbore by using the traveltimes of the direct arrivals and the primary reflections. The inversion method involves a “layer stripping” approach in which the dips of the shallow layers are estimated before proceeding to estimate deeper dips. Examples demonstrate that the primary reflections become essential whenever the ratio of source offset to layer depth becomes small. Traveltime inversion also requires careful estimation of layer velocities and proper statics corrections. Aside from these difficulties and the ubiquitous nonuniqueness problem, the VSP traveltime inversion was able to produce a valid earth model for tests on a real data case.

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.

Measurements of attenuation from vertical seismic profiles by iterative modeling

Geophysics ◽  
1985 ◽  
Vol 50 (6) ◽  
pp. 931-949 ◽  
Author(s):  
Michel Dietrich ◽  
Michel Bouchon
Keyword(s):  
Velocity Dispersion ◽  
Synthetic Data ◽  
Layered Media ◽  
Spectral Ratio ◽  
Ratio Method ◽  
Seismic Profiles ◽  
Vertical Seismic Profiles ◽  
Anelastic Attenuation ◽  
Vsp Data ◽  
Intrinsic Dissipation

We present a numerical simulation of vertical seismic profiles (VSP) using the discrete horizontal wavenumber representation of seismic wave fields. The theoretical seismograms are computed in the acoustic case for flat layered media, and they include the effects of absorption and velocity dispersion. A study using the synthetic seismograms was conducted to investigate the accuracy and resolution of attenuation measurements from VSP data. It is shown that in finely layered media estimates of the anelastic attenuation obtained by use of the reduced spectral ratio method are usually inaccurate when the attenuation is measured over a small vertical extent. An iterative method is presented which improves the resolution of the measurements of intrinsic dissipation. This method allows determination for synthetic data of the quality factor over depth intervals of about one wavelength of the dominant seismic frequency.

Estimation of the discrete Fourier transform, a linear inversion approach

Geophysics ◽  
1996 ◽  
Vol 61 (4) ◽  
pp. 1128-1136 ◽  
Author(s):  
Mauricio D. Sacchi ◽  
Tadeusz J. Ulrych
Keyword(s):  
Fourier Transform ◽  
Array Processing ◽  
Broad Band ◽  
Temporal Analysis ◽  
Seismic Profile ◽  
Spectral Signature ◽  
Seismic Profiles ◽  
Linear Inversion ◽  
Spatial Coverage ◽  
Spatio Temporal

Spatio‐temporal analysis of seismic records is of particular relevance in many geophysical applications, e.g., vertical seismic profiles, plane‐wave slowness estimation in seismographic array processing and in sonar array processing. The goal is to estimate from a limited number of receivers the 2-D spectral signature of a group of events that are recorded on a linear array of receivers. When the spatial coverage of the array is small, conventional f-k analysis based on Fourier transform leads to f-k panels that are dominated by sidelobes. An algorithm that uses a Bayesian approach to design an artifacts‐reduced Fourier transform has been developed to overcome this shortcoming. A by‐product of the method is a high‐resolution periodogram. This extrapolation gives the periodogram that would have been recorded with a longer array of receivers if the data were a limited superposition of monochromatic planes waves. The technique is useful in array processing for two reasons. First, it provides spatial extrapolation of the array (subject to the above data assumption) and second, missing receivers within and outside the aperture are treated as unknowns rather than as zeros. The performance of the technique is illustrated with synthetic examples for both broad‐band and narrow‐band data. Finally, the applicability of the procedure is assessed analyzing the f-k spectral signature of a vertical seismic profile (VSP).

Calculation of zero-offset vertical seismic profiles generated by a horizontal point force acting on the surface of an anelastic half-space

1990 ◽  
Vol 80 (4) ◽  
pp. 832-856
Author(s):  
Hsi-Ping Liu
Keyword(s):  
Fourier Transform ◽  
Half Space ◽  
Impulse Response ◽  
Point Force ◽  
Seismic Profiles ◽  
Elementary Functions ◽  
Near Surface ◽  
Vertical Seismic Profiles ◽  
Zero Offset ◽  
The Fourier Transform

Abstract Impulse responses including near-field terms have been obtained in closed form for the zero-offset vertical seismic profiles generated by a horizontal point force acting on the surface of an anelastic half-space. The method is based on the correspondence principle. Through transformation of variables, the Fourier transform of the elastic impulse response is put in a form such that the Fourier transform of the corresponding anelastic impulse response can be expressed as elementary functions and their definite integrals involving distance, angular frequency, phase velocities, and attenuation factors. These results are used for accurate calculation of shear-wave arrival rise times of synthetic seismograms needed for data interpretation of anelastic-attenuation measurements in near-surface sediment.

Sign in / Sign up

Export Citation Format

Share Document