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.

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.

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.

Separation of signal and noise applied to vertical seismic profiles

Geophysics ◽  
1988 ◽  
Vol 53 (7) ◽  
pp. 932-946 ◽  
Author(s):  
William S. Harlan
Keyword(s):  
Least Squares ◽  
Earth Model ◽  
Seismic Profiles ◽  
One Dimensional ◽  
Vertical Seismic Profiles ◽  
Probability Densities ◽  
Vsp Data ◽  
Band Limited ◽  
Tube Wave ◽  
Impedance Functions

Inversion of the band‐limited one‐dimensional VSP response is nonunique because impedance functions with very different statistics produce equivalent responses. Least‐squares methods of inversion linearly transform noise and tend to produce impedance functions with a Gaussian distribution of amplitudes. I modify a least‐squares inversion procedure to exclude nonzero impedance derivatives that are significantly influenced by noise. The resulting earth model shows homogeneous intervals unless the data have reliable information to the contrary. The data are modeled with a one‐dimensional wave equation and three invertible functions: acoustic impedance, a source wavelet, and the traces’ amplification. First, a linearized least‐squares inverse perturbs the source function to model the downgoing wave. A relinearized inverse finds perturbations of all three modeling functions to account for first‐order reflections. Further iterations explain higher order reflections. To estimate the reliability of impedance perturbations, each linearized inversion is repeated for pure noise that equals or exceeds the noise in the data. Amplitude histograms are used to estimate probability density functions for the amplitudes of the signal and of the noise in the perturbations. Nonzero impedance derivatives are accepted as reliable if, according to the probability functions, the perturbations contain, with a high probability, only a small amount of noise. For a set of VSP data provided by L’Institut Francais du Petrole, four iterations allowed only a few nonzero impedance derivatives and modeled a recorded VSP as well as did a least‐squares inversion that accepted all proposed perturbations. Estimated probability densities for the remaining signal and noise were used to extract a tube wave that contained little signal.

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.

Determination of anisotropic velocity models from walkaway VSP data acquired in the presence of dip

Geophysics ◽  
1997 ◽  
Vol 62 (3) ◽  
pp. 723-729 ◽  
Author(s):  
Colin M. Sayers
Keyword(s):  
Transversely Isotropic ◽  
Seismic Profile ◽  
Slowness Surface ◽  
Velocity Models ◽  
Receiver Array ◽  
Strike Direction ◽  
Vsp Data ◽  
Walkaway Vsp ◽  
Oriented Parallel

Wide‐aperture walkaway vertical seismic profile (VSP) data acquired through transversely isotropic horizontal layers can be used to determine the P phase‐slowness surface, local to a receiver array in a borehole. In the presence of dip, errors in the slowness surface may occur if the medium is assumed to be layered horizontally. If the acquisition plane is oriented parallel to the dip direction, the derived slowness is too large for sources offset from the well in the down‐dip direction and too small for sources offset from the well in the up‐dip direction. For acquisition parallel to the strike of the layers, the recovery of the P phase‐slowness in the vicinity of the receiver array is excellent. It is therefore preferable to orient the walkaway VSP in the strike direction to estimate the anisotropic parameters of the medium in the vicinity of a receiver array. However, this may not be possible. If the dip direction of all layers has the same azimuth, the variation of walkaway traveltimes with azimuth has a simple form. This allows data from a single walkaway VSP extending both sides of a well to be inverted for the local anisotropic P phase‐slowness surface at the receivers even in the presence of dip. If data are acquired at more than one azimuth, the dip direction can be determined.

Tomographic determination of three‐dimensional seismic velocity structure using well logs, vertical seismic profiles, and surface seismic data

Geophysics ◽  
1987 ◽  
Vol 52 (8) ◽  
pp. 1085-1098 ◽  
Author(s):  
Stephen K. L. Chiu ◽  
Robert R. Stewart
Keyword(s):  
Velocity Structure ◽  
Seismic Velocity ◽  
Random Noise ◽  
Three Dimensional ◽  
Real Data ◽  
Well Logs ◽  
Seismic Profiles ◽  
Vertical Seismic Profiles ◽  
The Earth ◽  
Vsp Data

A tomographic technique (traveltime inversion) has been developed to obtain a two‐ or three‐dimensional velocity structure of the subsurface from well logs, vertical seismic profiles (VSP), and surface seismic measurements. The earth was modeled by continuous curved interfaces (polynomial or sinusoidal series), separating regions of constant velocity or transversely isotropic velocity. Ray tracing for each seismic source‐receiver pair was performed by solving a system of nonlinear equations which satisfy the generalized Snell’s law. Surface‐to‐borehole and surface‐to‐surface rays were included. A damped least‐squares formulation provided the updating of the earth model by minimizing the difference between the traveltimes picked from the real data and calculated traveltimes. Synthetic results indicated the following conclusions. For noise‐free cases, the inversion converged closely from the initial guess to the true model for either surface or VSP data. Adding random noise to the observations and performing the inversion indicated that (1) using surface data alone allows reconstruction of the broad velocity structure but with some inaccuracy; (2) using VSP data alone gives a very accurate but laterally limited velocity structure; and (3) the integration of both data sets produces a more laterally extensive, accurate image of the subsurface. Finally, a field example illustrates the viability of the method to construct a velocity structure from real data.

Transmission‐reflection tomography: Application to reverse VSP data

Geophysics ◽  
1997 ◽  
Vol 62 (3) ◽  
pp. 884-894 ◽  
Author(s):  
Weijian Mao ◽  
Graham W. Stuart
Keyword(s):  
Seismic Profile ◽  
Transmission Tomography ◽  
Data Set ◽  
Lower Velocity ◽  
Surface Reflection ◽  
Reflection Data ◽  
Vsp Data ◽  
Reflection Tomography ◽  
Transmission And Reflection

A multiphase tomographic algorithm is presented that allows 2-D and 3-D slowness (inverse of velocity) and variable reflector depth to be reconstructed simultaneously from both transmission and reflection traveltimes. We analyze the ambiguity in the determination of velocity and depth in transmission and reflection data and realize that depth perturbation is more sensitive to reflection traveltime anomalies than slowness perturbation, whereas the reverse is true of transmission traveltime anomalies. Because of the constraints on velocity and depth provided by the different wave types, this algorithm reduces the ambiguity substantially between velocity and depth prevalent in reflection tomography and also avoids the undetermined problem in transmission tomography. The linearized inversion was undertaken iteratively by decoupling velocity parameters from reflector depths. A rapid 2-D and 3-D ray‐tracing algorithm is used to compute transmission and reflection traveltimes and partial derivatives with respect to slowness and reflector depth. Both depth and velocity are parameterized in terms of cubic B‐spline functions. Synthetic examples indicate the improvement in tomographic results when both transmission and reflection times are included. The method has been applied to a reverse vertical seismic profile (VSP) data set recorded on the British coal measures along a crossed‐linear array. Traveltimes were picked automatically by the simultaneous determination of time delays and stacking weights using a waveform matching technique. The tomographic inversion of the observed reverse VSP images two fault‐zones of lower velocity than the surrounding media. The location of the faults was confirmed by near‐by reflection lines. The technique can be applied to offset VSPs or reverse VSPs and coincident VSP and surface reflection data.

Vertical seismic profiling depth migration of a salt dome flank

Geophysics ◽  
1986 ◽  
Vol 51 (5) ◽  
pp. 1087-1109 ◽  
Author(s):  
N. D. Whitmore ◽  
Larry R. Lines
Keyword(s):  
Data Processing ◽  
Survey Design ◽  
Velocity Model ◽  
Salt Dome ◽  
Velocity Estimation ◽  
Seismic Profiles ◽  
Depth Migration ◽  
Vertical Seismic Profiles ◽  
Interval Velocity ◽  
Vsp Data

Vertical seismic profiles (VSPs) can supply information about both velocity and subsurface interface locations. Properly designed VSPs can be used to map steeply dipping interfaces such as salt dome flanks. Mapping subsurface interfaces with VSP data requires careful survey design, appropriate data processing, interval velocity estimation, and reflector mapping. The first of these four ingredients is satisfied, in most cases, by preacquisition modeling. The second is accomplished by careful data processing. Initial velocity estimates are provided by seismic tomography. Velocity‐model refinement is accomplished by a combination of iterative modeling and iterative least‐squares inversion. Finally, the resultant interval velocities are used in depth migration of the processed VSP. These four ingredients have been combined to map a salt dome flank.

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