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.

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.

scholarly journals Pressure in a fluid‐filled borehole caused by a seismic source in stratified media

Geophysics ◽  
1996 ◽  
Vol 61 (1) ◽  
pp. 43-55 ◽  
Author(s):  
Chengbin Peng ◽  
Jung M. Lee ◽  
M. Nafi Toksöz
Keyword(s):  
Field Measurements ◽  
Seismic Source ◽  
P Wave ◽  
Stratified Medium ◽  
Stratified Media ◽  
Coupling Theory ◽  
Seismic Profiles ◽  
Matrix Formulation ◽  
Vertical Seismic Profiles ◽  
Vsp Data

A method for numerically simulating hydrophone vertical seismic profiles (VSP) and crosswell data measured in a fluid‐filled borehole (either open or cased) embedded in stratified media is presented. The method makes use of both the borehole coupling theory and the global matrix formulation for computing synthetic seismograms in a stratified medium. The global matrix formulation is used to calculate the stress field at the borehole location. Borehole coupling theory is then employed to obtain the pressure in the borehole fluid. Comparisons with exact solutions for an open borehole in a homogeneous and unbounded formation show that this method is accurate for frequencies below 2 kHz. This method is used to model the Kent Cliffs hydrophone VSP data, where good agreement between the numerical simulations and the field measurements has been found, in both traveltimes and rms amplitudes of the direct P‐wave. Examples show that this method is efficient and accurate, and can be applied to model VSP and crosswell experiments using an array of hydrophones.

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.

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.

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.

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.

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.

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