Interpretation of borehole sonic measurements acquired in vertical transversely isotropic formations penetrated by vertical wells

Geophysics ◽  
2018 ◽  
Vol 83 (6) ◽  
pp. D187-D202 ◽  
Author(s):  
Elsa Maalouf ◽  
Carlos Torres-Verdín
Keyword(s):  
Transversely Isotropic ◽  
Depth Interval ◽  
Bias Error ◽  
Layer By Layer ◽  
Spatial Averaging ◽  
Vertical Wells ◽  
Frequency Dependent ◽  
Sensitivity Functions ◽  
Stiffness Coefficients ◽  
Sonic Logs

Detecting vertical transversely isotropic (VTI) formations and quantifying the magnitude of anisotropy are fundamental for describing organic mudrocks. Methods used to estimate stiffness coefficients of VTI formations often provide discontinuous or spatially averaged results over depth intervals where formation layers are thinner than the receiver aperture of acoustic tools. We have developed an inversion-based method to estimate stiffness coefficients of VTI formations that are continuous over the examined depth interval and that are mitigated for spatial averaging effects. To estimate the coefficients, we use logs of frequency-dependent compressional, Stoneley, and quadrupole/flexural modes measured with wireline or logging-while-drilling (LWD) instruments in vertical wells penetrating horizontal layers. First, we calculate the axial sensitivity functions of borehole sonic modes to stiffness coefficients; next, we use the sensitivity functions to estimate the stiffness coefficients of VTI layers sequentially from frequency-dependent borehole sonic logs. Because sonic logs exhibit spatial averaging effects, we deaverage the logs by calculating layer-by-layer slownesses of formations prior to estimating stiffness coefficients. The method is verified with synthetic models of homogeneous and thinly bedded formations constructed from field examples of organic mudrocks. Results consist of layer-by-layer estimates of [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text]. We observe three sources of error in the estimated coefficients: (1) bias error originating from deaveraging the sonic logs prior to the sequential inversion, (2) error propagated during the sequential inversion, and (3) error associated with noisy slowness logs. We found that the relative bias and uncertainty of the estimated coefficients are largest for [Formula: see text] and [Formula: see text] because borehole modes exhibit low sensitivity to these two coefficients. The main advantage of our method is that it mitigates spatial averaging effects of sonic logs, while at the same time it detects the presence of anisotropic layers and yields continuous estimations of stiffness coefficients along the depth interval of interest.

Inversion-based method to mitigate noise in borehole sonic logs

Geophysics ◽  
2018 ◽  
Vol 83 (2) ◽  
pp. D61-D71 ◽  
Author(s):  
Elsa Maalouf ◽  
Carlos Torres-Verdín
Keyword(s):  
Effective Medium Theory ◽  
Joint Inversion ◽  
Seismic Inversion ◽  
Sampling Interval ◽  
In Situ Stress ◽  
Processing Unit ◽  
Layer By Layer ◽  
Spatial Averaging ◽  
Central Processing ◽  
Sonic Logs

A major challenge in the interpretation of seismic measurements and sonic logs is the presence of deleterious noise that impacts the quality and reliability of the estimated seismic wavelets and seismic inversion products. Spatial averaging effects and borehole drilling damage can also bias the estimation of in situ stress and elastic properties from sonic logs. We have developed an inversion-based method to mitigate processing errors, spatial averaging effects, and borehole environmental noise on sonic logs, which does not require arbitrary numerical filters, effective-medium theory models, or time-consuming waveform reprocessing. The inversion-based method estimates layer-by-layer slownesses via joint inversion of shear and compressional logs measured in a vertical well, and it uses the estimated slownesses of the assumed horizontal layers to model noise-mitigated sonic logs. By making use of geometric and physical constraints for noise reduction implicit in the inversion-based method, we obtain sonic logs that more accurately reflect the physical properties of rock formations penetrated by wells. Sonic logs are efficiently modeled by invoking axial sensitivity functions. First, we test the inversion-based method with synthetic sonic logs contaminated with noise. Estimated layer-by-layer slownesses agree with those of the original model within a standard deviation of [Formula: see text], while effectively reducing the numerical noise included in the input measurements. When bed-boundary locations are unknown, we perform the inversion-based method by assuming bed boundaries uniformly spaced at the same sampling interval of sonic logs; in this case, although the accuracy of the estimated layer slownesses decreases, the noise on sonic logs decreases. Then, we apply the method to sonic logs acquired in the North Sea and estimate angle reflectivity from the noise-mitigated logs. Results verify the reliability of the inversion-based method to reduce biases in the calculated angle reflectivity within a few minutes of central processing unit time.

Low-frequency layer-induced kinematic parameters in transversely isotropic media and orthorhombic media

2019 ◽  
Vol 220 (2) ◽  
pp. 839-855
Author(s):  
Da Shuai ◽  
Alexey Stovas
Keyword(s):  
Volume Fraction ◽  
Velocity Ratio ◽  
Symmetry Plane ◽  
Low Frequency ◽  
Transversely Isotropic ◽  
Kinematic Parameters ◽  
Frequency Dependent ◽  
Cross Term ◽  
Transversely Isotropic Media ◽  
Isotropic Media

SUMMARY We develop a method to compute frequency-dependent kinematic parameters for an effective orthorhombic (ORT) medium. In order to investigate the influence of fracture weaknesses on the kinematic parameters, the effective ORT medium is composed based on the linear slip theory and derived by applying the limited Baker–Campbell–Hausdorff series. The frequency-dependent kinematic parameters including vertical velocity, two normal moveout velocities defined in vertical symmetry planes, and three anelliptic parameters (two of them are defined in vertical symmetry plane and one parameter is the cross-term one). We also investigate the influence of volume fraction, frequency, velocity ratio and fracture weaknesses on the effective kinematic parameters.

scholarly journals Precise inversion of logged slownesses for elastic parameters in a gas shale formation

Geophysics ◽  
2012 ◽  
Vol 77 (4) ◽  
pp. B197-B206 ◽  
Author(s):  
Douglas E. Miller ◽  
Steve A. Horne ◽  
John Walsh
Keyword(s):  
Inclination Angle ◽  
Vertical Direction ◽  
Transversely Isotropic ◽  
Gas Shale ◽  
Elastic Parameters ◽  
Associated Production ◽  
Sonic Log ◽  
Inclination Angles ◽  
Shale Formation ◽  
Sonic Logs

Dipole sonic log data recorded in a vertical pilot well and the associated production well are analyzed over a [Formula: see text]-ft section of a North American gas shale formation. The combination of these two wells enables angular sampling in the vertical direction and over a range of inclination angles from 54° to 90°. Dipole sonic logs from these wells show that the formation’s average properties are, to a very good approximation, explained by a transversely isotropic medium with a vertical symmetry axis and with elastic parameters satisfying [Formula: see text], but inconsistent with the additional ANNIE relation ([Formula: see text]). More importantly, these data clearly show that, at least for fast anisotropic formations such as this gas shale, sonic logs measure group slownesses for propagation with the group angle equal to the borehole inclination angle. Conversely, the data are inconsistent with an interpretation that they measure phase slownesses for propagation with the phase angle equal to the borehole inclination angle.

Petrophysical inversion of borehole array-induction logs: Part II — Field data examples

Geophysics ◽  
2006 ◽  
Vol 71 (5) ◽  
pp. G261-G268 ◽  
Author(s):  
Carlos Torres-Verdín ◽  
Faruk O. Alpak ◽  
Tarek M. Habashy
Keyword(s):  
Electromagnetic Induction ◽  
Layer By Layer ◽  
Laboratory Measurements ◽  
Inversion Algorithm ◽  
Vertical Wells ◽  
Gas Field ◽  
Rock Formations ◽  
Resistivity Logs ◽  
Porosity And Permeability ◽  
Induction Logs

We describe the application of Alpak et al.’s (2006) petrophysical inversion algorithm to the interpretation of borehole array induction logs acquired in an active North American gas field. Layer-by-layer values of porosity and permeability were estimated in two closely spaced vertical wells that penetrated the same horizontal rock formation. The wells were drilled with different muds and overbalance pressures, and the corresponding electromagnetic induction logs were acquired with different tools. Rock-core laboratory measurements available in one of the two wells were used to constrain the efficiency of gas displacement by water-based mud during the process of invasion. Estimated values of porosity and permeability agree well with measurements performed on rock-core samples. In addition to estimating porosity and permeability, the petrophysical inversion algorithm provided accurate spatial distributions of gas saturation in the invaded rock formations that were not possible to obtain with conventional procedures based solely on the use of density and resistivity logs.

scholarly journals Estimation of the Elasticity Modulus of Composite Electroplated Coatings during Their Layer-by-Layer Deposition

2021 ◽  
Vol 31 (3) ◽  
pp. 430-448
Author(s):  
Sergey Yu. Zhachkin ◽  
Anatoliy I. Zavrazhnov ◽  
Nikita A. Penkov ◽  
Alexei V. Martynov ◽  
Roman N. Zadorozhny
Keyword(s):  
Elasticity Modulus ◽  
Friction Pair ◽  
Composite Coatings ◽  
Multilayer Coating ◽  
Point Of View ◽  
Practical Significance ◽  
Complete Agreement ◽  
Layer By Layer ◽  
Stiffness Coefficients ◽  
Operation Conditions

Introduction. To keep automobiles and tractors in operation conditions, it is necessary to restore the inner cylindrical surfaces of the friction pair parts. This is the most laborintensive activity. The method of electroplated contact deposition of composite coatings, based on elastic plastic deformation of formed layers, is used for repairing surfaces. To use this method it is necessary to determine the values of the elasticity modulus, on which the wear resistance of tribocouplings depends. Materials and Methods. For the study, cylindrical samples made of 30 HGSA and 30 HGSNA steels were used. Electrolyte containing 200–250 g/l chromium oxide, 2.0–2.5 g/l sulfuric acid, and distilled water was used for electroplating the coatings. When calculating the stress-strain state, the apparatus of continuum mechanics was used. Results. The dependence of the coating pliability as a function of the parameters of individual elementary layers is determined. When the multilayer coating of three types (orthogonal-reinforced, cross-reinforced and quasi-isotropic) is applied, its structure does not depend on the angles of kinematic tool movement on the inner cylindrical surface of the part. For each type of coatings, the way to determine the constant stiffness coefficients of the layers is specified. The dependences for calculating the elasticity modulus of the applied material are derived from the values of the stiffness coefficients. Discussion and Conclusion. In determining the modulus of elasticity of multilayered composite coatings, the calculation is made for the individual layers by passing to the convective coordinates, which is in complete agreement with the Lagrange point of view on the study of the motion of a continuous medium. The results obtained are of practical significance in the selection of the coating material to be applied for the restoration of internal cylindrical surfaces.

Inversion of P-wave VSP data for local anisotropy: Theory and case study

Geophysics ◽  
2007 ◽  
Vol 72 (4) ◽  
pp. D69-D79 ◽  
Author(s):  
Vladimir Grechka ◽  
Albena Mateeva
Keyword(s):  
Wave Velocity ◽  
Transversely Isotropic ◽  
P Wave ◽  
Depth Interval ◽  
Clear Correlation ◽  
S Wave ◽  
Local Anisotropy ◽  
Data Set ◽  
Rock Formations ◽  
Vsp Data

We discuss, improve, and apply the slowness-polarization method for estimating local anisotropy from VSP data. Although the idea of fitting a given anisotropic model to the apparent slownesses measured along a well and polarization vectors recorded by three-component downhole geophones is hardly new, we extend the area of applicability of the technique and make the anisotropic inversion more robust by eliminating the most operationally difficult and noisy portion of the data, the shear waves. We show that the shear-wave velocity is actually unnecessary for fitting the slowness-of-polarization dependence of P-wave VSP data. For the most common geometry of a vertical borehole in a vertically transversely isotropic subsurface, such data are governed by the P-wave vertical velocity [Formula: see text] and two quantities, [Formula: see text] and [Formula: see text], that describe the influence of anisotropy. These quantities depend on conventional anisotropic coefficients [Formula: see text] and [Formula: see text] and absorb the S-wave velocity. We apply the developed theory to a 2D walkaway VSP acquired over a subsalt prospect in the Gulf of Mexico. Our data set contains geophones placed both inside the salt and beneath it, allowing us to estimate the anisotropy of different rock formations. We find the salt to be nearly isotropic in the examined [Formula: see text] [Formula: see text] depth interval. In contrast, the sediments below the salt exhibit substantial anisotropy. While the physical origins of subsalt anisotropy are still to be fully understood, we observe a clear correlation between lithology and the values of [Formula: see text] and [Formula: see text]: both anisotropic coefficients are greater in shales and smaller in the sandier portion of the well.

scholarly journals Impact of poroelastic effects on the inversion of fracture properties from amplitude variation with offset and azimuth data in horizontal transversely isotropic media

Geophysics ◽  
2020 ◽  
Vol 85 (5) ◽  
pp. N27-N39
Author(s):  
Nicolás D. Barbosa ◽  
Corinna Köpke ◽  
Eva Caspari ◽  
J. Germán Rubino ◽  
James Irving ◽  
...  
Keyword(s):  
Volume Fraction ◽  
Transversely Isotropic ◽  
Single Frequency ◽  
Amplitude Variation ◽  
Frequency Dependent ◽  
Seismic Reflection Data ◽  
Amplitude Variation With Offset ◽  
Transversely Isotropic Media ◽  
Isotropic Media ◽  
Wave Induced

The identification and characterization of fractures is an important objective in many areas of earth and environmental sciences. Amplitude variation with offset and azimuth (AVOAz) analysis of seismic reflection data is a key method for achieving these tasks. Theoretical and experimental studies have shown that the presence of pore fluids together with the strong mechanical contrast between the fractures and their embedding background give rise to wave-induced fluid flow (WIFF) effects. This implies that the effective stiffness tensor of a fluid-saturated fractured rock defining its seismic response becomes viscoelastic and frequency-dependent. In spite of this, AVOAz analysis typically relies on end-member-type elastic stiffness models that either assume a relaxed (i.e., equilibrated) or unrelaxed (i.e., unequilibrated) state of the wave-induced fluid pressure in the rock. In general, however, neither the appropriateness of the chosen model nor the associated errors in the inversion process are known. To investigate this topic, we have considered a poroelastic medium containing parallel vertical fractures and generate synthetic seismic AVOAz data using the classic Rüger approximations for PP-wave reflection coefficients in horizontally transversely isotropic media. A Markov chain Monte Carlo method is used to perform a Bayesian inversion of the synthetic seismic AVOAz data. We quantify the influence of WIFF effects on the AVOAz inversion results when elastic relaxed and unrelaxed models are used as forward solvers of inversion schemes to estimate the fracture volume fraction, the elastic moduli, and the porosity of the background rock, as well as the overall weakness of the medium due to the presence of fractures. Our results indicate that, when dealing with single-frequency data, relaxed elastic models provide biased but overall better inversion results than unrelaxed ones, for which some fracture parameters cannot be resolved. Improved inversion performance is achieved when using frequency-dependent data, which illustrates the importance of accounting for poroelastic effects.

3D P-wave traveltime computation in transversely isotropic media using layer-by-layer wavefront marching

2018 ◽  
Vol 66 (7) ◽  
pp. 1303-1314
Author(s):  
Jiangtao Hu ◽  
Junxing Cao ◽  
Huazhong Wang ◽  
Xingjian Wang ◽  
Renfei Tian
Keyword(s):  
Transversely Isotropic ◽  
P Wave ◽  
Layer By Layer ◽  
Transversely Isotropic Media ◽  
Isotropic Media

SEISMIC WAVE ATTENUATION IN NONRESOLVABLE CYCLIC STRATIFICATION

Geophysics ◽  
1977 ◽  
Vol 42 (5) ◽  
pp. 939-949 ◽  
Author(s):  
T. W. Spencer ◽  
C. M. Edwards ◽  
J. R. Sonnad
Keyword(s):  
Frequency Band ◽  
Seismic Wave ◽  
Linear Dependence ◽  
Wave Attenuation ◽  
Seismic Exploration ◽  
Reflection Coefficients ◽  
Seismic Wave Attenuation ◽  
Frequency Dependent ◽  
Sonic Logs

Situations arise in seismic exploration in which thick zones generate no well‐defined reflection events even though the sonic logs exhibit significant velocity stratification. In many cases, reflections are not generated because the stratification is so fine that it cannot be resolved by the seismic frequency band. Nonresolvable sections in which the impedance structure is cyclic in character, such as sand‐shale sequences, are shown to exhibit frequency dependent attenuation which differs from the linear dependence commonly attributed to absorption. This difference may be exploited to separate the absorptive and stratigraphic components of attenuation and to compare their relative magnitudes. Only in depth intervals in which the reflection coefficients are unusually large can stratigraphic attenuation account for observed attenuation of the order of a few tenths of a decibel per hundred feet. Relations are derived for determining the effect on the stratigraphic attenuation of scaling the parameters which characterize the section.

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