Numerical analysis of near‐borehole and anisotropeic layer effects on the response of multicomponent induction logging tools

Geophysics ◽  
2004 ◽  
Vol 69 (1) ◽  
pp. 140-151 ◽  
Author(s):  
Michael J. Tompkins ◽  
David L. Alumbaugh ◽  
Darrell T. Stanley ◽  
Xinyou Lu
Keyword(s):  
Transversely Isotropic ◽  
Sensitivity Analyses ◽  
Measurable Effect ◽  
Tool Orientation ◽  
Induction Logging ◽  
Anisotropic Layers ◽  
Dip Angle ◽  
Multicomponent Data ◽  
Insight Into ◽  
Formation Dip Angle

We present finite‐difference simulation results that lend new insight into the behavior of multicomponent induction logging tools when in the presence of anisotropic layers, boreholes, and invasion zones. We use four independent models to investigate multicomponent tool properties as well as typical magnetic field responses. In addition, model variations with respect to formation dip angle, layer geometry, and conductivity provide data about the effects of geological variation on the multicomponent responses. Simulations suggest a coaxial tool configuration senses a depth of twice the source–receiver offset, although this depth is reduced to the source–receiver offset with coplanar configurations. Numerical responses in the presence of transversely isotropic layers provide evidence that anisotropy can have a measurable effect on both coaxial and coplanar magnetic fields; these effects increase as layer dip increases. Sensitivity analyses substantiate these numerical results. An investigation of tool responses to varying borehole and invasion zone conductivities and diameters demonstrates that the coplanar tool orientation is much more sensitive to near‐borehole variations than the coaxial configuration. A frequency‐differencing technique is presented to mitigate unwanted borehole‐induced bias in multicomponent data; however, drawbacks include decreased signal strength and possible geological signal destruction.

Stacking-velocity tomography for tilted orthorhombic media

Geophysics ◽  
2019 ◽  
Vol 84 (3) ◽  
pp. C171-C180 ◽  
Author(s):  
Qifan Liu ◽  
Ilya Tsvankin
Keyword(s):  
Parameter Estimation ◽  
Subsurface Layer ◽  
Synthetic Data ◽  
Transversely Isotropic ◽  
P Waves ◽  
Additional Information ◽  
Reflection Data ◽  
Anisotropic Layers ◽  
Zero Offset ◽  
Velocity Tomography

Tilted orthorhombic (TOR) models are typical for dipping anisotropic layers, such as fractured shales, and can also be due to nonhydrostatic stress fields. Velocity analysis for TOR media, however, is complicated by the large number of independent parameters. Using multicomponent wide-azimuth reflection data, we develop stacking-velocity tomography to estimate the interval parameters of TOR media composed of homogeneous layers separated by plane dipping interfaces. The normal-moveout (NMO) ellipses, zero-offset traveltimes, and reflection time slopes of P-waves and split S-waves ([Formula: see text] and [Formula: see text]) are used to invert for the interval TOR parameters including the orientation of the symmetry planes. We show that the inversion can be facilitated by assuming that the reflector coincides with one of the symmetry planes, which is a common geologic constraint often employed for tilted transversely isotropic media. This constraint makes the inversion for a single TOR layer feasible even when the initial model is purely isotropic. If the dip plane is also aligned with one of the symmetry planes, we show that the inverse problem for [Formula: see text]-, [Formula: see text]-, and [Formula: see text]-waves can be solved analytically. When only [Formula: see text]-wave data are available, parameter estimation requires combining NMO ellipses from a horizontal and dipping interface. Because of the increase in the number of independent measurements for layered TOR media, constraining the reflector orientation is required only for the subsurface layer. However, the inversion results generally deteriorate with depth because of error accumulation. Using tests on synthetic data, we demonstrate that additional information such as knowledge of the vertical velocities (which may be available from check shots or well logs) and the constraint on the reflector orientation can significantly improve the accuracy and stability of interval parameter estimation.

scholarly journals Frequency domain multiparameter acoustic inversion for transversely isotropic media with a vertical axis of symmetry

Geophysics ◽  
2019 ◽  
Vol 84 (1) ◽  
pp. C1-C14 ◽  
Author(s):  
Ramzi Djebbi ◽  
Tariq Alkhalifah
Keyword(s):  
Frequency Domain ◽  
Transversely Isotropic ◽  
Vertical Axis ◽  
The Other ◽  
Sensitivity Analyses ◽  
Data Set ◽  
Trade Off ◽  
Transversely Isotropic Media ◽  
Isotropic Media ◽  
Axis Of Symmetry

Multiparameter full-waveform inversion for transversely isotropic media with a vertical axis of symmetry (VTI) suffers from the trade-off between the parameters. The trade-off results in the leakage of one parameter’s update into the other. It affects the accuracy and convergence of the inversion. The sensitivity analyses suggested a parameterization using the horizontal velocity [Formula: see text], Thomsen’s parameter [Formula: see text], and the anelliptic parameter [Formula: see text] to reduce the trade-off for surface recorded seismic data. We aim to invert for this parameterization using the scattering integral (SI) method. The available Born sensitivity kernels, within this approach, can be used to calculate additional inversion information. We mainly compute the diagonal of the approximate Hessian, used as a conjugate-gradient preconditioner, and the gradients’ step lengths. We consider modeling in the frequency domain. The large computational cost of the SI method can be avoided with direct Helmholtz equation solvers. We applied our method to the VTI Marmousi II model for various inversion strategies. We found that we can invert the [Formula: see text] accurately. For the [Formula: see text] parameter, only the short wavelengths are well-recovered. On the other hand, the [Formula: see text] parameter impact is weak on the inversion results and can be fixed. However, a good background [Formula: see text], with accurate long wavelengths, is needed to correctly invert for [Formula: see text]. Furthermore, we invert a real data set acquired by CGG from offshore Australia. We simultaneously invert all three parameters using our inversion approach. The velocity model is improved, and additional layers are recovered. We confirm the accuracy of the results by comparing them with well-log information, as well as looking at the data and angle gathers.

A weak-anisotropy approximation to multicomponent induction responses in cross-bedded formations

Geophysics ◽  
2006 ◽  
Vol 71 (4) ◽  
pp. F61-F66 ◽  
Author(s):  
Tsili Wang
Keyword(s):  
Apparent Resistivity ◽  
Transversely Isotropic ◽  
Anisotropy Ratio ◽  
Weak Anisotropy ◽  
Bedding Planes ◽  
Geometric Average ◽  
Induction Logging ◽  
Anisotropic Formation ◽  
The Cross

The multicomponent induction logging response to a cross-bedded formation has been modeled under a weak-anisotropy approximation. With the approximation, a cross-bedded formation can be modeled as a transversely isotropic (TI) medium. The validity of the approximation has been tested for the main (coplanar and coaxial) components of the induction response. The conditions for the weak-anisotropy approximation to be valid depend on the component of the response. For the coplanar components, the approximation is valid for an anisotropy ratio up to 2 if the relative dipping angle between the cross-bedded formation and the borehole axis is below [Formula: see text]. For the coaxial component, the approximation reduces to a previously established result that the apparent resistivity for such a component is the geometric average of the resistivities, parallel and perpendicular to the bedding planes of an anisotropic formation, respectively, if the borehole is ignored. Hence, the approximation holds for the coaxial component regardless of the anisotropy ratio.

Interpretation of synthetic common‐depth‐point gathers for a single anisotropic layer

Geophysics ◽  
1982 ◽  
Vol 47 (3) ◽  
pp. 323-335 ◽  
Author(s):  
Stuart Crampin ◽  
Barbara J. Radovich
Keyword(s):  
Angular Velocity ◽  
Elastic Constants ◽  
Arrival Time ◽  
Transversely Isotropic ◽  
Orthorhombic Symmetry ◽  
Isotropic Layer ◽  
Anisotropic Layer ◽  
Wide Range ◽  
Velocity Variations ◽  
Anisotropic Layers

Analysis of synthetic traveltime gathers shows that anisotropy may have a large enough effect on P, SH, and SV propagation to alter significantly the interpretation of the subsurface below the anisotropic layers. Consequently, if anisotropy exists below a seismic line, it is important to estimate the anisotropic parameters correctly. We discuss the effects of anisotropy on seismic waves and present a method for estimating the elastic constants of a transversely isotropic layer from P and SH arrival‐time gathers. The technique may be extended to more general anisotropic symmetries by analyzing gathers from several azimuths. To illustrate the possible effect of anisotropy on exploration surveys, P, SH, and SV velocity variations are calculated for several types of anisotropic sedimentary fabrics. Alignments due to bedding, shale lithology, and dry parallel cracks may have similar velocity variations. Fabrics with other configurations of cracks may still possess overall transversely isotropic symmetry, but they have a wide range of angular velocity variations with different polarities and periodicities. Synthetic gather curves are generated for a range of models with an anisotropic layer over an isotropic substrate. They show departures from hyperbolas, and erroneous depth determinations, that depend upon the elastic constants of the anisotropic layer. The elastic constants of the anisotropic layers are estimated from the synthetic gather curves by means of approximate equations for the angular velocity variations, which are linear in the elastic constants. Formulas are developed which relate tangents to the gather curves directly in terms of the elastic constants. These are tested for single‐layer transversely isotropic models and allow the five elastic constants to be estimated by drawing three tangents to P and SH synthetic arrival‐time gathers in [Formula: see text] space. Comparisons of estimated with original elastic constants are good for a number of different types of transversely isotropic fabrics. Gathers are also calculated at two azimuths in an anisotropic layer with orthorhombic symmetry and are analyzed with some success.

Determination of relative angles and anisotropic resistivity using multicomponent induction logging data

Geophysics ◽  
2004 ◽  
Vol 69 (4) ◽  
pp. 898-908 ◽  
Author(s):  
Zhiyi Zhang ◽  
Liming Yu ◽  
Berthold Kriegshäuser ◽  
Lev Tabarovsky
Keyword(s):  
Sensitivity Analysis ◽  
Azimuth Angle ◽  
Inversion Method ◽  
Inversion Algorithm ◽  
Data Set ◽  
Simultaneous Inversion ◽  
Induction Logging ◽  
Em Induction ◽  
Whole Space ◽  
Dip Angle

We have developed a new algorithm that retrieves information about relative dip angle, relative azimuth angle, vertical resistivity, and horizontal resistivity from multicomponent EM induction logging data. To investigate how relative dip and azimuth angles affect multicomponent induction logging data, we performed a sensitivity analysis using an anisotropic whole space model. Based upon the sensitivity analysis, we designed a two‐step procedure to recover relative dip, relative azimuth, horizontal resistivity, and vertical resistivity. In the first step, the observed data are transformed into a new data set independent of the azimuth angle; a simultaneous inversion method recovers relative dip angle, vertical resistivity, and horizontal resistivity. In the second step, a 1D line search is performed to decide relative azimuth angle. Synthetic and field data tests indicate that the new inversion algorithm can extract information about relative dip and azimuth angles as well as the anisotropic resistivity structure from multicomponent induction loggingdata.

scholarly journals Insight into intraindividual variability across neuropsychological tests and its association with cognitive dysfunction in patients with lupus

2021 ◽  
Vol 8 (1) ◽  
pp. e000511
Author(s):  
Jennifer Wei He ◽  
Juan Pablo Diaz Martinez ◽  
Kathleen Bingham ◽  
Jiandong Su ◽  
Mahta Kakvan ◽  
...  
Keyword(s):  
Cognitive Dysfunction ◽  
Cognitive Status ◽  
Sensitivity Analyses ◽  
Neuropsychological Battery ◽  
Assessment Visit ◽  
Unit Increase ◽  
Z Scores ◽  
The Mean ◽  
Anxiety Depression ◽  
Insight Into

ObjectiveDispersion, or variability in an individual’s performance across multiple tasks at a single assessment visit, has been associated with cognitive dysfunction (CD) in many neurodegenerative and neurodevelopmental disorders. We aimed to compute a dispersion score using neuropsychological battery (NB) tests and determine its association with CD in patients with SLE.MethodsCD was defined as a z-score of ≤−1.5 on ≥2 domains of the NB. To compute a type of dispersion score known as the intraindividual SD (ISD), the SD of age-adjusted and sex-adjusted z-scores was calculated for each visit in each patient. To estimate the association between ISD and cognitive status (CD and non-CD), we used multilevel logistic regression, adjusting for clinically important covariates.ResultsA total of 301 adult patients with SLE completed the NB at baseline, 187 of whom were reassessed at 6 months and 189 at 12 months. CD was observed in 35.2% of patients at baseline, 27.8% at 6 months and 28.0% at 12 months. Prior to covariate adjustment, the mean ISD for non-CD was 1.10±0.31 compared with 1.50±0.70 for CD. After adjusting for ethnicity, education, employment, socioeconomic status and anxiety/depression, there was a statistically significant association between ISD and CD (OR for one-unit increase in ISD: 13.56, 95% CI 4.80 to 38.31; OR for 1/10th-unit increase in ISD: 1.30, 95% CI 1.17 to 1.44). Findings were valid across multiple sensitivity analyses.ConclusionThis is the first study to show that patients with SLE who were classified as having CD by the NB had more variability across the NB tests (ie, higher ISD score) compared with those who were not classified as having CD.

Non-Double-Couple Components of the Moment Tensor in a Transversely Isotropic Medium

2020 ◽  
Vol 110 (3) ◽  
pp. 1125-1133
Author(s):  
William Menke ◽  
Joshua B. Russell
Keyword(s):  
Symmetry Axis ◽  
Fault Plane ◽  
Moment Tensor ◽  
Source Region ◽  
Transversely Isotropic ◽  
Earth Model ◽  
Double Couple ◽  
Axis Of Symmetry ◽  
The Moment ◽  
Insight Into

ABSTRACT The non-double-couple (non-DC) components of the moment tensor provide insight into the earthquake processes and anisotropy of the near-source region. We investigate the behavior of the isotropic (ISO) and compensated linear vector dipole (CLVD) components of the moment tensor for shear faulting in a transversely ISO medium with an arbitrarily oriented symmetry axis. Analytic formulas for ISO and CLVD depend on the orientation of the fault relative to the anisotropy symmetry axis as well as three anisotropic parameters, which describe deviations of the medium from isotropy. Numerical experiments are presented for the preliminary reference Earth model. Both ISO and CLVD components are zero when the axis of symmetry is within the fault plane or the auxiliary plane. For any orientation in which the ISO component is zero, the CLVD component is also zero, but the opposite is not always true (e.g., for strong anisotropy). The relative signs of the non-DC components of neighboring earthquakes may help distinguish source processes from source-region anisotropy. We prove that an inversion of ISO and CLVD components of a set of earthquakes with different focal mechanisms can uniquely determine the orientation and strength of anisotropy. This study highlights the importance of the ISO component for constraining deep slab anisotropy and demonstrates that it cannot be neglected.

Novel transient multicomponent induction logging method for the determination of dip angle and anisotropy of formation

Geophysics ◽  
2020 ◽  
Vol 85 (6) ◽  
pp. D181-D197
Author(s):  
Xiyong Yuan ◽  
Shaogui Deng ◽  
Yiren Fan ◽  
Xufei Hu ◽  
Zhenguan Wu ◽  
...  
Keyword(s):  
Coordinate System ◽  
Measurement Errors ◽  
Dipole Moments ◽  
Algebraic Method ◽  
Inversion Process ◽  
True Value ◽  
Induction Logging ◽  
Dip Angle ◽  
Source Dipole

The relative dip angle and anisotropy of the anisotropic formation are generally determined through an inversion process. We have studied the responses of the novel transient multicomponent induction logging method and find that all of the components measured in the instrument coordinate system have the same decay with time. However, the cross component decays much faster than the coaxial or coplanar components in the formation coordinate system. We adopt an algebraic time-domain method to calculate the dip angle and anisotropy coefficient and thereby avoid the inversion process. The accuracy and applicability of this pseudoinversion method are studied theoretically. Numerical results demonstrate that coaxial, coplanar, and cross components are used to calculate the apparent relative dip angle that yields the exactly true value at very early times and then goes through a transition deviating from the true dip and gradually approaches the true value again at late times. The apparent anisotropy is calculated by the coaxial and coplanar components and is equal to zero at early times and nonzero to the true anisotropy during the transition times. Moreover, by using realistic source dipole moments as well as adding random measurement errors, the practicality of this algebraic method is also investigated. Determination of the relative dip is still stable and valid. Determination of the anisotropy is more easily affected by measurement error and has some application limitations.

Moveout approximations for P- and SV-waves in dip-constrained transversely isotropic media

Geophysics ◽  
2013 ◽  
Vol 78 (6) ◽  
pp. C53-C59 ◽  
Author(s):  
Véronique Farra ◽  
Ivan Pšenčík
Keyword(s):  
Transversely Isotropic ◽  
Arbitrary Orientation ◽  
Transversely Isotropic Medium ◽  
Weak Anisotropy ◽  
Transversely Isotropic Media ◽  
Isotropic Media ◽  
Axis Of Symmetry ◽  
Dip Angle ◽  
P And Sv Waves ◽  
Axes Of Symmetry

We generalize the P- and SV-wave moveout formulas obtained for transversely isotropic media with vertical axes of symmetry (VTI), based on the weak-anisotropy approximation. We generalize them for 3D dip-constrained transversely isotropic (DTI) media. A DTI medium is a transversely isotropic medium whose axis of symmetry is perpendicular to a dipping reflector. The formulas are derived in the plane defined by the source-receiver line and the normal to the reflector. In this configuration, they can be easily obtained from the corresponding VTI formulas. It is only necessary to replace the expression for the normalized offset by the expression containing the apparent dip angle. The final results apply to general 3D situations, in which the plane reflector may have arbitrary orientation, and the source and the receiver may be situated arbitrarily in the DTI medium. The accuracy of the proposed formulas is tested on models with varying dip of the reflector, and for several orientations of the horizontal source-receiver line with respect to the dipping reflector.

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