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.

Shear‐wave velocity and density estimation from PS-wave AVO analysis: Application to an OBS dataset from the North Sea

Geophysics ◽  
2000 ◽  
Vol 65 (5) ◽  
pp. 1446-1454 ◽  
Author(s):  
Side Jin ◽  
G. Cambois ◽  
C. Vuillermoz
Keyword(s):  
Wave Velocity ◽  
North Sea ◽  
Random Noise ◽  
P Wave ◽  
S Wave ◽  
Data Set ◽  
Avo Analysis ◽  
The North ◽  
Avo Inversion ◽  
The North Sea

S-wave velocity and density information is crucial for hydrocarbon detection, because they help in the discrimination of pore filling fluids. Unfortunately, these two parameters cannot be accurately resolved from conventional P-wave marine data. Recent developments in ocean‐bottom seismic (OBS) technology make it possible to acquire high quality S-wave data in marine environments. The use of (S)-waves for amplitude variation with offset (AVO) analysis can give better estimates of S-wave velocity and density contrasts. Like P-wave AVO, S-wave AVO is sensitive to various types of noise. We investigate numerically and analytically the sensitivity of AVO inversion to random noise and errors in angles of incidence. Synthetic examples show that random noise and angle errors can strongly bias the parameter estimation. The use of singular value decomposition offers a simple stabilization scheme to solve for the elastic parameters. The AVO inversion is applied to an OBS data set from the North Sea. Special prestack processing techniques are required for the success of S-wave AVO inversion. The derived S-wave velocity and density contrasts help in detecting the fluid contacts and delineating the extent of the reservoir sand.

Inversion of reflection traveltimes for transverse isotropy

Geophysics ◽  
1995 ◽  
Vol 60 (4) ◽  
pp. 1095-1107 ◽  
Author(s):  
Ilya Tsvankin ◽  
Leon Thomsen
Keyword(s):  
Wave Velocity ◽  
Vertical Velocity ◽  
Joint Inversion ◽  
Transverse Isotropy ◽  
Taylor Series Expansion ◽  
High Sensitivity ◽  
Transversely Isotropic ◽  
P Wave ◽  
S Wave ◽  
Quartic Term

In anisotropic media, the short‐spread stacking velocity is generally different from the root‐mean‐square vertical velocity. The influence of anisotropy makes it impossible to recover the vertical velocity (or the reflector depth) using hyperbolic moveout analysis on short‐spread, common‐midpoint (CMP) gathers, even if both P‐ and S‐waves are recorded. Hence, we examine the feasibility of inverting long‐spread (nonhyperbolic) reflection moveouts for parameters of transversely isotropic media with a vertical symmetry axis. One possible solution is to recover the quartic term of the Taylor series expansion for [Formula: see text] curves for P‐ and SV‐waves, and to use it to determine the anisotropy. However, this procedure turns out to be unstable because of the ambiguity in the joint inversion of intermediate‐spread (i.e., spreads of about 1.5 times the reflector depth) P and SV moveouts. The nonuniqueness cannot be overcome by using long spreads (twice as large as the reflector depth) if only P‐wave data are included. A general analysis of the P‐wave inverse problem proves the existence of a broad set of models with different vertical velocities, all of which provide a satisfactory fit to the exact traveltimes. This strong ambiguity is explained by a trade‐off between vertical velocity and the parameters of anisotropy on gathers with a limited angle coverage. The accuracy of the inversion procedure may be significantly increased by combining both long‐spread P and SV moveouts. The high sensitivity of the long‐spread SV moveout to the reflector depth permits a less ambiguous inversion. In some cases, the SV moveout alone may be used to recover the vertical S‐wave velocity, and hence the depth. Success of this inversion depends on the spreadlength and degree of SV‐wave velocity anisotropy, as well as on the constraints on the P‐wave vertical velocity.

Full-waveform matching of VP and VS models from surface waves

2019 ◽  
Vol 218 (3) ◽  
pp. 1873-1891 ◽  
Author(s):  
Farbod Khosro Anjom ◽  
Daniela Teodor ◽  
Cesare Comina ◽  
Romain Brossier ◽  
Jean Virieux ◽  
...  
Keyword(s):  
Surface Waves ◽  
Wave Velocity ◽  
Real Data ◽  
Test Site ◽  
P Wave ◽  
S Wave ◽  
Surface Wave Dispersion ◽  
Data Set ◽  
Near Surface ◽  
Velocity Models

SUMMARY The analysis of surface wave dispersion curves (DCs) is widely used for near-surface S-wave velocity (VS) reconstruction. However, a comprehensive characterization of the near-surface requires also the estimation of P-wave velocity (VP). We focus on the estimation of both VS and VP models from surface waves using a direct data transform approach. We estimate a relationship between the wavelength of the fundamental mode of surface waves and the investigation depth and we use it to directly transform the DCs into VS and VP models in laterally varying sites. We apply the workflow to a real data set acquired on a known test site. The accuracy of such reconstruction is validated by a waveform comparison between field data and synthetic data obtained by performing elastic numerical simulations on the estimated VP and VS models. The uncertainties on the estimated velocity models are also computed.

Advances in surface-wave tomography for near-surface applications

2021 ◽  
Vol 40 (8) ◽  
pp. 567-575
Author(s):  
Myrto Papadopoulou ◽  
Farbod Khosro Anjom ◽  
Mohammad Karim Karimpour ◽  
Valentina Laura Socco
Keyword(s):  
Surface Wave ◽  
Wave Velocity ◽  
P Wave ◽  
Seismic Exploration ◽  
S Wave ◽  
Data Set ◽  
Near Surface ◽  
Processing Times ◽  
Spatial Coverage ◽  
Wave Tomography

Surface-wave (SW) tomography is a technique that has been widely used in the field of seismology. It can provide higher resolution relative to the classical multichannel SW processing and inversion schemes that are usually adopted for near-surface applications. Nevertheless, the method is rarely used in this context, mainly due to the long processing times needed to pick the dispersion curves as well as the inability of the two-station processing to discriminate between higher SW modes. To make it efficient and to retrieve pseudo-2D/3D S-wave velocity (VS) and P-wave velocity (VP) models in a fast and convenient way, we develop a fully data-driven two-station dispersion curve estimation, which achieves dense spatial coverage without the involvement of an operator. To handle higher SW modes, we apply a dedicated time-windowing algorithm to isolate and pick the different modes. A multimodal tomographic inversion is applied to estimate a VS model. The VS model is then converted to a VP model with the Poisson's ratio estimated through the wavelength-depth method. We apply the method to a 2D seismic exploration data set acquired at a mining site, where strong lateral heterogeneity is expected, and to a 3D pilot data set, recorded with state-of-the-art acquisition technology. We compare the results with the ones retrieved from classical multichannel analysis.

The effects of transverse isotropy on reflection amplitude versus offset

Geophysics ◽  
1987 ◽  
Vol 52 (4) ◽  
pp. 564-567 ◽  
Author(s):  
J. Wright
Keyword(s):  
Wave Velocity ◽  
Transverse Isotropy ◽  
Transversely Isotropic ◽  
P Wave ◽  
S Wave ◽  
Reflection Amplitude ◽  
Amplitude Versus Offset ◽  
Transversely Isotropic Media ◽  
P Wave Velocity ◽  
Isotropic Media

Studies have shown that elastic properties of materials such as shale and chalk are anisotropic. With the increasing emphasis on extraction of lithology and fluid content from changes in reflection amplitude with shot‐to‐group offset, one needs to know the effects of anisotropy on reflectivity. Since anisotropy means that velocity depends upon the direction of propagation, this angular dependence of velocity is expected to influence reflectivity changes with offset. These effects might be particularly evident in deltaic sand‐shale sequences since measurements have shown that the P-wave velocity of shales in the horizontal direction can be 20 percent higher than the vertical P-wave velocity. To investigate this behavior, a computer program was written to find the P- and S-wave reflectivities at an interface between two transversely isotropic media with the axis of symmetry perpendicular to the interface. Models for shale‐chalk and shale‐sand P-wave reflectivities were analyzed.

Experimental study of fracture size effect on elastic-wave velocity dispersion and anisotropy

Geophysics ◽  
2018 ◽  
Vol 83 (1) ◽  
pp. C49-C59 ◽  
Author(s):  
Da Shuai ◽  
Jianxin Wei ◽  
Bangrang Di ◽  
Sanyi Yuan ◽  
Jianyong Xie ◽  
...  
Keyword(s):  
Wave Velocity ◽  
Seismic Velocity ◽  
Effective Medium Theory ◽  
Transversely Isotropic ◽  
Elastic Wave Velocity ◽  
P Wave ◽  
S Wave ◽  
P Wave Velocity ◽  
Fracture Size ◽  
Good Agreement

We have designed transversely isotropic models containing penny-shaped rubber inclusions, with the crack diameters ranging from 2.5 to 6.2 mm to study the influence of fracture size on seismic velocity under controlled conditions. Three pairs of transducers with different frequencies (0.5, 0.25, and 0.1 MHz) are used for P- and S-wave ultrasonic sounding, respectively. The P-wave measurements indicate that the scattering effect is dominant when the waves propagate perpendicular to the fractures. Our experimental results demonstrate that when the wavelength-to-crack-diameter ratio ([Formula: see text]) is larger than 14, the P-wave velocity can be described predominantly by the effective medium theory. Although the ratio is larger than four, the S-wave velocity is close to the equivalent medium results. When [Formula: see text] < 14 or [Formula: see text] is < 4, the elastic velocity is dominated by scattering. The magnitudes of the Thomsen anisotropic parameters [Formula: see text] and [Formula: see text] are scale and frequency dependent on the assumption that the transversely isotropic models are vertical transversely isotropic medium. Furthermore, we compare the experimental velocities with the Hudson theory. The results illustrate that there is a good agreement between the observed P-wave velocity and the Hudson theory when [Formula: see text] > 7 in the directions parallel and perpendicular to the fractures. For small fracture diameters, however, the P-wave velocity perpendicular to the fractures predicted from the Hudson theory is not accurate. When [Formula: see text] < 4, there is good agreement between the experimental fast S-wave velocity and the Hudson theory, whereas the experimental slow S-wave velocity diverges with the Hudson theory. When [Formula: see text] > 4, the deviation of fast and slow S-wave velocities with the Hudson prediction is stable.

Bayesian linearized AVO inversion

Geophysics ◽  
2003 ◽  
Vol 68 (1) ◽  
pp. 185-198 ◽  
Author(s):  
Arild Buland ◽  
Henning Omre
Keyword(s):  
Wave Velocity ◽  
Posterior Distribution ◽  
Acoustic Impedance ◽  
Velocity Ratio ◽  
P Wave ◽  
Inversion Method ◽  
Inversion Algorithm ◽  
S Wave ◽  
Data Set ◽  
Avo Inversion

A new linearized AVO inversion technique is developed in a Bayesian framework. The objective is to obtain posterior distributions for P‐wave velocity, S‐wave velocity, and density. Distributions for other elastic parameters can also be assessed—for example, acoustic impedance, shear impedance, and P‐wave to S‐wave velocity ratio. The inversion algorithm is based on the convolutional model and a linearized weak contrast approximation of the Zoeppritz equation. The solution is represented by a Gaussian posterior distribution with explicit expressions for the posterior expectation and covariance; hence, exact prediction intervals for the inverted parameters can be computed under the specified model. The explicit analytical form of the posterior distribution provides a computationally fast inversion method. Tests on synthetic data show that all inverted parameters were almost perfectly retrieved when the noise approached zero. With realistic noise levels, acoustic impedance was the best determined parameter, while the inversion provided practically no information about the density. The inversion algorithm has also been tested on a real 3‐D data set from the Sleipner field. The results show good agreement with well logs, but the uncertainty is high.

Seismic vertical transversely isotropic parameter inversion from P- and S-wave cross-borehole measurements in an aquifer environment

Geophysics ◽  
2019 ◽  
Vol 84 (3) ◽  
pp. D101-D116
Author(s):  
Julius K. von Ketelhodt ◽  
Musa S. D. Manzi ◽  
Raymond J. Durrheim ◽  
Thomas Fechner
Keyword(s):  
Transversely Isotropic ◽  
P Wave ◽  
Perturbation Equation ◽  
S Wave ◽  
P Waves ◽  
Data Set ◽  
Near Surface ◽  
S Waves ◽  
Wave Measurements ◽  
Wave Splitting

Joint P- and S-wave measurements for tomographic cross-borehole analysis can offer more reliable interpretational insight concerning lithologic and geotechnical parameter variations compared with P-wave measurements on their own. However, anisotropy can have a large influence on S-wave measurements, with the S-wave splitting into two modes. We have developed an inversion for parameters of transversely isotropic with a vertical symmetry axis (VTI) media. Our inversion is based on the traveltime perturbation equation, using cross-gradient constraints to ensure structural similarity for the resulting VTI parameters. We first determine the inversion on a synthetic data set consisting of P-waves and vertically and horizontally polarized S-waves. Subsequently, we evaluate inversion results for a data set comprising jointly measured P-waves and vertically and horizontally polarized S-waves that were acquired in a near-surface ([Formula: see text]) aquifer environment (the Safira research site, Germany). The inverted models indicate that the anisotropy parameters [Formula: see text] and [Formula: see text] are close to zero, with no P-wave anisotropy present. A high [Formula: see text] ratio of up to nine causes considerable SV-wave anisotropy despite the low magnitudes for [Formula: see text] and [Formula: see text]. The SH-wave anisotropy parameter [Formula: see text] is estimated to be between 0.05 and 0.15 in the clay and lignite seams. The S-wave splitting is confirmed by polarization analysis prior to the inversion. The results suggest that S-wave anisotropy may be more severe than P-wave anisotropy in near-surface environments and should be taken into account when interpreting cross-borehole S-wave data.

Joint inversion of receiver functions and apparent incidence angles to investigate the crustal structure of Mars

2021 ◽  
Author(s):  
Rakshit Joshi ◽  
Brigitte Knapmeyer-Endrun ◽  
Klaus Mosegaard ◽  
Felix Bissig ◽  
Amir Khan ◽  
...  
Keyword(s):  
Wave Velocity ◽  
Crustal Structure ◽  
Joint Inversion ◽  
Landing Site ◽  
Crustal Thickness ◽  
Receiver Functions ◽  
P Wave ◽  
S Wave ◽  
Data Set ◽  
Insight Mission

&lt;p&gt;Since InSight (the Interior Exploration using Geodesy and Heat Transport) landed 26 months ago and deployed an ultra sensitive broadband seismometer(SEIS) on the surface of Mars, around 500 seismic events of diverse variety have been detected, making it possible to directly analyze the subsurface properties of Mars for the very first time. One of the primary goals of the mission is to retrieve the crustal structure below the landing site. Current estimates differ by more than 100% for the average crustal thickness. Since data from orbital gravity measurementsprovide information on relative variations of crustal thickness but not absolute values, this landing site measurement could serve as a tie point to retrieve global crustal structure models. To do so, we propose using a joint inversion of receiver functions and apparent incidence angles, which contain information on absolute S-wave velocities of the subsurface. Since receiver function inversions suffer from a velocity depth trade-off, we in addition exploit a simple relation which defines apparent S-wave velocity as a function of observed apparent P-wave incidence angles to constrain the parameter space. Finally we use the Neighbourhood Algorithm for the inversion of a suitable joint objective function. The resulting ensemble of models is then used to derive the full uncertainty estimates for each model parameter. Before its application on data from InSight mission, we successfully tested the method on Mars synthetics and terrestrial data from various geological settings using both single and multiple events. Using the same method, we have previously been able to constrain the S-wave velocity and depth for the first inter-crustal layer of Mars between 1.7 to 2.1 km/s and 8 to 11 km, respectively. Here we present the results of applying this technique on our selected data set from the InSight mission. Results show that the data can be explained equally well by models with 2 or 3 crustal layers with constant velocities. Due to the limited data set it is difficult to resolve the ambiguity of this bi-modal solution. We therefore investigate information theoretic statistical tests as a model selection criteria and discuss their relevance and implications in seismological framework.&lt;/p&gt;&lt;div&gt;&lt;/div&gt;&lt;div&gt;&lt;/div&gt;&lt;div&gt;&lt;/div&gt;

Decoupled approximation and separate extrapolation of P- and SV-waves in transversely isotropic media

Geophysics ◽  
2021 ◽  
pp. 1-57
Author(s):  
Bowen Li ◽  
Alexey Stovas
Keyword(s):  
Phase Velocity ◽  
Wave Velocity ◽  
Transversely Isotropic ◽  
P Wave ◽  
S Wave ◽  
Wave Phase ◽  
Wave Phase Velocity ◽  
Tti Media ◽  
Vti Media ◽  
Acoustic Approximation

Characterizing the kinematics of seismic waves in elastic vertical transversely isotropic (VTI) media involves four independent parameters. To reduce the complexity, the acoustic approximation for P-waves reduces the number of required parameters to three by setting the vertical S-wave velocity to zero. However, since only the SV-wave phase velocities parallel or perpendicular to the symmetry axis are indirectly set to zero, the acoustic approximation leads to coupled P-wave components and SV-wave artifacts. The new acoustic approximation suggests setting the vertical S-wave velocity as a phase angle-dependent variable so that the SV-wave phase velocity is zero at all phase angles. We find that manipulating this parameter is a valid way for P-wave approximation, but doing so inevitably leads to zero- or non-zero-valued spurious SV-wave components. Thus, we have developed a novel approach to efficiently approximate and thoroughly separate the two wave modes in VTI media. First, the exact P- and SV-wave phase velocity expressions are rewritten by introducing an auxiliary function. After confirming the insensitivity of this function, we construct a new expression for it and obtain simplified P- and SV-wave phase velocity expressions, which are three- and four-parameter, respectively. This approximation process leads to the same reasonable error for both wave modes. Accuracy analysis indicates that for the P-wave, the overall accuracy performance of our approach is comparable to that of some existing three-parameter approximations. We then derive the corresponding P- and SV-wave equations in tilted transversely isotropic (TTI) media and provide two available solutions, the hybrid finite-difference/pseudo-spectral scheme and the low-rank approach. Numerical examples illustrate the separability and high accuracy of the proposed P- and SV-wave simulation methods in TTI media.

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