Chapter 23: Vertical Transverse Isotropy FWI

2017 ◽  
pp. 293-300
Keyword(s):  
Transverse Isotropy ◽  
Vertical Transverse Isotropy

scholarly journals Prior Analysis in Determination of TI Anisotropy Type through Well-Based Modelling: A Case Study on the Deep Water Environment

2021 ◽  
Vol 873 (1) ◽  
pp. 012102
Author(s):  
Madaniya Oktariena ◽  
Wahyu Triyoso ◽  
Fatkhan Fatkhan ◽  
Sigit Sukmono ◽  
Erlangga Septama ◽  
...  
Keyword(s):  
Wave Velocity ◽  
Deep Water ◽  
Initial Conditions ◽  
Transverse Isotropy ◽  
Water Environment ◽  
Horizontal Stress ◽  
P Wave ◽  
S Wave ◽  
Geomechanical Analysis ◽  
Vertical Transverse Isotropy

Abstract The existence of anisotropy phenomena in the subsurface will affect the image quality of seismic data. Hence a prior knowledge of the type of anisotropy is quite essential, especially when dealing with deep water targets. The preliminary result of the anisotropy of the well-based modelling in deep water exploration and development is discussed in this study. Anisotropy types are modelled for Vertical Transverse Isotropy (VTI) and Horizontal Transverse Isotropy (HTI) based on Thomsen Parameters of ε and γ. The parameters are obtained from DSI Logging paired with reference δ value for modelling. Three initial conditions are then analysed. The first assumption is isotropic, in which the P-Wave Velocity, S-Wave Velocity, and Density Log modelled at their in-situ condition. The second and third assumptions are anisotropy models that are VTI and HTI. In terms of HTI, the result shows that the model of CDP Gather in the offset domain has a weak distortion in Amplitude Variation with Azimuth (AVAz). However, another finding shows a relatively strong hockey effect in far offset, which indicates that the target level is a VTI dominated type. It is supported by the geomechanical analysis result in which vertical stress acts as the maximum principal axis while horizontal stress is close to isotropic one. To sum up, this prior anisotropy knowledge obtained based on this study could guide the efficiency guidance in exploring the deep water environment.

Constraints on the anisotropic parameters for pseudoelastic vertical transverse isotropy wave equations and the applications on imaging carbonate reservoirs

Geophysics ◽  
2019 ◽  
Vol 84 (2) ◽  
pp. C85-C94 ◽  
Author(s):  
Houzhu (James) Zhang ◽  
Hongwei Liu ◽  
Yang Zhao
Keyword(s):  
Wave Equation ◽  
Elastic Wave ◽  
Wave Velocity ◽  
Wave Equations ◽  
Transverse Isotropy ◽  
S Wave ◽  
Elastic Wave Equation ◽  
Computation Efficiency ◽  
The Stability ◽  
Vertical Transverse Isotropy

Seismic anisotropy is an intrinsic elastic property. Appropriate accounting of anisotropy is critical for correct and accurate positioning seismic events in reverse time migration. Although the full elastic wave equation may serve as the ultimate solution for modeling and imaging, pseudoelastic and pseudoacoustic wave equations are more preferable due to their computation efficiency and simplicity in practice. The anisotropic parameters and their relations are not arbitrary because they are constrained by the energy principle. Based on the investigation of the stability condition of the pseudoelastic wave equations, we have developed a set of explicit formulations for determining the S-wave velocity from given Thomsen’s parameters [Formula: see text] and [Formula: see text] for vertical transverse isotropy and tilted transverse isotropy media. The estimated S-wave velocity ensures that the wave equations are stable and well-posed in the cases of [Formula: see text] and [Formula: see text]. In the case of [Formula: see text], a common situation in carbonate, a positive value of S-wave velocity is needed to avoid the wavefield instability. Comparing the stability constraints of the pseudoelastic- with the full-elastic wave equation, we conclude that the feasible range of [Formula: see text] and [Formula: see text] was slightly larger for the pseudoelastic assumption. The success of achieving high-accuracy images and high-quality angle gathers using the proposed constraints is demonstrated in a synthetic example and a field example from Saudi Arabia.

Locating microseismic events using both head and direct waves traveling in vertical transverse isotropic media

2020 ◽  
Author(s):  
Dowan Kim ◽  
Joongmoo Byun ◽  
Soon Jee Seol
Keyword(s):  
Transverse Isotropy ◽  
Microseismic Monitoring ◽  
Head Wave ◽  
Hydraulic Fractures ◽  
Path Diversity ◽  
Isotropic Media ◽  
Transverse Isotropic ◽  
Microseismic Events ◽  
Vertical Transverse Isotropy ◽  
The Waves

Summary Microseismic monitoring is widely used to detect hydraulic fractures. Accurate mapping of microseismic events is essential to detect such fractures enhancing productivity. The eikonal solver is an efficient forward-modeling method used to map microseismic events. However, traditional eikonal solvers do not distinguish between head and direct waves, computing only the traveltimes of the waves that arrive first. We developed a new eikonal solver that computes the traveltimes of direct waves by imposing new constraints on the conventional, vertical transverse isotropy (VTI) solver. We then performed numerical experiments exploiting the traveltimes of direct waves. We used the traveltimes of only the first arrivals, and those of both first and direct arrivals, when performing inverted event mapping. The results showed that the uncertainties of event locations were minimized when both head and direct waves were analyzed due to the increased both the number of available data and the traveling path diversity. Also, we found that the use of only direct-arrival traveltimes was valuable when head-wave first arrivals were difficult to detect because the signal-to-noise (S/N) ratio was low.

Nonhyperbolic reflection moveout for horizontal transverse isotropy

Geophysics ◽  
1998 ◽  
Vol 63 (5) ◽  
pp. 1738-1753 ◽  
Author(s):  
AbdulFattah Al‐Dajani ◽  
Ilya Tsvankin
Keyword(s):  
Transverse Isotropy ◽  
Single Layer ◽  
Azimuthal Velocity ◽  
Azimuthal Anisotropy ◽  
P Wave ◽  
Analytic Description ◽  
Pure Mode ◽  
Quartic Term ◽  
Hti Media ◽  
Vertical Transverse Isotropy

The transversely isotropic model with a horizontal axis of symmetry (HTI) has been used extensively in studies of shear‐wave splitting to describe fractured formations with a single system of parallel vertical penny‐shaped cracks. Here, we present an analytic description of longspread reflection moveout in horizontally layered HTI media with arbitrary strength of anisotropy. The hyperbolic moveout equation parameterized by the exact normal‐moveout (NMO) velocity is sufficiently accurate for P-waves on conventional‐length spreads (close to the reflector depth), although the NMO velocity is not, in general, usable for converting time to depth. However, the influence of anisotropy leads to the deviation of the moveout curve from a hyperbola with increasing spread length, even in a single‐layer model. To account for nonhyperbolic moveout, we have derived an exact expression for the azimuthally dependent quartic term of the Taylor series traveltime expansion [t2(x2)] valid for any pure mode in an HTI layer. The quartic moveout coefficient and the NMO velocity are then substituted into the nonhyperbolic moveout equation of Tsvankin and Thomsen, originally designed for vertical transverse isotropy (VTI). Numerical examples for media with both moderate and uncommonly strong nonhyperbolic moveout show that this equation accurately describes azimuthally dependent P-wave reflection traveltimes in an HTI layer, even for spread lengths twice as large as the reflector depth. In multilayered HTI media, the NMO velocity and the quartic moveout coefficient reflect the influence of layering as well as azimuthal anisotropy. We show that the conventional Dix equation for NMO velocity remains entirely valid for any azimuth in HTI media if the group‐velocity vectors (rays) for data in a common‐midpoint (CMP) gather do not deviate from the vertical incidence plane. Although this condition is not exactly satisfied in the presence of azimuthal velocity variations, rms averaging of the interval NMO velocities represents a good approximation for models with moderate azimuthal anisotropy. Furthermore, the quartic moveout coefficient for multilayered HTI media can also be calculated with acceptable accuracy using the known averaging equations for vertical transverse isotropy. This allows us to extend the nonhyperbolic moveout equation to horizontally stratified media composed of any combination of isotropic, VTI, and HTI layers. In addition to providing analytic insight into the behavior of nonhyperbolic moveout, these results can be used in modeling and inversion of reflection traveltimes in azimuthally anisotropic media.

An open-source full 3D electromagnetic modeler for 1D VTI media in Python: empymod

Geophysics ◽  
2017 ◽  
Vol 82 (6) ◽  
pp. WB9-WB19 ◽  
Author(s):  
Dieter Werthmüller
Keyword(s):  
Fourier Transform ◽  
Time Domain ◽  
Fourier Transforms ◽  
Transverse Isotropy ◽  
Hankel Transform ◽  
Transform Methods ◽  
Electromagnetic Responses ◽  
The Time Domain ◽  
Ground Penetrating ◽  
Vertical Transverse Isotropy

The Python-code empymod computes the 3D electromagnetic field in a layered earth with vertical transverse isotropy by combining and extending two earlier presented algorithms in this journal. The bottleneck in frequency- and time-domain calculations of electromagnetic responses derived in the wavenumber-frequency domain is the transformations from the wavenumber to the space domain and from the frequency to the time domain, the so-called Hankel and Fourier transforms. Three different Hankel transform methods (quadrature, quadrature-with-extrapolation [QWE], and filters) and four different Fourier transform methods (fast Fourier transform [FFT], FFTLog, QWE, and filters) are included in empymod, which allows us to compare these different methods in terms of speed and precision. The best transform in terms of speed and precision depends on the modeled frequencies. Published digital filters for the Hankel transform are very fast and precise for frequencies in the range of controlled-source electromagnetic data, but they fail in the frequency range of ground-penetrating radar. Conventional quadrature, on the other hand, is in comparison very slow but can model any frequency. Examples comparing empymod with analytical solutions and with existing electromagnetic modelers illustrate the capabilities of empymod.

scholarly journals The Use of Core & Log Anisotropy Parameters into Seismic Data Processing: A Case Study of Deep-Water Reservoir

2021 ◽  
Vol 873 (1) ◽  
pp. 012038
Author(s):  
Madaniya Oktariena ◽  
Wahyu Triyoso ◽  
Dona Sita Ambarsari ◽  
Sigit Sukmono ◽  
Erlangga Septama ◽  
...  
Keyword(s):  
Seismic Velocity ◽  
Transverse Isotropy ◽  
Anisotropy Parameter ◽  
Water Reservoir ◽  
Velocity Analysis ◽  
Subsurface Imaging ◽  
Sonic Log ◽  
Anisotropy Parameters ◽  
Vertical Transverse Isotropy

Abstract The seismic far-offset data plays important role in seismic subsurface imaging and reservoir parameters derivation, however, it is often distorted by the hockey stick effect due to improper correction of the Vertical Transverse Isotropy (VTI) during the seismic velocity analysis. The anisotropy parameter η is needed to properly correct the VTI effect. The anisotropy parameters of ε and δ obtained from log and core measurements, can be used to estimate the η values, however, the upscaling effects due to the different frequencies of the wave sources used in the measurements must be carefully taken into account. The objective is to get better understanding on the proper uses of anisotropy parameters in the the velocity analysis of deepwater seismic gather data. To achieve the objective, the anisotropy parameters from ultrasonic core measurements and dipole sonic log were used to model the seismic CDP gathers. The upscaling effects is reflected by the big difference of measured anisotropy values, in which the core measurement value is about 40 times higher than the log measurement value. The CDP gathers modelling results show that, due to the upscaling effect, the log and core-based models show significant differences of far-offset amplitude and hockey sticks responses. The differences can be minimized by scaling-down the log anisotropy values to core anisotropy values by using equations established from core – log anisotropy values cross-plot. The study emphasizes the importances of integrating anisotropy parameters from core and log data to minimize the upscaling effect to get the best η for the VTI correction in seismic velocity analysis.

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