Approximations for traveltime, slope, curvature, and geometric spreading of elastic waves in layered transversely isotropic media

Abedi, Mohammad Mahdi; Pardo, David; Stovas, Alexey

doi:10.1190/geo2021-0215.1

Cited by 3 publications

(1 citation statement)

References 41 publications

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“…They are defined as fast or slow S waves (Ravve & Koren, 2016). The approximation for kinematic properties like traveltime and geometrical spreading in the ORT model can be found in (Abedi, 2020; Abedi et al., 2021; Alkhalifah & Tsvankin, 1995; Farra & Pšenčík, 2021; Masmoudi & Alkhalifah, 2016a, b; Ravve & Koren, 2017; Xu & Stovas, 2017; Xu et al., 2017, 2018).…”

Section: Introductionmentioning

confidence: 99%

Umbilic points of slowness surface in elastic orthorhombic media

Xu¹,

Stovas²,

Huang

2023

Geophysical Prospecting

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For 3D seismic data processing, azimuth plays an important role, especially in complex subsurface regions. In such regions, elliptical or anelliptical orthorhombic models are commonly used to describe wave propagation. In these models, the behaviour of the slowness surface needs more detailed analysis. Umbilic points defined by the equal principal curvatures exist in a complex 3D model. In the vicinity of the umbilic points, the traveltime surface has the shifted hyperbola form that needs to be considered in processing operations like velocity analysis. Fractured media characterized by the orthorhombic model are more likely to have umbilic points, and it is important to address their positions. If exists, umbilic points can provide additional constraints in inverting for model parameters. Through a defined condition, we examine the position of the umbilic point and derive their explicit formulas. We analyse umbilic points for elliptical and anelliptical orthorhombic models in the numerical example. For the elliptical orthorhombic model, the formulas for the umbilic point position on different symmetry planes are derived and corresponding conditions are also identified. Further, we numerically examine umbilic point positions for anelliptical orthorhombic models and observe that the umbilic points are located out of two vertical symmetry planes. Moreover, caused by interference from two neighbouring umbilic points, a more significant deviation in traveltime is found in the anelliptical orthorhombic model.

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Section: Introductionmentioning

confidence: 99%

Umbilic points of slowness surface in elastic orthorhombic media

Xu¹,

Stovas²,

Huang

2023

Geophysical Prospecting

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Evaluation of Depth Dependent Seismic Anisotropy within Limited Offset on Vertical Transverse Isotropy Media: Deep Water Reservoir Case Study

Oktariena,

Triyoso,

Fatkhan

et al. 2024

IOP Conf. Ser.: Earth Environ. Sci.

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Hydrocarbon bearing sediment in deep water reservoirs are uniquely characterized by the body of water being an additional weight on the top of vertical sedimentary layering. While large aerial extent of deep water reservoirs is known for their ability to contain substantial amount of reserves, they come with technical difficulties mainly in acquisition and imaging aspect. Deep water seismic imaging more often than not suffers from the hockey stick effect found in the long offset. At the same time, the presence of hockey stick in seismic long offset could be utilized as a tool to extract anisotropy information from seismic data. However, the deep target level requires a rather long offset in seismic data to be able in capturing a proper hockey stick condition. This research intends to evaluate seismic anisotropy behaviour in various depth level within a limited offset range instead of the commonly used very long offset. Seismic related anisotropy (η) is extracted from travel time error as a delta to the isotropic travel time. The extracted anisotropy η is to be plotted against several known VTI travel time approximation in order to identified the equation that most fitted to the deep water real data condition. Several depth levels are to be analysed as an attempt to capture depth related variation in multi reservoir scenarios. Observation is conducted on PMBG Seismic Gather around several well location as point of validation. The result shows indication of seismic anisotropy degree variation within progressed depth that could be concluded as depth dependant behaviour. The fact that the observed area has a typical character of weak anisotropy which only has a small impact on seismic data encourages a possibility to delineate anisotropy from seismic data with a certain treatment. Analysis on limited range offset seismic promotes the utilization of old vintage seismic data for seismic anisotropy extraction that contribute to the vision of using a new insight on the existing data as part of enhanced oil recovery strategies.

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The approximation for relative geometric spreading in the elastic vertical transversely isotropic medium

Stovas

Huang

2022

GEOPHYSICS

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In seismic data processing, compensation for geometrical spreading along the ray path is necessary. The accurate approximation of the relative geometrical spreading is critical since the traveltime parameters in the approximation can be estimated from velocity analysis. Two approximation types (Direct and Indirect) are generalized based on the procedure to derive the explicit expression. We propose perturbation-based approximations of the relative geometrical spreading for P and S waves with these two types in the elastic transversely isotropic media with a vertical symmetry axis (VTI). The Rational Approximation (RA) and the General Moveout Approximation (GMA) counterparts are compared to verify the superiority of our approach. Our study is to compare the performance of Direct and Indirect approximation for the optimal selection under different cases. In the numerical examples, we apply the error sensitivity in the layer depth, anellipticity value, and vertical velocity ratio. It is found that the P wave case is much more accurate than the S wave case, and the Direct type obtains relatively higher accuracy than the Indirect one. In addition, the perturbation coefficients for the acoustic VTI model are also derived not only with a much simpler expression but also achieve a highly accurate result that is recommended for the P wave seismic processing.

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Approximations for traveltime, slope, curvature, and geometric spreading of elastic waves in layered transversely isotropic media

Cited by 3 publications

References 41 publications

Umbilic points of slowness surface in elastic orthorhombic media

Umbilic points of slowness surface in elastic orthorhombic media

Evaluation of Depth Dependent Seismic Anisotropy within Limited Offset on Vertical Transverse Isotropy Media: Deep Water Reservoir Case Study

The approximation for relative geometric spreading in the elastic vertical transversely isotropic medium

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