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In velocity model building using full waveform inversion, diving waves are a source of the low-frequency information needed to update the low- to intermediate wavenumber components in the velocity model. Because full waveform inversion is a highly nonlinear optimization problem attempting to fit the information from the whole wavefield, it is prone to get stuck in local minimums and experience cycle skipping if the initial model does not contain accurate enough information about the low-wavenumbers to constrain the kinematics. Such initial velocity models will typically be estimated using alternative inversion methods that only apply information from parts of the wavefield in the forward modelling and recorded data. In migration velocity analysis, the unfocusing of the image, caused by inconsistency in the kinematics of reflected waves, is measured and is used to update the velocity model by applying differential semblance optimization. The same concept is applicable when using information from diving waves. For diving waves, little is known about the focusing behaviour, also known as imaging moveout, especially in the presence of azimuthal anisotropy, such as orthorhombic anisotropy, which is a good approximation for volcanic plains and sedimentary basins. Obtaining more knowledge about the focusing behaviour of diving waves for this type of anisotropy may help when choosing parameters to invert during inversion that yield a low trade-off between the parameters. Here, we derive approximate series-based equations describing the imaging moveout of diving qP waves in acoustic factorized orthorhombic anisotropic media. Due to the complexity of the analytical solutions for diving wave properties in such models, we find a vertical transverse isotropic type of simplification that manages to conserve the curvature and horizontal velocity of the diving qP wave. The accuracy of the simplified expressions is compared to the exact form and found to yield small errors. To verify the validity of the derived equations for imaging moveout, we compare the generated surfaces with images containing the shape of the unfocusing obtained using reverse time migration, showing a good fit. Of the anisotropic parameters defining the acoustic factorized orthorhombic model, the |$\epsilon _1$| and |$\epsilon _2$| parameters have the largest influence on the shape of the surface. The anelliptical parameters are shown only to induce minimal changes. Our method to obtain the series expressions describing the imaging moveout in the acoustic factorized orthorhombic model is also applicable to higher symmetry special cases of orthorhombic anisotropy by setting appropriate conditions. Here, this is demonstrated by additionally finding an approximate series expression describing the imaging moveout in acoustic factorized vertical transversely isotropic media, yielding a good match with the image obtained from reverse time migration. [ABSTRACT FROM AUTHOR]

Seismic response from porous sediments can be used in reservoir characterization and fluid detection. Reflection coefficient at the isotropic/poroelastic interface is essential to reveal seismic response from the fluid‐saturated deposits. The exact normal incidence reflection coefficient is given by complex mathematic expression and not very clear relations with solid and fluid properties. Therefore, we derive the reflection coefficient approximate formula in series with respect to the square root of the imaginary unit multiplying by the ratio between angular frequency and the characteristic angular frequency. Compared to the exact reflection coefficient, the proposed approximate formula has a more concise mathematical form and clearer relationship with the moduli and densities. Meanwhile, there is no need to calculate the complex wavenumbers of poroelastic media from the dispersion equation as the exact reflection coefficient. When the frequency tends to zero, the approximate formula is consistent with reflection coefficient for the isotropic/isotropic interface. The proposed formula's applicability is verified through two models with an interface separating the mudstone and fully fluid‐saturated sandstone with pore fluids as water or carbon dioxide. [ABSTRACT FROM AUTHOR]

The acoustic orthorhombic model is widely used in seismic modeling and processing of P-wave data. However, the anisotropic acoustic models have so called S-wave artifacts (1 artifact in transversely isotropic acoustic medium and two artifacts in orthorhombic acoustic medium). I show that S-wave artifacts can have one singularity point that results in complications in polarization field and the group velocity surface. The conditions of the existence of this point are defined in terms of anellipticity parameters. This singularity point and its group velocity image are the objects of my analysis. [ABSTRACT FROM AUTHOR]

The critical angle plays a crucial role in data processing for refraction seismology. In the context of three‐dimensional data, the critical angle exhibits azimuthal dependence, particularly in the presence of an anisotropic model. In this paper, we propose a method to determine the critical angle (phase angle) and analyse the sensitivity of the critical angle to the model parameters and the available azimuthal range for both transversely isotropic medium with a vertical symmetry axis and orthorhombic models. For more complex orthorhombic models, the critical angle can be computed while considering changes in azimuth. In a numerical example, we apply sensitivity analysis to examine the existence of the critical angle and determine its corresponding values to variations in model parameters and the azimuthal range. Additionally, we conduct computations of the critical angle for the simplified acoustic and elliptical orthorhombic models. This analysis can be extended to encompass all model parameters for different wave modes (pure and converted waves), and they provide generalized predictions for the available range of data in seismic data processing applications. [ABSTRACT FROM AUTHOR]

The low porosity and low permeability of tight sandstone pose considerable challenges on characterizing the reservoir fluid. Moreover, the geophysical characteristics of the tight sandstone are usually similar to the surrounding rocks, leading to small impedance contrast, compounding the difficulty of reservoir parameters inversion. Amplitude‐versus‐offset technology is an important tool to invert the reservoir parameters from seismic data. The existing amplitude‐versus‐offset inversion methods are challenged to predict the tight sandstone reservoir parameters for the reasons above. In this paper, we propose a new workflow based on amplitude‐versus‐offset attributes to characterize the tight sandstone gas reservoirs in the Xihu Depression, East China Sea. The proposed workflow utilizes the Backus average method and Gassmann's equation to construct the rock physics model. Based on the analysis of the anisotropic model, we introduce Rüger's anisotropic equation for amplitude‐versus‐offset forward modelling. We compare the amplitude‐versus‐offset gathers with the real data and adjust the reservoir parameters. Through the sensitivity analysis, we select the gas saturation and porosity as the inversion parameters. The relationship between the reservoir parameters and amplitude‐versus‐offset attributes is established by fitting the fifth‐order polynomials. We use Shuey's equation and the least squares inversion method to calculate the amplitude‐versus‐offset attributes (intercept and gradient). For real data, we introduce the Toeplitz‐sparse matrix factorization method to calculate the reflectivity of the amplitude‐versus‐offset gathers. Finally, we proposed a multi‐well joint inversion approach to invert the gas saturation and porosity. The application results demonstrate the effectiveness of the proposed workflow for the characterization of the gas reservoir in tight sandstone for the describedcase. [ABSTRACT FROM AUTHOR]

The eikonal equation for transversely isotropic media is a complex quartic partial differential equation that causes instability in traveltime inversion. The phenomenon of shear wave splitting in a transversely isotropic model with a horizontal symmetry axis (HTI) provides information for inversion. However, the involvement of shear waves makes the computation of forward modelling and inversion more time-consuming than when only using P waves. Most studies of traveltime approximation based on the eikonal equation are based on an acoustic assumption, which does not work for shear waves. Therefore, based on perturbation theory, we derive approximate solutions of the eikonal equation in a heterogeneous elastic HTI model for P, SV and SH waves to improve the traveltime computation efficiency. The approximate solutions of linear, quadratic and Shanks forms are based on the linearization of the traveltime function in terms of fracture weaknesses in an isotropic background, which are suitable for joint P -, SV - and SH -wave traveltime inversion and tomography for fracture parameters. When applied for a homogenous model, the proposed formulation results in a simple and accurate traveltime approximation. The first- and second-order perturbation coefficients are used to analyse the sensitivity of the traveltime to fracture weakness. To improve the accuracy of our approximation, we also expand the approximation of the P -wave traveltime with respect to the anellipticity parameter η in an elliptic background, which is evaluated by performing an error test. Based on the accuracy and stability of the perturbation, we select a set of linear equations with respect to the fracture weaknesses and a set of more accurate nonlinear equations to serve different needs. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]