Wave characteristics in elliptical orthorhombic media

Geophysics ◽  
2021 ◽  
pp. 1-52
Author(s):  
Alexey Stovas ◽  
Yuriy Roganov ◽  
Vyacheslav Roganov
Keyword(s):  
Anisotropic Medium ◽  
Wave Equations ◽  
Reference Model ◽  
Relative Magnitude ◽  
P Wave ◽  
S Wave ◽  
Wave Characteristics ◽  
Singularity Point ◽  
Wave Properties ◽  
Wave Modes

An elliptical anisotropic medium is defined as a simplified representation of anisotropy in which the anelliptic parameters are set to zero in all symmetry planes. Despite of the fact that this model is rather seldom observed for real rocks, it is often used as a reference model. The P-wave equations for an elliptical anisotropic medium is well known. However, the S-wave equations have not been derived. Thus, we define all wave modes in elliptical orthorhombic models focusing mostly on the S-wave properties. We show that all wave modes in elliptical orthorhombic model are generally coupled and analyze the effect of additive coupling term. As the result, there is an S wave fundamental singularity point located in one of the symmetry planes depending on the relative magnitude of S wave stiffness coefficients.

PURE MODE P AND S WAVE PHASE VELOCITY EQUATIONS IN ELASTIC ORTHORHOMBIC MEDIA

Geophysics ◽  
2021 ◽  
pp. 1-82
Author(s):  
Alexey Stovas ◽  
Yuriy Roganov ◽  
Vyacheslav Roganov
Keyword(s):  
Wave Equations ◽  
Approximate Equation ◽  
Approximate Solutions ◽  
P Wave ◽  
Orthorhombic Symmetry ◽  
Elastic Model ◽  
Pure Mode ◽  
S Wave ◽  
Practical Applications ◽  
Independent Parameters

In an elastic model with orthorhombic symmetry, there are nine independent stiffness coefficients that control the propagation of all intrinsically coupled wave modes. For practical applications in P-wave modeling and inversion, it is important to derive the approximate solutions that support propagation of P waves only and depends on fewer independent parameters. Due to the increasing interest in shear-wave propagation in anisotropic media, we also derive an approximate equation that supports propagation of S waves only. However, the reduction in number of independent parameters for the S wave equation is not possible. We derive pure P and S wave equations in an elastic orthorhombic model and show that the accuracy is sufficient for practical applications.

Approximation of pure acoustic seismic wave propagation in TTI media

Geophysics ◽  
2011 ◽  
Vol 76 (5) ◽  
pp. WB97-WB107 ◽  
Author(s):  
Chunlei Chu ◽  
Brian K. Macy ◽  
Phil D. Anno
Keyword(s):  
Wave Propagation ◽  
Wave Equation ◽  
Elastic Wave ◽  
Wave Equations ◽  
Computational Cost ◽  
P Wave ◽  
Anisotropy Axis ◽  
S Wave ◽  
Time Migration ◽  
Tti Media

Pseudoacoustic anisotropic wave equations are simplified elastic wave equations obtained by setting the S-wave velocity to zero along the anisotropy axis of symmetry. These pseudoacoustic wave equations greatly reduce the computational cost of modeling and imaging compared to the full elastic wave equation while preserving P-wave kinematics very well. For this reason, they are widely used in reverse time migration (RTM) to account for anisotropic effects. One fundamental shortcoming of this pseudoacoustic approximation is that it only prevents S-wave propagation along the symmetry axis and not in other directions. This problem leads to the presence of unwanted S-waves in P-wave simulation results and brings artifacts into P-wave RTM images. More significantly, the pseudoacoustic wave equations become unstable for anisotropy parameters [Formula: see text] and for heterogeneous models with highly varying dip and azimuth angles in tilted transversely isotropic (TTI) media. Pure acoustic anisotropic wave equations completely decouple the P-wave response from the elastic wavefield and naturally solve all the above-mentioned problems of the pseudoacoustic wave equations without significantly increasing the computational cost. In this work, we propose new pure acoustic TTI wave equations and compare them with the conventional coupled pseudoacoustic wave equations. Our equations can be directly solved using either the finite-difference method or the pseudospectral method. We give two approaches to derive these equations. One employs Taylor series expansion to approximate the pseudodifferential operator in the decoupled P-wave equation, and the other uses isotropic and elliptically anisotropic dispersion relations to reduce the temporal frequency order of the P-SV dispersion equation. We use several numerical examples to demonstrate that the newly derived pure acoustic wave equations produce highly accurate P-wave results, very close to results produced by coupled pseudoacoustic wave equations, but completely free from S-wave artifacts and instabilities.

Extraction of reflected events from sonic-log waveforms using the Karhunen-Loève transform

Geophysics ◽  
2017 ◽  
Vol 82 (5) ◽  
pp. D265-D277 ◽  
Author(s):  
Junxiao Li ◽  
Kristopher A. Innanen ◽  
Guo Tao
Keyword(s):  
Principal Components ◽  
Laboratory Data ◽  
Synthetic Data ◽  
P Wave ◽  
Stoneley Wave ◽  
S Wave ◽  
Data Set ◽  
Sonic Log ◽  
Karhunen Loeve Transform ◽  
Wave Modes

Sonic-reflection logging, a recently developed borehole geophysical scheme, is in principle capable of providing a clear view of outside the well bore. In this type of acoustic well logging, a key technical obstacle is that the reflected wave signal is almost entirely obscured by the directly arriving P-, S-, and Stoneley wave modes. Effective extraction of these reflection signals from the full acoustic waveforms is therefore a critical data-processing step. We have examined the use of the Karhunen-Loève (KL) transform, combined with a band-limiting filter, as a technique for the extraction of reflections of interest from a mixture with directly arriving wave modes of much higher amplitude. Under the assumption that large energy (squared-amplitude) differences exist between each wave component, the direct Stoneley wave, S-wave, and the P-wave are eliminated sequentially by subtracting the most significant principal components, after which the remaining signal is seen to be dominated by reflected events. Thereafter, the extracted reflections can be used in migration to provide interpretable images of the structures outside the borehole. Synthetic data are used to develop and justify our procedure for subtraction of appropriate KL principal components. Laboratory data are used to demonstrate in detail the suppression of unwanted modes. For comparison, the multiscale slowness-time-coherence method is applied to extract reflections from the same data set. The procedure is exemplified on a field data case with attention paid in particular to the consequences to imaging of near-borehole structures.

Local and global fluid effects on sonic wave modes

Geophysics ◽  
2017 ◽  
Vol 82 (6) ◽  
pp. D369-D381 ◽  
Author(s):  
Elliot J. H. Dahl ◽  
Kyle T. Spikes
Keyword(s):  
Rayleigh Wave ◽  
Wave Velocity ◽  
Fluid Pressure ◽  
Wave Mode ◽  
P Wave ◽  
Stoneley Wave ◽  
S Wave ◽  
Local Pressure ◽  
Wave Velocities ◽  
Wave Modes

Most subsurface formations of value to exploration contain a heterogeneous fluid-filled pore space, where local fluid-pressure effects can significantly change the velocities of passing seismic waves. To better understand the effect of these local pressure gradients on borehole wave propagation, we combined Chapman’s squirt-flow model with Biot’s poroelastic theory. We applied the unified theory to a slow and fast formation with permeable borehole walls containing different quantities of compliant pores. These results are compared with those for a formation with no soft pores. The discrete wavenumber summation method with a monopole point source generates the wavefields consisting of the P-, S-, leaky-P, Stoneley, and pseudo-Rayleigh waves. The resulting synthetic wave modes are processed using a weighted spectral semblance (WSS) algorithm. We found that the resulting WSS dispersion curves closely matched the analytical expressions for the formation compressional velocity and solutions to the period equation for dispersion for the P-wave, Stoneley-wave, and pseudo-Rayleigh wave phase velocities in the slow and fast formations. The WSS applied to the S-wave part of the waveforms, however, did not correlate as well with its respective analytical expression for formation S-wave velocity, most likely due to interference of the pseudo-Rayleigh wave. To separate changes in formation P- and S-wave velocities versus fluid-flow effects on the Stoneley-wave mode, we computed the slow-P wave dispersion for the same formations. We found that fluid-saturated soft pores significantly affected the P- and S-wave effective formation velocities, whereas the slow-P wave velocity was rather insensitive to the compliant pores. Thus, the large phase-velocity effect on the Stoneley wave mode was mainly due to changes in effective formation P- and S-wave velocities and not to additional fluid mobility.

A finite-difference approach for solving pure quasi-P-wave equations in transversely isotropic and orthorhombic media

Geophysics ◽  
2018 ◽  
Vol 83 (4) ◽  
pp. C161-C172 ◽  
Author(s):  
Xueyan Li ◽  
Hejun Zhu
Keyword(s):  
Finite Difference ◽  
Wave Equations ◽  
Differential Operators ◽  
Transversely Isotropic ◽  
Coupled Systems ◽  
P Wave ◽  
Finite Difference Schemes ◽  
S Wave ◽  
P Waves ◽  
Pseudo Differential Operators

Starting from the dispersion relation and setting S-wave velocity along symmetry axes to zero, pseudoacoustic-wave equations have been proposed to describe the kinematics of acoustic wavefields in transversely isotropic (TI) and orthorhombic media. To date, the numerical stability of the pseudoacoustic-wave equations has been improved by developing coupled systems of wave equations; however, most simulations still suffer from S-wave artifacts that are the fundamental solutions of the fourth- and sixth-order partial differential equations. Pure quasi-P-wave equations accurately describe the traveltimes of P-waves in TI and orthorhombic media and are free of S-wave artifacts. However, it is difficult to directly solve the pure quasi-P-wave equations using conventional finite-difference schemes due to the presence of pseudo-differential operators. We approximated these pseudo-differential operators by algebraic expressions, whose coefficients can be determined by minimizing differences between the true and approximated values of the pseudo-differential operators in the wavenumber domain. The derived new coupled systems involve modified acoustic-wave equations and a Poisson’s equation that can be solved by conventional finite-difference stencils and fast Poisson’s solver. Several 2D and 3D numerical examples demonstrate that the simulations based on the new systems are free of S-wave artifacts and have correct kinematics of quasi-P-waves in TI and orthorhombic media.

scholarly journals Reflection Full Waveform Inversion with Decoupled Elastic-wave Equations in Inhomogeneous Medium

2021 ◽  
Vol 64 (1) ◽  
Author(s):  
Zhanyuan Liang ◽  
Guochen Wu ◽  
Xiaoyu Zhang ◽  
Qingyang Li
Keyword(s):  
Elastic Wave ◽  
Inhomogeneous Medium ◽  
Wave Velocity ◽  
Wave Equations ◽  
Waveform Inversion ◽  
P Wave ◽  
Full Waveform Inversion ◽  
S Wave ◽  
Full Waveform ◽  
Elastic Wave Equations

Reflection full-waveform inversion (RFWI) can reduce the nonlinearity of inversion providing an accurate initial velocity model for full-waveform inversion (FWI) through the tomographic components (low-wavenumber). However, elastic-wave reflection full-waveform inversion (ERFWI) is more vulnerable to the problem of local minimum due to the complicated multi-component wavefield. Our algorithm first divides kernels of ERFWI into four subkernels based on the theory of decoupled elastic-wave equations. Then we try to construct the tomographic components of ERFWI with only single-component wavefields, similarly to acoustic inversions. However, the S-wave velocity is still vulnerable to the coupling effects because of P-wave components contained in the S-wavefield in an inhomogeneous medium. Therefore we develop a method for decoupling elastic- wave equations in an inhomogeneous medium, which is applied to the decomposition of kernels in ERFWI. The new decoupled system can improve the accuracy of S-wavefield and hence further reduces the high-wavenumber crosstalk in the subkernel of S-wave velocity after kernels are decomposed. The numerical examples of Sigsbee2A model demonstrate that our ERFWI method with decoupled elastic-wave equations can efficiently recover the low-wavenumber components of the model and improve the precision of the S-wave velocity.

scholarly journals Post-collisional mantle delamination in the Dinarides implied from staircases of Oligo-Miocene uplifted marine terraces

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Philipp Balling ◽  
Christoph Grützner ◽  
Bruno Tomljenović ◽  
Wim Spakman ◽  
Kamil Ustaszewski
Keyword(s):  
Balkan Peninsula ◽  
Receiver Functions ◽  
P Wave ◽  
S Wave ◽  
Slab Geometry ◽  
Surface Uplift ◽  
River Incision ◽  
Marine Terraces ◽  
Convergence System ◽  
Internal Dinarides

AbstractThe Dinarides fold-thrust belt on the Balkan Peninsula resulted from convergence between the Adriatic and Eurasian plates since Mid-Jurassic times. Under the Dinarides, S-wave receiver functions, P-wave tomographic models, and shear-wave splitting data show anomalously thin lithosphere overlying a short down-flexed slab geometry. This geometry suggests a delamination of Adriatic lithosphere. Here, we link the evolution of this continental convergence system to hitherto unreported sets of extensively uplifted Oligocene–Miocene (28–17 Ma) marine terraces preserved at elevations of up to 600 m along the Dinaric coastal range. River incision on either side of the Mediterranean-Black Sea drainage divide is comparable to the amounts of terrace uplift. The preservation of the uplifted terraces implies that the most External Dinarides did not experience substantial deformation other than surface uplift in the Neogene. These observations and the contemporaneous emplacement of igneous rocks (33–22 Ma) in the internal Dinarides suggest that the Oligo-Miocene orogen-wide uplift was driven by post-break-off delamination of the Adriatic lithospheric mantle, this was followed by isostatic readjustment of the remaining crust. Our study details how lithospheric delamination exerts an important control on crustal deformation and that its crustal signature and geomorphic imprint can be preserved for millions of years.

scholarly journals S-wave experiments for the exploration of a deep geothermal carbonate reservoir in the German Molasse Basin

2021 ◽  
Vol 9 (1) ◽  
Author(s):  
Britta Wawerzinek ◽  
Hermann Buness ◽  
Hartwig von Hartmann ◽  
David C. Tanner
Keyword(s):  
Upper Jurassic ◽  
Carbonate Reservoir ◽  
P Wave ◽  
Seismic Survey ◽  
Seismic Exploration ◽  
Molasse Basin ◽  
S Wave ◽  
Induced Earthquakes ◽  
Conversion Point ◽  
Facies Classification

AbstractThere are many successful geothermal projects that exploit the Upper Jurassic aquifer at 2–3 km depth in the German Molasse Basin. However, up to now, only P-wave seismic exploration has been carried out. In an experiment in the Greater Munich area, we recorded S-waves that were generated by the conventional P-wave seismic survey, using 3C receivers. From this, we built a 3D volume of P- to S-converted (PS) waves using the asymptotic conversion point approach. By combining the P-volume and the resulting PS-seismic volume, we were able to derive the spatial distribution of the vp/vs ratio of both the Molasse overburden and the Upper Jurassic reservoir. We found that the vp/vs ratios for the Molasse units range from 2.0 to 2.3 with a median of 2.15, which is much higher than previously assumed. This raises the depth of hypocenters of induced earthquakes in surrounding geothermal wells. The vp/vs ratios found in the Upper Jurassic vary laterally between 1.5 and 2.2. Since no boreholes are available for verification, we test our results against an independently derived facies classification of the conventional 3D seismic volume and found it correlates well. Furthermore, we see that low vp/vs ratios correlate with high vp and vs velocities. We interpret the latter as dolomitized rocks, which are connected with enhanced permeability in the reservoir. We conclude that 3C registration of conventional P-wave surveys is worthwhile.

Inverse design of layered periodic wave barriers based on deep learning

2021 ◽  
pp. 146442072110168
Author(s):  
Chen-Xu Liu ◽  
Gui-Lan Yu
Keyword(s):  
Deep Learning ◽  
Activation Function ◽  
Periodic Wave ◽  
P Wave ◽  
Soil Parameters ◽  
S Wave ◽  
Output Frequency ◽  
Great Generality ◽  
Typical Range ◽  
Deep Learning Model

This study presents an approach based on deep learning to design layered periodic wave barriers with consideration of typical range of soil parameters. Three cases are considered where P wave and S wave exist separately or simultaneously. The deep learning model is composed of an autoencoder with a pretrained decoder which has three branches to output frequency attenuation domains for three different cases. A periodic activation function is used to improve the design accuracy, and condition variables are applied in the code layer of the autoencoder to meet the requirements of practical multi working conditions. Forty thousand sets of data are generated to train, validate, and test the model, and the designed results are highly consistent with the targets. The presented approach has great generality, feasibility, rapidity, and accuracy on designing layered periodic wave barriers which exhibit good performance in wave suppression in targeted frequency range.

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