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1
Valentina Socco, Laura, and Cesare Comina. "Time-average velocity estimation through surface-wave analysis: Part 2 — P-wave velocity." GEOPHYSICS 82, no. 3 (May 1, 2017): U61—U73. http://dx.doi.org/10.1190/geo2016-0368.1.
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Surface waves (SWs) in seismic records can be used to extract local dispersion curves (DCs) along a seismic line. These curves can be used to estimate near-surface S-wave velocity models. If the velocity models are used to compute S-wave static corrections, the required information consists of S-wave time-average velocities that define the one-way time for a given datum plan depth. However, given the wider use of P-wave reflection seismic with respect to S-wave surveys, the estimate of P-wave time-average velocity would be more useful. We therefore focus on the possibility of also extracting time-average P-wave velocity models from SW dispersion data. We start from a known 1D S-wave velocity model along the line, with its relevant DC, and we estimate a wavelength/depth relationship for SWs. We found that this relationship is sensitive to Poisson’s ratio, and we develop a simple method for estimating an “apparent” Poisson’s ratio profile, defined as the Poisson’s ratio value that relates the time-average S-wave velocity to the time-average P-wave velocity. Hence, we transform the time-average S-wave velocity models estimated from the DCs into the time-average P-wave velocity models along the seismic line. We tested the method on synthetic and field data and found that it is possible to retrieve time-average P-wave velocity models with uncertainties mostly less than 10% in laterally varying sites and one-way traveltime for P-waves with less than 5 ms uncertainty with respect to P-wave tomography data. To our knowledge, this is the first method for reliable estimation of P-wave velocity from SW data without any a priori information or additional data.
2
Chen, S. T. "Shear‐wave logging with dipole sources." GEOPHYSICS 53, no. 5 (May 1988): 659–67. http://dx.doi.org/10.1190/1.1442500.
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Laboratory measurements have verified a novel technique for direct shear‐wave logging in hard and soft formations with a dipole source, as recently suggested in theoretical studies. Conventional monopole logging tools are not capable of measuring shear waves directly. In particular, no S waves are recorded in a soft formation with a conventional monopole sonic tool because there are no critically refracted S rays when the S-wave velocity of the rock is less than the acoustic velocity of the borehole fluid. The present studies were conducted in the laboratory with scale models representative of sonic logging conditions in the field. We have used a concrete model to represent hard formations and a plastic model to simulate a soft formation. The dipole source, operating at frequencies lower than those conventionally used in logging, substantially suppressed the P wave and excited a wave train whose first arrival traveled at the S-wave velocity. As a result, one can use a dipole source to log S-wave velocity directly on‐line by picking the first arrival of the full wave train, in a process similar to that used in conventional P-wave logging. Laboratory experiments with a conventional monopole source in a soft formation did not produce S waves. However, the S-wave velocity was accurately estimated by using Biot’s theory, which required measuring the Stoneley‐wave velocity and knowing other borehole parameters.
3
Steiner, Brian, Erik H. Saenger, and Stefan M. Schmalholz. "Time-reverse imaging with limited S-wave velocity model information." GEOPHYSICS 76, no. 5 (September 2011): MA33—MA40. http://dx.doi.org/10.1190/geo2010-0303.1.
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Time-reverse imaging is a wave propagation algorithm for locating sources. Signals recorded by synchronized receivers are reversed in time and propagated back to the source location by elastic wavefield extrapolation. Elastic wavefield extrapolation requires a P-wave as well as an S-wave velocity model. The velocity models available from standard reflection seismic methods are usually restricted to only P-waves. In this study, we use synthetically produced time signals to investigate the accuracy of seismic source localization by means of time-reverse imaging with the correct P-wave and a perturbed S-wave velocity model. The studies reveal that perturbed S-wave velocity models strongly influence the intensity and position of the focus. Imaging the results with the individual maximum energy density for both body wave types instead of mixed modes allows individual analysis of the two body waves. P-wave energy density images render stable focuses in case of a correct P-wave and incorrect S-wave velocity model. Thus, P-wave energy density seems to be a more suitable imaging condition in case of a high degree of uncertainty in the S-wave velocity model.
4
Li, Lun, and Yuanyuan V. Fu. "Surface-Wave Tomography of Eastern and Central Tibet from Two-Plane-Wave Inversion: Rayleigh-Wave and Love-Wave Phase Velocity Maps." Bulletin of the Seismological Society of America 110, no. 3 (March 17, 2020): 1359–71. http://dx.doi.org/10.1785/0120190199.
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ABSTRACT An understanding of mantle dynamics occurring beneath the Tibetan plateau requires a detailed image of its seismic velocity and anisotropic structure. Surface waves at long periods (>50 s) could provide such critical information. Though Rayleigh-wave phase velocity maps have been constructed in the Tibetan regions using ambient-noise tomography (ANT) and regional earthquake surface-wave tomography, Love-wave phase velocity maps, especially those at longer periods (>50 s), are rare. In this study, two-plane-wave teleseismic surface-wave tomography is applied to develop 2D Rayleigh-wave and Love-wave phase velocity maps at periods between 20 and 143 s across eastern and central Tibet and its surroundings using four temporary broadband seismic experiments. These phase velocity maps share similar patterns and show high consistency with those previously obtained from ANT at overlapping periods (20–50 s), whereas our phase velocity maps carry useful information at longer periods (50–143 s). Prominent slow velocity is imaged at periods of 20–143 s beneath the interior of the Tibetan plateau (i.e., the Songpan–Ganzi terrane, the Qiangtang terrane, and the Lhasa terrane), implying the existence of thick Tibetan crust along with warm and weak Tibetan lithosphere. In contrast, the dispersal of fast velocity anomalies coincides with mechanically strong, cold tectonic blocks, such as the Sichuan basin and the Qaidam basin. These phase velocity maps could be used to construct 3D shear-wave velocity and radial seismic anisotropy models of the crust and upper mantle down to 250 km across the eastern and central Tibetan plateau.
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Tang, Huai-Gu, Bing-Shou He, and Hai-Bo Mou. "P- and S-wave energy flux density vectors." GEOPHYSICS 81, no. 6 (November 2016): T357—T368. http://dx.doi.org/10.1190/geo2016-0245.1.
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The conventional energy flux density vector indicates the propagation direction of mixed P- and S-wave wavefields, which means when a wavefront of P-wave encounters a wavefront of S-wave with different propagation directions, the vectors cannot indicate both directions accurately. To avoid inaccuracies caused by superposition of P- and S-waves in a conventional energy flux density vector, P- and S-wave energy flux density vectors should be calculated separately. Because the conventional energy flux density vector is obtained by multiplying the stress tensor by the particle-velocity vector, the common way to calculate P- and S-wave energy flux density vectors is to decompose the stress tensor and particle-velocity vector into the P- and S-wave parts before multiplication. However, we have found that the P-wave still interfere with the S-wave energy flux density vector calculated by this method. Therefore, we have developed a new method to calculate P- and S-wave energy flux density vectors based on a set of new equations but not velocity-stress equations. First, we decompose elastic wavefield by the set of equations to obtain the P- and S-wave particle-velocity vectors, dilatation scalar, and rotation vector. Then, we calculate the P-wave energy flux density vector by multiplying the P-wave particle-velocity vector by dilatation scalar, and we calculate the S-wave energy flux density vector as a cross product of the S-wave particle-velocity vector and rotation vector. The vectors can indicate accurate propagation directions of P- and S-waves, respectively, without being interfered by the superposition of the two wave modes.
6
Zhang, Zhen-Dong, and Tariq Alkhalifah. "Wave-equation Rayleigh-wave dispersion inversion using fundamental and higher modes." GEOPHYSICS 84, no. 4 (July 1, 2019): EN57—EN65. http://dx.doi.org/10.1190/geo2018-0506.1.
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Recorded surface waves often provide reasonable estimates of the S-wave velocity in the near surface. However, existing algorithms are mainly based on the 1D layered-model assumption and require picking the dispersion curves either automatically or manually. We have developed a wave-equation-based inversion algorithm that inverts for S-wave velocities using fundamental and higher mode Rayleigh waves without picking an explicit dispersion curve. Our method aims to maximize the similarity of the phase velocity spectrum ([Formula: see text]) of the observed and predicted surface waves with all Rayleigh-wave modes (if they exist) included in the inversion. The [Formula: see text] spectrum is calculated using the linear Radon transform applied to a local similarity-based objective function; thus, we do not need to pick velocities in spectrum plots. As a result, the best match between the predicted and observed [Formula: see text] spectrum provides the optimal estimation of the S-wave velocity. We derive S-wave velocity updates using the adjoint-state method and solve the optimization problem using a limited-memory Broyden-Fletcher-Goldfarb-Shanno algorithm. Our method excels in cases in which the S-wave velocity has vertical reversals and lateral variations because we used all-modes dispersion, and it can suppress the local minimum problem often associated with full-waveform inversion applications. Synthetic and field examples are used to verify the effectiveness of our method.
7
Socco, Laura Valentina, Cesare Comina, and Farbod Khosro Anjom. "Time-average velocity estimation through surface-wave analysis: Part 1 — S-wave velocity." GEOPHYSICS 82, no. 3 (May 1, 2017): U49—U59. http://dx.doi.org/10.1190/geo2016-0367.1.
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In some areas, the estimation of static corrections for land seismic data is a critical step of the processing workflow. It often requires the execution of additional surveys and data analyses. Surface waves (SWs) in seismic records can be processed to extract local dispersion curves (DCs) that can be used to estimate near-surface S-wave velocity models. Here we focus on the direct estimation of time-average S-wave velocity models from SW DCs without the need to invert the data. Time-average velocity directly provides the value of one-way time, given a datum plan depth. The method requires the knowledge of one 1D S-wave velocity model along the seismic line, together with the relevant DC, to estimate a relationship between SW wavelength and investigation depth on the time-average velocity model. This wavelength/depth relationship is then used to estimate all the other time-average S-wave velocity models along the line directly from the DCs by means of a data transformation. This approach removes the need for extensive data inversion and provides a simple method suitable for industrial workflows. We tested the method on synthetic and field data and found that it is possible to retrieve the time-average velocity models with uncertainties less than 10% in sites with laterally varying velocities. The error on one-way times at various depths of the datum plan retrieved by the time-average velocity models is mostly less than 5 ms for synthetic and field data.
8
Mora, Peter. "Elastic wave‐field inversion of reflection and transmission data." GEOPHYSICS 53, no. 6 (June 1988): 750–59. http://dx.doi.org/10.1190/1.1442510.
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Elastic inversion of multioffset seismic data by wave‐ field fitting yields a maximum probability P-wave and S-wave velocity and density model of the Earth. Theoretically, the inversion accounts for all elastic waves including reflected and transmitted waves, mode conversions, shear waves, head waves, Rayleigh waves, etc. These different wave types tend to resolve different components of the Earth properties. By inverting two‐ component synthetic data, I show that reflection data mainly resolve high wavenumbers, while transmission data mainly resolve low wavenumbers of the P-wave and S-wave velocity model. The inversion of reflection data (shot gathers) yields a result that looks like a prestack elastic migration but the meaning of the inverted data is not simply reflectivity: it is the P-wave and S-wave velocity perturbation. The inversion of transmission data (VSPs) yields a solution that contains useful interval velocity information and is comparable to an elastic diffraction tomography result.
9
Chmiel, M., A. Mordret, P. Boué, F. Brenguier, T. Lecocq, R. Courbis, D. Hollis, X. Campman, R. Romijn, and W. Van der Veen. "Ambient noise multimode Rayleigh and Love wave tomography to determine the shear velocity structure above the Groningen gas field." Geophysical Journal International 218, no. 3 (May 24, 2019): 1781–95. http://dx.doi.org/10.1093/gji/ggz237.
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SUMMARY The Groningen gas field is one of the largest gas fields in Europe. The continuous gas extraction led to an induced seismic activity in the area. In order to monitor the seismic activity and study the gas field many permanent and temporary seismic arrays were deployed. In particular, the extraction of the shear wave velocity model is crucial in seismic hazard assessment. Local S-wave velocity-depth profiles allow us the estimation of a potential amplification due to soft sediments. Ambient seismic noise tomography is an interesting alternative to traditional methods that were used in modelling the S-wave velocity. The ambient noise field consists mostly of surface waves, which are sensitive to the Swave and if inverted, they reveal the corresponding S-wave structures. In this study, we present results of a depth inversion of surface waves obtained from the cross-correlation of 1 month of ambient noise data from four flexible networks located in the Groningen area. Each block consisted of about 400 3-C stations. We compute group velocity maps of Rayleigh and Love waves using a straight-ray surface wave tomography. We also extract clear higher modes of Love and Rayleigh waves. The S-wave velocity model is obtained with a joint inversion of Love and Rayleigh waves using the Neighbourhood Algorithm. In order to improve the depth inversion, we use the mean phase velocity curves and the higher modes of Rayleigh and Love waves. Moreover, we use the depth of the base of the North Sea formation as a hard constraint. This information provides an additional constraint for depth inversion, which reduces the S-wave velocity uncertainties. The final S-wave velocity models reflect the geological structures up to 1 km depth and in perspective can be used in seismic risk modelling.
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Su, Yuanda, Xinding Fang, and Xiaoming Tang. "Measurement of the shear slowness of slow formations from monopole logging-while-drilling sonic logs." GEOPHYSICS 85, no. 1 (December 6, 2019): D45—D52. http://dx.doi.org/10.1190/geo2019-0236.1.
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Acoustic logging-while-drilling (LWD) is used to measure formation velocity/slowness during drilling. In a fast formation, in which the S-wave velocity is higher than the borehole-fluid velocity, monopole logging can be used to obtain P- and S-wave velocities by measuring the corresponding refracted waves. In a slow formation, in which the S-wave velocity is less than the borehole-fluid velocity, because the fully refracted S-wave is missing, quadrupole logging has been developed and used for S-wave slowness measurement. A recent study based on numerical modeling implies that monopole LWD can generate a detectable transmitted S-wave in a slow formation. This nondispersive transmitted S-wave propagates at the formation S-wave velocity and thus can be used for measuring the S-wave slowness of a slow formation. We evaluate a field example to demonstrate the applicability of monopole LWD in determining the S-wave slowness of slow formations. We compare the S-wave slowness extracted from a monopole LWD data set acquired in a slow formation and the result derived from the quadrupole data recorded in the same logging run. The results indicated that the S-wave slowness can be reliably determined from monopole LWD sonic data in fairly slow formations. However, we found that the monopole approach is not applicable to very slow formations because the transmitted S-wave becomes too weak to detect when the formation S-wave slowness is much higher than the borehole-fluid slowness.
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Li, Bowen, and Alexey Stovas. "Decoupling approximation of P- and S-wave phase velocities in orthorhombic media." GEOPHYSICS 87, no. 2 (February 16, 2022): T169—T182. http://dx.doi.org/10.1190/geo2021-0394.1.
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Characterizing the kinematics of seismic waves in elastic orthorhombic media involves nine independent parameters. All wave modes, P-, S1-, and S2-waves, are intrinsically coupled. Because the P-wave propagation in orthorhombic media is weakly dependent on the three S-wave velocity parameters, they are set to zero under the acoustic assumption. The number of parameters required for the corresponding acoustic wave equation is thus reduced from nine to six, which is very practical for the inversion algorithm. However, the acoustic wavefields generated by the finite-difference scheme suffer from two types of S-wave artifacts, which may result in noticeable numerical dispersion and even instability issues. Avoiding such artifacts requires a class of spectral methods based on the low-rank decomposition. To implement a six-parameter pure P-wave approximation in orthorhombic media, we have developed a novel phase velocity approximation approach from the perspective of decoupling P- and S-waves. In the exact P-wave phase velocity expression, we find that the two algebraic expressions related to the S1- and S2-wave phase velocities play a negligible role. After replacing these two algebraic expressions with the designed constant and variable, respectively, the exact P-wave phase velocity expression is greatly simplified and naturally decoupled from the characteristic equation. Similarly, the number of required parameters is reduced from nine to six. We also derive an approximate S-wave phase velocity equation, which supports the coupled S1- and S2-waves and involves nine independent parameters. Error analyses based on several orthorhombic models confirm the reasonable and stable accuracy performance of our phase velocity approximation. We further derive the approximate dispersion relations for the P-wave and the S-wave system in orthorhombic media. Numerical experiments demonstrate that the corresponding P- and S-wavefields are free of artifacts and exhibit good accuracy and stability.
12
Dai, Fucai, Feng Zhang, and Xiangyang Li. "SH-SH wave inversion for S-wave velocity and density." GEOPHYSICS 87, no. 3 (February 23, 2022): A25—A32. http://dx.doi.org/10.1190/geo2021-0314.1.
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SS-waves (SV-SV waves and SH-SH waves) are capable of inverting S-wave velocity ([Formula: see text]) and density ([Formula: see text]) because they are sensitive to both parameters. SH-SH waves can be separated from multicomponent data sets more effectively than the SV-SV wave because the former is decoupled from the PP-wave in isotropic media. In addition, the SH-SH wave can be better modeled than the SV-SV wave in the case of strong velocity/impedance contrast because the SV-SV wave has multicritical angles, some of which can be quite small when velocity/impedance contrast is strong. We derive an approximate equation of the SH-SH wave reflection coefficient as a function of [Formula: see text] and [Formula: see text] in natural logarithm variables. The approximation has high accuracy, and it enables the inversion of [Formula: see text] and [Formula: see text] in a direct manner. Both coefficients corresponding to [Formula: see text] and [Formula: see text] are “model-parameter independent” and thus there is no need for prior estimate of any model parameter in inversion. Then, we develop an SH-SH wave inversion method and demonstrate it by using synthetic data sets and a real SH-SH wave prestack data set from the west of China. We find that [Formula: see text] and [Formula: see text] can be reliably estimated from the SH-SH wave of small angles.
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Groos, Lisa, Martin Schäfer, Thomas Forbriger, and Thomas Bohlen. "Application of a complete workflow for 2D elastic full-waveform inversion to recorded shallow-seismic Rayleigh waves." GEOPHYSICS 82, no. 2 (March 1, 2017): R109—R117. http://dx.doi.org/10.1190/geo2016-0284.1.
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The S-wave velocity of the shallow subsurface can be inferred from shallow-seismic Rayleigh waves. Traditionally, the dispersion curves of the Rayleigh waves are inverted to obtain the (local) S-wave velocity as a function of depth. Two-dimensional elastic full-waveform inversion (FWI) has the potential to also infer lateral variations. We have developed a novel workflow for the application of 2D elastic FWI to recorded surface waves. During the preprocessing, we apply a line-source simulation (spreading correction) and perform an a priori estimation of the attenuation of waves. The iterative multiscale 2D elastic FWI workflow consists of the preconditioning of the gradients in the vicinity of the sources and a source-wavelet correction. The misfit is defined by the least-squares norm of normalized wavefields. We apply our workflow to a field data set that has been acquired on a predominantly depth-dependent velocity structure, and we compare the reconstructed S-wave velocity model with the result obtained by a 1D inversion based on wavefield spectra (Fourier-Bessel expansion coefficients). The 2D S-wave velocity model obtained by FWI shows an overall depth dependency that agrees well with the 1D inversion result. Both models can explain the main characteristics of the recorded seismograms. The small lateral variations in S-wave velocity introduced by FWI additionally explain the lateral changes of the recorded Rayleigh waves. The comparison thus verifies the applicability of our 2D FWI workflow and confirms the potential of FWI to reconstruct shallow small-scale lateral changes of S-wave velocity.
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Cova, Raul, David Henley, and Kristopher A. Innanen. "Computing near-surface velocity models for S-wave static corrections using raypath interferometry." GEOPHYSICS 83, no. 3 (May 1, 2018): U23—U34. http://dx.doi.org/10.1190/geo2017-0340.1.
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A near-surface velocity model is one of the typical products generated when computing static corrections, particularly in the processing of PP data. Critically refracted waves are the input usually needed for this process. In addition, for the converted PS mode, S-wave near-surface corrections must be applied at the receiver locations. In this case, however, critically refracted S-waves are difficult to identify when using P-wave energy sources. We use the [Formula: see text]-[Formula: see text] representation of the converted-wave data to capture the intercept-time differences between receiver locations. These [Formula: see text]-differences are then used in the inversion of a near-surface S-wave velocity model. Our processing workflow provides not only a set of raypath-dependent S-wave static corrections, but also a velocity model that is based on those corrections. Our computed near-surface S-wave velocity model can be used for building migration velocity models or to initialize elastic full-waveform inversions. Our tests on synthetic and field data provided superior results to those obtained by using a surface-consistent solution.
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Wang, Chenlong, Jiubing Cheng, Wiktor Waldemar Weibull, and Børge Arntsen. "Elastic wave-equation migration velocity analysis preconditioned through mode decoupling." GEOPHYSICS 84, no. 3 (May 1, 2019): R341—R353. http://dx.doi.org/10.1190/geo2018-0181.1.
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Multicomponent seismic data acquisition can reveal more information about geologic structures and rock properties than single component acquisition. Full elastic wave seismic imaging, which uses multicomponent seismic to its full potential, is promising because it provides more opportunities to understand the material properties of the earth by the joint use of P- and S-waves. A prerequisite of seismic imaging is the availability of a reliable macrovelocity model. Migration velocity analysis for P-waves, which can fill that requirement for the P-wave velocity, has been well-studied, especially under the acoustic approximation. However, a reliable estimation of the S-wave velocities remains troublesome. Elastic wave-equation migration velocity analysis has the potential to build P- and S-wave velocity models together, but it inevitably suffers from the effects of mode coupling and conversion in the forward and adjoint wavefield reconstructions. We have developed a differential semblance optimization approach to sequentially invert the background P- and S-wave velocity models from extended PP- and PS-images in the subsurface offset domain. Preconditioning of the gradients with respect to the S-wave velocity through mode decoupling can improve the reliability of the optimization. Numerical investigations with synthetic examples demonstrate the effectiveness of gradient preconditioning and the feasibility of our migration velocity analysis approach for elastic wave imaging.
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Athanasopoulos, Nikolaos, Edgar Manukyan, Thomas Bohlen, and Hansruedi Maurer. "Time–frequency windowing in multiparameter elastic FWI of shallow seismic wavefield." Geophysical Journal International 222, no. 2 (May 15, 2020): 1164–77. http://dx.doi.org/10.1093/gji/ggaa242.
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SUMMARY Full-waveform inversion of shallow seismic wavefields is a promising method to infer multiparameter models of elastic material properties (S-wave velocity, P-wave velocity and mass density) of the shallow subsurface with high resolution. Previous studies used either the refracted Pwaves to reconstructed models of P-wave velocity or the high-amplitude Rayleigh waves to infer the S-wave velocity structure. In this work, we propose a combination of both wavefields using continuous time–frequency windowing. We start with the contribution of refracted P waves and gradually increase the time window to account for scattered body waves, higher mode Rayleigh waves and finally the fundamental Rayleigh wave mode. The opening of the time window is combined with opening the frequency bandwidth of input signals to avoid cycle skipping. Synthetic reconstruction tests revealed that the reconstruction of P-wave velocity model and mass density can be improved. The S-wave velocity reconstruction is still accurate and robust and is slightly benefitted by time–frequency windowing. In a field data application, we observed that time–frequency windowing improves the consistency of multiparameter models. The inferred models are in good agreement with independent geophysical information obtained from ground-penetrating radar and full-waveform inversion of SH waves.
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Xu, Gang, Jiawei Liu, Yunlong Wang, Hongwei Jin, and Chaofeng Wang. "Experimental Study on the Effect of Gas Adsorption and Desorption on Ultrasonic Velocity and Elastic Mechanical Parameters of Coal." Sustainability 14, no. 22 (November 14, 2022): 15055. http://dx.doi.org/10.3390/su142215055.
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The rapid and accurate identification of the physical characteristics of coal by means of ultrasonic detection is of great significance to ensure safe mining of coal and efficient development of coal seam methane. In this paper, the ultrasonic velocity testing experiments of coal during gas adsorption and desorption were carried out, utilizing a low frequency petrophysical measurement device with primary and fractured coal as the research objects. The variations in the elastic mechanical parameters and ultrasonic velocity of coal samples were analyzed to elucidate the influence mechanism that gas adsorption and desorption have on them. During gas adsorption and desorption, the longitudinal wave velocity of the primary structure coal varies from 1990 m/s to 2200 m/s, and the transverse wave velocity varies from 1075 m/s to 1160 m/s, while the longitudinal wave velocity of the fractured structure coal varies from 1540 m/s to 1950 m/s, and the transverse wave velocity varies from 800 m/s to 1000 m/s. The elastic modulus and wave velocities, in both directions of the primary structural coal, were higher than those of the fractured structural coal. In comparison to the fractured structural coal, the main structural coal had a lower Poisson’s ratio. In addition, the spread of the elastic mechanical parameters and wave velocities, in both the longitudinal and transverse directions, was more pronounced in the fracture−structured coal than in the primary−structured coal. During gas adsorption and desorption, the speed of the coal’s longitudinal waves increased, and then decreased, due to the combined effect of gas adsorption expansion and pore gas pressure compression matrix effect. For this experiment, the maximum longitudinal wave velocity of the coal occurred at a gas pressure of 1.5 MPa. Primary structural coal has a longitudinal wave speed of 2103 m/s, whereas fragmented structural coal has a speed of 1925 m/s. The variation in the shear wave velocity of the coal is controlled only by the gas adsorption expansion effects. The shear wave velocity increases during gas adsorption and decreases during gas desorption. With the change of gas pressure, the longitudinal wave velocity can increase by 23.34%, and the shear wave velocity can increase by 17.97%. Coal undergoes changes to both its Poisson’s ratio and elastic modulus as a result of gas adsorption and desorption; these modifications are analogous to the velocity of longitudinal and shear waves, respectively.
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DU, QIZHEN, HUIZHU YANG, and YUAN DONG. "A STUDY ON SHEAR WAVE VELOCITY ESTIMATION AND FRACTURE DETECTION IN HTI MEDIA." Journal of Computational Acoustics 10, no. 03 (September 2002): 331–47. http://dx.doi.org/10.1142/s0218396x02001681.
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The paper presents estimates of the S-wave velocity and the crack density at which fractured reservoirs begin to play an important role in oil exploration. Transverse isotropy with a horizontal axis of symmetry (HTI) is the simplest azimuthally anisotropic model used to describe fractured reservoirs that contain parallel vertical cracks. A double profile concept is used to develop an equation for the P-S wave normal-moveout (NMO) velocity. The azimuthal NMO velocities of the P- and P-S waves can then be used to estimate the velocities of the S-waves and Thomsen's coefficient, γ. For multilayered media, a recursive equation is developed for the NMO velocity in each layer. The numerical results indicate that the S-wave NMO velocity can be accurately estimated using the P- and P-S wave NMO velocities in HTI media. An important parameter of fracture systems that can be measured from seismic data is the crack density which can be estimated using the NMO velocities of the P- and S-waves from horizontal reflectors. Therefore, fractures can be completely characterized by the joint inversion of P-waves and converted P-S waves in HTI media.
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Zhang, Shukui, and Shaoping Lu. "Residual moveout in angle gathers for converted waves." GEOPHYSICS 87, no. 3 (March 29, 2022): U81—U92. http://dx.doi.org/10.1190/geo2021-0366.1.
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Multicomponent seismic data have been increasingly collected, for example, with ocean-bottom node/cable surveys. Although the converted waves recorded in multicomponent seismic data have the potential to better illuminate the areas underneath complex structures than P-waves, they have not been widely used in depth imaging. Common industry practice is still limited to P-waves only mainly because the successful imaging of converted waves in prestack depth migration relies on accurate velocity models for P- and S-waves. However, the S-wave velocity model estimation via analysis of converted-wave moveout and tomography is still immature. We derive a general residual moveout (RMO) relation as a function of incident angle or as a reflection angle for converted waves, which can be used for converted-wave tomography based on angle-domain common-image gathers. Our derivation does not have certain limitations, such as slowly changing reflection angles or constant P/S-wave velocity ratios, as in existing algorithms available in the literature. Therefore, the proposed RMO equations are more accurate and can be helpful for S-wave velocity model building. The derived equations are validated using different numerical tests.
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Sun, Robert, Jinder Chow, and Kuang‐Jung Chen. "Phase correction in separating P‐ and S‐waves in elastic data." GEOPHYSICS 66, no. 5 (September 2001): 1515–18. http://dx.doi.org/10.1190/1.1487097.
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Two‐dimensional elastic data containing reflected P‐waves and converted S‐wave generated by a P‐source may be separated using dilatation and rotation calculation (Sun, 1999). The algorithm is a combination of elastic full wavefield extrapolation (Sun and McMechan, 1986; Chang and McMechan, 1987, 1994) and wave‐type separation using dilatation (divergence) and rotation (curl) calculations (Dellinger and Etgen, 1990). It includes (1) downward extrapolating the (multicomponent) elastic data in an elastic velocity model using the elastic wave equation, (2) calculating the dilatation to represent pure P‐waves and calculating the rotation to represent pure S‐waves at some depth, and (3) upward extrapolating the dilatation in a P‐velocity model and upward extrapolating the rotation in an S‐velocity model, using the acoustic wave equation for each.
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Ren, Zhiming, Qianzong Bao, and Bingluo Gu. "Joint wave-equation traveltime inversion of diving/direct and reflected waves for P- and S-wave velocity macromodel building." GEOPHYSICS 86, no. 4 (July 1, 2021): R603—R621. http://dx.doi.org/10.1190/geo2020-0762.1.
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Full-waveform inversion (FWI) suffers from the local minima problem and requires a sufficiently accurate starting model to converge to the correct solution. Wave-equation traveltime inversion (WETI) is an effective tool to retrieve the long-wavelength components of the velocity model. We have developed a joint diving/direct and reflected wave WETI (JDRWETI) method to build P- and S-wave velocity macromodels. We estimate the traveltime shifts of seismic events (diving/direct waves and PP- and PS-reflections) through the dynamic warping scheme and construct a misfit function using the time shifts of diving/direct and reflected waves. We derive the adjoint wave equations and the gradients with respect to the background models based on the joint misfit function. We apply the kernel decomposition scheme to extract the kernel of the diving/direct wave and the tomography kernels of PP- and PS-reflections. For an explosive source, the kernels of the diving/direct wave and PP-reflections and the kernel of the PS-reflections are used to compute the P- and S-wave gradients of the background models, respectively. We implement JDRWETI by a two-stage inversion workflow: First, we invert the P- and S-wave velocity models using the P-wave gradients, and then we improve the S-wave velocity model using the S-wave gradients. Numerical tests on synthetic and field data sets reveal that the JDRWETI method successfully recovers the long-wavelength components of P- and S-wave velocity models, which can be used for an initial model for the subsequent elastic FWI. Moreover, the JDRWETI method prevails over the existing reflection WETI method and the cascaded diving/direct and reflected wave WETI method, especially when large velocity errors are present in the shallow part of the starting models. The JDRWETI method with the two-stage inversion workflow can give rise to reasonable inversion results even for the model with different P- and S-wave velocity structures.
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Gao, Lingli, Yudi Pan, and Thomas Bohlen. "2-D multiparameter viscoelastic shallow-seismic full-waveform inversion: reconstruction tests and first field-data application." Geophysical Journal International 222, no. 1 (April 27, 2020): 560–71. http://dx.doi.org/10.1093/gji/ggaa198.
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SUMMARY 2-D full-waveform inversion (FWI) of shallow-seismic wavefields has recently become a novel way to reconstruct S-wave velocity models of the shallow subsurface with high vertical and lateral resolution. In most applications, seismic wave attenuation is ignored or considered as a passive modelling parameter only. In this study, we explore the feasibility and performance of multiparameter viscoelastic 2-D FWI in which seismic velocities and attenuation of P and S waves, respectively, and mass density are inverted simultaneously. Synthetic reconstruction experiments reveal that multiple crosstalks between all viscoelastic material parameters may occur. The reconstruction of S-wave velocity is always robust and of high quality. The parameters P-wave velocity and density exhibit weaker sensitivity and can be reconstructed more reliably by multiparameter viscoelastic FWI. Anomalies in S-wave attenuation can be recovered but with limited resolution. In a field-data application, a small-scale refilled trench is nicely delineated as a low P- and S-wave velocity anomaly. The reconstruction of P-wave velocity is improved by the simultaneous inversion of attenuation. The reconstructed S-wave attenuation reveals higher attenuation in the shallow weathering zone and weaker attenuation below. The variations in the reconstructed P- and S-wave velocity models are consistent with the reflectivity observed in a ground penetrating radar (GPR) profile.
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Huang, Huey-Chu, Tien-Han Shih, Cheng-Ta Hsu, and Cheng-Feng Wu. "Estimation of Shear-Wave Velocity Structures in Taichung, Taiwan, Using Array Measurements of Microtremors." Applied Sciences 12, no. 1 (December 24, 2021): 170. http://dx.doi.org/10.3390/app12010170.
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Near-surface S-wave velocity structures (VS) are crucial in site-effect studies and ground-motion simulations or predictions. We explored S-wave velocity structures in Taichung, the second-largest city in Taiwan by population, by employing array measurements of microtremors at a total of 53 sites. First, the fundamental-mode dispersion curves of Rayleigh waves were estimated by adopting the frequency–wavenumber analysis method. Second, the surface-wave inversion technique was used to calculate the S-wave velocity structures of the area. At many sites, observed phase velocities were almost flat, with a phase velocity of approximately 800–1300 m/s in the frequency range of 0.6–2 Hz. A high-velocity zone (VS of 900–1500 m/s) with a convex shape was observed at the shallow S-wave structures of these sites (depths of 50–500 m). On the basis of the inversion results, we constructed two-dimensional and three-dimensional contour maps to elucidate the variations of VS structures in Taichung. According to VS-contour maps at different depths, lowest S-wave velocities are found at the western coastal plain, whereas highest S-wave velocities appear on the eastern side. The S-wave velocity gradually decreases from east to west. Moreover, the S-wave velocity of the Tertiary bedrock is assumed to be 1500 m/s in the area. According to the depth-contour map (VS = 1500 m/s), the depths of the bedrock range from 250 m (the eastern part) to 1550 m (the western part). The thicknesses of the alluvium gradually decrease from west to east. Our results are consistent with the geology of the Taichung area.
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Xu, Shibo, Alexey Stovas, Tariq Alkhalifah, and Hitoshi Mikada. "New acoustic approximation for transversely isotropic media with a vertical symmetry axis." GEOPHYSICS 85, no. 1 (November 22, 2019): C1—C12. http://dx.doi.org/10.1190/geo2019-0100.1.
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Seismic data processing in the elastic anisotropic model is complicated due to multiparameter dependency. Approximations to the P-wave kinematics are necessary for practical purposes. The acoustic approximation for P-waves in a transversely isotropic medium with a vertical symmetry axis (VTI) simplifies the description of wave propagation in elastic media, and as a result, it is widely adopted in seismic data processing and analysis. However, finite-difference implementations of that approximation are plagued with S-wave artifacts. Specifically, the resulting wavefield also includes artificial diamond-shaped S-waves resulting in a redundant signal for many applications that require pure P-wave data. To derive a totally S-wave-free acoustic approximation, we have developed a new acoustic approximation for pure P-waves that is totally free of S-wave artifacts in the homogeneous VTI model. To keep the S-wave velocity equal to zero, we formulate the vertical S-wave velocity to be a function of the model parameters, rather than setting it to zero. Then, the corresponding P-wave phase and group velocities for the new acoustic approximation are derived. For this new acoustic approximation, the kinematics is described by a new eikonal equation for pure P-wave propagation, which defines the new vertical slowness for the P-waves. The corresponding perturbation-based approximation for our new eikonal equation is used to compare the new equation with the original acoustic eikonal. The accuracy of our new P-wave acoustic approximation is tested on numerical examples for homogeneous and multilayered VTI models. We find that the accuracy of our new acoustic approximation is as good as the original one for the phase velocity, group velocity, and the kinematic parameters such as vertical slowness, traveltime, and relative geometric spreading. Therefore, the S-wave-free acoustic approximation could be further applied in seismic processing that requires pure P-wave data.
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Yue, Chongwang, and Xiaopeng Yue. "Influence of Relaxation Frequency on Acoustic Wave in Unconsolidated Sands and Acoustic Logging Simulation." Journal of Theoretical and Computational Acoustics 26, no. 02 (June 2018): 1850014. http://dx.doi.org/10.1142/s2591728518500147.
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Apart from consolidated rocks, the effect of relaxation on acoustic propagation in unconsolidated sands cannot be neglected. In this paper, we study the influence of relaxation frequency on the propagation of acoustic waves. We compute the frequency-dependent velocities and attenuation of P1-wave, P2-wave, and S-wave at different bulk or shear relaxation frequency for plane wave. In addition, we derive the integral solutions of acoustic field equations in cylindrical coordinate system to simulate acoustic logging. The reflected acoustic waveforms in a borehole are calculated at different bulk or shear relaxation frequency. Calculation results show that the increase of bulk relaxation frequency will cause the velocity of P1-wave to decrease slightly, and the velocity of P2-wave to decrease substantially. The change of bulk relaxation frequency has no effect on the velocity of S-wave. The increase of bulk relaxation frequency will cause the attenuation of P1-wave or P2-wave to decrease or increase in different wave frequency range. The change of bulk relaxation frequency has no effect on the attenuation of S-wave. The increase of shear relaxation frequency will cause the velocity of P1-wave to increase slightly, and the velocity of P2-wave or S-wave to decrease substantially. The increase of the shear relaxation frequency will cause the attenuation of P1-wave, P2-wave or S-wave to decrease. For acoustic field in a borehole surrounded by unconsolidated sands, the effect of bulk or shear relaxation frequency on the velocity of reflected waves in a borehole is negligible at the dimension of the distance from a logging source. The increase of bulk or shear relaxation frequency will cause the amplitude of the reflected waveforms from the borehole wall to increase.
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Wang, Guanchao, Shangxu Wang, Jianyong Song, Chunhui Dong, and Mingqiang Zhang. "Elastic reflection traveltime inversion with decoupled wave equation." GEOPHYSICS 83, no. 5 (September 1, 2018): R463—R474. http://dx.doi.org/10.1190/geo2017-0631.1.
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Elastic full-waveform inversion (FWI) updates high-resolution model parameters by minimizing the residuals of multicomponent seismic records between the field and model data. FWI suffers from the potential to converge to local minima and more serious nonlinearity than acoustic FWI mainly due to the absence of low frequencies in seismograms and the extended model domain (P- and S-velocities). Reflection waveform inversion can relax the nonlinearity by relying on the tomographic components, which can be used to update the low-wavenumber components of the model. Hence, we have developed an elastic reflection traveltime inversion (ERTI) approach to update the low-wavenumber component of the velocity models for the P- and S-waves. In our ERTI algorithm, we took the P- and S-wave impedance perturbations as elastic reflectivity to generate reflections and a weighted crosscorrelation as the misfit function. Moreover, considering the higher wavenumbers (lower velocity value) of the S-wave velocity compared with the P-wave case, optimizing the low-wavenumber components for the S-wave velocity is even more crucial in preventing the elastic FWI from converging to local minima. We have evaluated an equivalent decoupled velocity-stress wave equation to ERTI to reduce the coupling effects of different wave modes and to improve the inversion result of ERTI, especially for the S-wave velocity. The subsequent application on the Sigsbee2A model demonstrates that our ERTI method with the decoupled wave equation can efficiently update the low-wavenumber parts of the model and improve the precision of the S-wave velocity.
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Stovas, Alexey, Yuriy Roganov, and Vyacheslav Roganov. "Pure mode P- and S-wave phase velocity equations in elastic orthorhombic media." GEOPHYSICS 86, no. 5 (August 30, 2021): C143—C156. http://dx.doi.org/10.1190/geo2021-0067.1.
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In an elastic model with orthorhombic (ORT) 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 depend on fewer independent parameters. Due to the increasing interest in S-wave propagation in anisotropic media, we also derive an approximate equation that supports propagation of S-waves only. However, the reduction in the number of independent parameters for the S-wave equation is not possible. We derive pure P- and S-wave equations in an elastic ORT model and find that the accuracy is sufficient for practical applications.
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Abdul Aziz, Qahtan, and Hassan Abdul Hussein. "Development a Statistical Relationship between Compressional Wave Velocity and Petrophysical Properties from Logs Data for JERIBE Formation ASMARI Reservoir in FAUQI Oil Field." Iraqi Journal of Chemical and petroleum Engineering 22, no. 3 (September 30, 2021): 1–9. http://dx.doi.org/10.31699/ijcpe.2021.3.1.
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The Compressional-wave (Vp) data are useful for reservoir exploration, drilling operations, stimulation, hydraulic fracturing employment, and development plans for a specific reservoir. Due to the different nature and behavior of the influencing parameters, more complex nonlinearity exists for Vp modeling purposes. In this study, a statistical relationship between compressional wave velocity and petrophysical parameters was developed from wireline log data for Jeribe formation in Fauqi oil field south Est Iraq, which is studied using single and multiple linear regressions. The model concentrated on predicting compressional wave velocity from petrophysical parameters and any pair of shear waves velocity, porosity, density, and fluid saturation in carbonate rocks. A strong linear correlation between P-wave velocity and S-wave velocity and between P-wave velocity and density rock was found. The resulting linear equations can be used to estimate P-wave velocity from the S-wave velocity in the case of both. The results of multiple regression analysis indicated that the density, porosity, water-saturated, and shear wave velocity (VS) are strongly related to Vp.
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Yang, Guojie, and Shuhua Wang. "Research on prediction method of S-wave velocity based on deep learning." Journal of Physics: Conference Series 2083, no. 4 (November 1, 2021): 042065. http://dx.doi.org/10.1088/1742-6596/2083/4/042065.
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Abstract Aiming at the s-wave velocity prediction problem, based on the analysis of the advantages and disadvantages of the empirical formula method and the rock physics modeling method, combined with the s-wave velocity prediction principle, the deep learning method is introduced, and a deep learning-based logging s-wave velocity prediction method is proposed. This method uses a deep neural network algorithm to establish a nonlinear mapping relationship between reservoir parameters (acoustic time difference, density, neutron porosity, shale content, porosity) and s-wave velocity, and then applies it to the s-wave velocity prediction at the well point. Starting from the relationship between p-wave and s-wave velocity, the study explained the feasibility of applying deep learning technology to s-wave prediction and the principle of sample selection, and finally established a reliable s-wave prediction model. The model was applied to s-wave velocity prediction in different research areas, and the results show that the s-wave velocity prediction technology based on deep learning can effectively improve the accuracy and efficiency of s-wave velocity prediction, and has the characteristics of a wide range of applications. It can provide reliable s-wave data for pre-stack AVO analysis and pre-stack inversion, so it has high practical application value and certain promotion significance.
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Wen, Genggeng, Kuiyuan Wan, Shaohong Xia, Huilong Xu, Chaoyan Fan, and Jinghe Cao. "Travel-Time Inversion Method of Converted Shear Waves Using RayInvr Algorithm." Applied Sciences 11, no. 8 (April 16, 2021): 3571. http://dx.doi.org/10.3390/app11083571.
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The detailed studies of converted S-waves recorded on the Ocean Bottom Seismometer (OBS) can provide evidence for constraining lithology and geophysical properties. However, the research of converted S-waves remains a weakness, especially the S-waves’ inversion. In this study, we applied a travel-time inversion method of converted S-waves to obtain the crustal S-wave velocity along the profile NS5. The velocities of the crust are determined by the following four aspects: (1) modelling the P-wave velocity, (2) constrained sediments Vp/Vs ratios and S-wave velocity using PPS phases, (3) the correction of PSS phases’ travel-time, and (4) appropriate parameters and initial model are selected for inversion. Our results show that the vs. and Vp/Vs of the crust are 3.0–4.4 km/s and 1.71–1.80, respectively. The inversion model has a similar trend in velocity and Vp/Vs ratios with the forward model, due to a small difference with ∆Vs of 0.1 km/s and ∆Vp/Vs of 0.03 between two models. In addition, the high-resolution inversion model has revealed many details of the crustal structures, including magma conduits, which further supports our method as feasible.
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Panea, Ionelia. "Physical Properties and Structure of the Near Subsurface in the Săcel Area, Romania, from Shallow Seismic Measurements." Journal of Environmental and Engineering Geophysics 24, no. 1 (March 2019): 151–58. http://dx.doi.org/10.2113/jeeg24.1.151.
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Results are presented for shallow seismic reflection measurements performed southwest of Săcel village in Romania for the purpose of obtaining information about the geological structure in the near subsurface. The P-wave and S-wave velocity distributions were also obtained below the soil surface. The measurements were performed along a nearly linear profile on the top of an elongated hill. Most of the shot gathers were characterized by a good signal-to-noise ratio. A depth-converted migrated section was obtained after the processing of shot gathers, on which an image of sedimentary deposits with various thicknesses, separated by shallow faults until a depth of about 80 m, were observed. The P-wave and S-wave velocity-depth models for two segments were of considerable interest for a geotechnical study proposed for the construction of a windmill park. The two- and three-layered P-wave velocity-depth models were comparable until depths of about 10 m after first-arrival traveltime inversions. The lateral variations in the subsurface geological structure and lithology reflected the variations in the P-wave velocity values from both models. The S-wave velocity-depth models for comparable depth intervals were similar to those from the P-wave velocity-depth models. Reliable S-wave velocity distributions were obtained after inversion of fundamental-mode and higher-mode surface waves.
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Levin, Franklyn K. "Estimating shear‐wave velocities from P-wave and converted‐wave data." GEOPHYSICS 64, no. 2 (March 1999): 504–7. http://dx.doi.org/10.1190/1.1444556.
Full textAbstract:
Tessmer and Behle (1988) show that S-wave velocity can be estimated from surface seismic data if both normal P-wave data and converted‐wave data (P-SV) are available. The relation of Tessmer and Behle is [Formula: see text] (1) where [Formula: see text] is the S-wave velocity, [Formula: see text] is the P-wave velocity, and [Formula: see text] is the converted‐wave velocity. The growing body of converted‐wave data suggest a brief examination of the validity of equation (1) for velocities that vary with depth.
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Winterstein, D. F., and B. N. P. Paulsson. "Velocity anisotropy in shale determined from crosshole seismic and vertical seismic profile data." GEOPHYSICS 55, no. 4 (April 1990): 470–79. http://dx.doi.org/10.1190/1.1442856.
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Crosshole and vertical seismic profile (VST) data made possible accurate characterization of the elastic properties, including noticeable velocity anisotropy, of a near‐surface late Tertiary shale formation. Shear‐wave splitting was obvious in both crosshole and VSP data. In crosshole data, two orthologonally polarrized shear (S) waves arrived 19 ms in the uppermost 246 ft (75 m). Vertically traveling S waves of the VSP separated about 10 ms in the uppermost 300 ft (90 m) but remained at nearly constant separation below that level. A transversely isotropic model, which incorporates a rapid increase in S-wave velocities with depth but slow increase in P-wave velocities, closely fits the data over most of the measured interval. Elastic constants of the transvesely isotropic model show spherical P- and [Formula: see text]wave velocity surfaces but an ellipsoidal [Formula: see text]wave surface with a ratio of major to minor axes of 1.15. The magnitude of this S-wave anisotropy is consistent with and lends credence to S-wave anisotropy magnitudes deduced less directly from data of many sedimentary basins.
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Diez, Anja, Olaf Eisen, Ilka Weikusat, Jan Eichler, Coen Hofstede, Pascal Bohleber, Thomas Bohlen, and Ulrich Polom. "Influence of ice crystal anisotropy on seismic velocity analysis." Annals of Glaciology 55, no. 67 (2014): 97–106. http://dx.doi.org/10.3189/2014aog67a002.
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AbstractIn 2010 a reflection seismic survey was carried out on the Alpine glacier Colle Gnifetti. The processed and depth-converted data could be compared to a nearby ice core, drilled almost to the bed. Comparisons showed that the depth of the P-wave bed reflection was too shallow, while the depth of the SH-wave bed reflection fitted the ice-core length well. We are now able to explain the major part of these differences using the existing crystal orientations of the ice at Colle Gnifetti. We calculate anisotropic velocities for P- and SH-waves that are usually picked for stacking and compare them with zero-offset velocities needed for the depth conversion. Here we take the firn pack at Colle Gnifetti into account for P- and S-wave analysis. To incorporate the S-wave analysis we first derive a new equation for the relationship between density and S-wave velocity from diving waves. We show that anisotropic fabrics observed at Colle Gnifetti introduce a difference of only 1% between stacking and depth-conversion velocities for the SH-wave, but 7% for the P-wave. We suggest that this difference in stacking and depth-conversion velocity for the P-wave can be used to derive information about the existing anisotropy by combining our seismic data with, for example, radar data.
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Boulfoul, M., and Doyle R. Watts. "Application of instantaneous rotations to S‐wave vertical seismic profiling." GEOPHYSICS 62, no. 5 (September 1997): 1365–68. http://dx.doi.org/10.1190/1.1444240.
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The petroleum exploration industry uses S‐wave vertical seismic profiling (VSP) to determine S‐wave velocities from downgoing direct arrivals, and S‐wave reflectivities from upgoing waves. Seismic models for quantitative calibration of amplitude variation with offset (AVO) data require S‐wave velocity profiles (Castagna et al., 1993). Vertical summations (Hardage, 1983) of the upgoing waves produce S‐wave composite traces and enable interpretation of S‐wave seismic profile sections. In the simplest application of amplitude anomalies, the coincidence of high amplitude P‐wave reflectivity and low amplitude S‐wave reflectivity is potentially a direct indicator of the presence of natural gas.
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Tarantola, Albert. "A strategy for nonlinear elastic inversion of seismic reflection data." GEOPHYSICS 51, no. 10 (October 1986): 1893–903. http://dx.doi.org/10.1190/1.1442046.
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The problem of interpretation of seismic reflection data can be posed with sufficient generality using the concepts of inverse theory. In its roughest formulation, the inverse problem consists of obtaining the Earth model for which the predicted data best fit the observed data. If an adequate forward model is used, this best model will give the best images of the Earth’s interior. Three parameters are needed for describing a perfectly elastic, isotropic, Earth: the density ρ(x) and the Lamé parameters λ(x) and μ(x), or the density ρ(x) and the P-wave and S-wave velocities α(x) and β(x). The choice of parameters is not neutral, in the sense that although theoretically equivalent, if they are not adequately chosen the numerical algorithms in the inversion can be inefficient. In the long (spatial) wavelengths of the model, adequate parameters are the P-wave and S-wave velocities, while in the short (spatial) wavelengths, P-wave impedance, S-wave impedance, and density are adequate. The problem of inversion of waveforms is highly nonlinear for the long wavelengths of the velocities, while it is reasonably linear for the short wavelengths of the impedances and density. Furthermore, this parameterization defines a highly hierarchical problem: the long wavelengths of the P-wave velocity and short wavelengths of the P-wave impedance are much more important parameters than their counterparts for S-waves (in terms of interpreting observed amplitudes), and the latter are much more important than the density. This suggests solving the general inverse problem (which must involve all the parameters) by first optimizing for the P-wave velocity and impedance, then optimizing for the S-wave velocity and impedance, and finally optimizing for density. The first part of the problem of obtaining the long wavelengths of the P-wave velocity and the short wavelengths of the P-wave impedance is similar to the problem solved by present industrial practice (for accurate data interpretation through velocity analysis and “prestack migration”). In fact, the method proposed here produces (as a byproduct) a generalization to the elastic case of the equations of “prestack acoustic migration.” Once an adequate model of the long wavelengths of the P-wave velocity and of the short wavelengths of the P-wave impedance has been obtained, the data residuals should essentially contain information on S-waves (essentially P-S and S-P converted waves). Once the corresponding model of S-wave velocity (long wavelengths) and S-wave impedance (short wavelengths) has been obtained, and if the remaining residuals still contain information, an optimization for density should be performed (the short wavelengths of impedances do not give independent information on density and velocity independently). Because the problem is nonlinear, the whole process should be iterated to convergence; however, the information from each parameter should be independent enough for an interesting first solution.
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Liu, Hongwei, Mustafa Naser Al-Ali, and Yi Luo. "Converted-wave model building and imaging based on common-focus-point methodology." GEOPHYSICS 85, no. 6 (October 13, 2020): U139—U149. http://dx.doi.org/10.1190/geo2019-0549.1.
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Seismic images can be viewed as photographs for underground rocks. These images can be generated from different reflections of elastic waves with different rock properties. Although the dominant seismic data processing is still based on the acoustic wave assumption, elastic wave processing and imaging have become increasingly popular in recent years. A major challenge in elastic wave processing is shear-wave (S-wave) velocity model building. For this reason, we have developed a sequence of procedures for estimating seismic S-wave velocities and the subsequent generation of seismic images using converted waves. We have two main essential new supporting techniques. The first technique is the decoupling of the S-wave information by generating common-focus-point gathers via application of the compressional-wave (P-wave) velocity on the converted seismic data. The second technique is to assume one common VP/ VS ratio to approximate two types of ratios, namely, the ratio of the average earth layer velocity and the ratio of the stacking velocity. The benefit is that we reduce two unknown ratios into one, so it can be easily scanned and picked in practice. The PS-wave images produced by this technology could be aligned with the PP-wave images such that both can be produced in the same coordinate system. The registration between the PP and PS images provides cross-validation of the migrated structures and a better estimation of underground rock and fluid properties. The S-wave velocity, computed from the picked optimal ratio, can be used not only for generating the PS-wave images, but also to ensure well registration between the converted-wave and P-wave images.
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Gaiser, James, Ivan Vasconcelos, Rosemarie Geetan, and John Faragher. "Elastic-wavefield interferometry using P-wave source VSPs at the Wamsutter field, Wyoming." GEOPHYSICS 77, no. 2 (March 2012): Q27—Q36. http://dx.doi.org/10.1190/geo2011-0162.1.
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In this study, elastic-wavefield interferometry was used to recover P- and S-waves from the 3D P-wave vibrator VSP data at Wamsutter field in Wyoming. S-wave velocity and birefringence is of particular interest for the geophysical objectives of lithology discrimination and fracture characterization in naturally fractured tight gas sand reservoirs. Because we rely on deconvolution interferometry for retrieving interreceiver P- and S-waves in the subsurface, the output fields are suitable for high-resolution, local reservoir characterization. In 1D media where the borehole is nearly vertical, data at the stationary-phase point is not conducive to conventional interferometry. Strong tube-wave noise generated by physical sources near the borehole interfere with S-wave splitting analyses. Also, converted P- to S-wave (PS-wave) polarity reversals occur at zero offset and cancel their recovery. We developed methods to eliminate tube-wave noise by removing physical sources at the stationary-phase point and perturbing the integration path in the integrand based on P-wave NMO velocity of the direct-arrival. This results in using nonphysical energy outside a Fresnel radius that could not have propagated between receivers. To limit the response near the stationary-phase point, we also applied a weighting condition to suppress energy from large offsets. For PS-waves, a derivative-like operator was applied to the physical sources at zero offset in the form of a polarity reversal. These methods resulted in effectively recovering P-wave dipole and PS-wave quadrupole pseudosource VSPs. The retrieved wavefields kinematically correspond to a vertical incidence representation of reflectivity/transmissivity and can be used for conventional P- and S-wave velocity analyses. Four-component PS-wave VSPs retrieve S-wave splitting in transmitted converted waves that provide calibration for PS-wave and P-wave azimuthal anisotropy measurements from surface-seismic data.
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Wang, Bo, Jialin Hao, Shengdong Liu, Fubao Zhou, Zhendong Zhang, Heng Zhang, and Huachao Sun. "Experimental Study on the Effect of Gas Pressure on Ultrasonic Velocity and Anisotropy of Anthracite." Geofluids 2019 (August 19, 2019): 1–10. http://dx.doi.org/10.1155/2019/3183816.
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To research the elasticity of gas-bearing coal fluid-solid two-phase medium with seismic exploration method is critical to the prevention of gas disasters. To investigate the elasticity, the ultrasonic elastic test of anthracite samples under different gas pressures was carried out and the ultrasonic velocity and anisotropy of the samples were analyzed in this study. The results show that the velocities (P- and S-waves) decrease in turn in the strike, dip, and vertical directions. However, a negative linear correlation is proved to exist between ultrasonic velocity and gas pressure. With the increase of gas pressure, the anisotropy degree of both the P-wave and the S-wave of the samples decreases but the declining degree of the P-wave is greater than that of the S-wave. In addition, the decrease in velocity and the anisotropy degree of the P-wave is greater than that of the S-wave, indicating that the P-wave is more sensitive to gas pressure changes in terms of velocity and its anisotropy degree.
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Sun, Robert, George A. McMechan, and Han-Hsiang Chuang. "Amplitude balancing in separating P- and S-waves in 2D and 3D elastic seismic data." GEOPHYSICS 76, no. 3 (May 2011): S103—S113. http://dx.doi.org/10.1190/1.3555529.
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The reflected P- and S-waves in elastic displacement component data recorded at the earth’s surface are separated by reverse-time (downward) extrapolation of the data in an elastic computational model, followed by calculations to give divergence (dilatation) and curl (rotation) at a selected reference depth. The surface data are then reconstructed by separate forward-time (upward) scalar extrapolations, from the reference depth, of the magnitude of the divergence and curl wavefields, and extraction of the separated P- and S-waves, respectively, at the top of the models. A P-wave amplitude will change by a factor that is inversely proportional to the P-velocity when it is transformed from displacement to divergence, and an S-wave amplitude will change by a factor that is inversely proportional to the S-velocity when it is transformed from displacement to curl. Consequently, the ratio of the P- to the S-wave amplitude (the P-S amplitude ratio) in the form of divergence and curl (postseparation) is different from that in the (preseparation) displacement form. This distortion can be eliminated by multiplying the separated S-wave (curl) by a relative balancing factor (which is the S- to P-velocity ratio); thus, the postseparation P-S amplitude ratio can be returned to that in the preseparation data. The absolute P- and S-wave amplitudes are also recoverable by multiplying them by a factor that depends on frequency, on the P-velocity α, and on the unit of α and is location-dependent if the near-surface P-velocity is not constant.
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Ikeda, Tatsunori, Toshifumi Matsuoka, Takeshi Tsuji, and Toru Nakayama. "Characteristics of the horizontal component of Rayleigh waves in multimode analysis of surface waves." GEOPHYSICS 80, no. 1 (January 1, 2015): EN1—EN11. http://dx.doi.org/10.1190/geo2014-0018.1.
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In surface-wave analysis, S-wave velocity estimations can be improved by the use of higher modes of the surface waves. The vertical component of P-SV waves is commonly used to estimate multimode Rayleigh waves, although Rayleigh waves are also included in horizontal components of P-SV waves. To demonstrate the advantages of using the horizontal components of multimode Rayleigh waves, we investigated the characteristics of the horizontal and vertical components of Rayleigh waves. We conducted numerical modeling and field data analyses rather than a theoretical study for both components of Rayleigh waves. As a result of a simulation study, we found that the estimated higher modes have larger relative amplitudes in the vertical and horizontal components as the source depth increases. In particular, higher-order modes were observed in the horizontal component data for an explosive source located at a greater depth. Similar phenomena were observed in the field data acquired by using a dynamite source at 15-m depth. Sensitivity analyses of dispersion curves to S-wave velocity changes revealed that dispersion curves additionally estimated from the horizontal components can potentially improve S-wave velocity estimations. These results revealed that when the explosive source was buried at a greater depth, the horizontal components can complement Rayleigh waves estimated from the vertical components. Therefore, the combined use of the horizontal component data with the vertical component data would contribute to improving S-wave velocity estimations, especially in the case of buried explosive source signal.
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Somasundaram, K., S. Manthiramoorthi, and A. Sathya Narayanan. "On the Existence of Hydromagnetic Interface Waves at a Structured Atmosphere." Symposium - International Astronomical Union 142 (1990): 262–63. http://dx.doi.org/10.1017/s0074180900088094.
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The conditions under which the hydromagnetic interface waves can exist at a magnetic interface is deduced. Using these conditons, it is shown that a slow interface wave with a phase velocity about 5Km/s and a fast interface wave with a phase velocity 6.5 to 8km/s at the photospheric level can exist.
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Geis, W. T., R. R. Stewart, M. J. Jones, and P. E. Katapodis. "Processing, correlating, and interpreting converted shear waves from borehole data in southern Alberta." GEOPHYSICS 55, no. 6 (June 1990): 660–69. http://dx.doi.org/10.1190/1.1442878.
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Borehole measurements coupled with phase information from Zoeppritz equation modeling has assisted in accurate correlation between a VSP converted S-wave section and both the surface and VSP P-wave sections from southern Alberta. For the most part, both the character and polarities of the sections agree; however, there are some differences. Some reflections are stronger and more distinct on the S-wave section than on the P-wave section. Spectral analysis of the time‐domain upgoing P-wave and S-wave energy shows that the frequency content of the S-waves is comparable to the P-waves. Thus, the slower velocity S-waves have a shorter wavelenght and provide better vertical resolution of some interfaces. Other upgoing S-wave modes can interfere with the P‐SV mode and contribute to the differences between the P- and S-wave sections. The match between P-wave and S-wave velocities ([Formula: see text] and [Formula: see text]), determined from VSP traveltime inversion and the full‐waveform sonic log, is best in the Paleozoic carbonate section; there is some discrepancy in Cretaceous sandstone intervals. A basal salt unit in the Paleozoic Beaverhill Lake formation has a VSP‐determined [Formula: see text] ratio of 1.97, suggesting that salt can be distinguished from carbonates using both P-wave and S-wave velocity information in this region.
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Liu, Zhaolun, Jing Li, Sherif M. Hanafy, and Gerard Schuster. "3D wave-equation dispersion inversion of Rayleigh waves." GEOPHYSICS 84, no. 5 (September 1, 2019): R673—R691. http://dx.doi.org/10.1190/geo2018-0543.1.
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The 2D wave-equation dispersion (WD) inversion method is extended to 3D wave-equation dispersion inversion of surface waves for the shear-velocity distribution. The objective function of 3D WD is the frequency summation of the squared wavenumber [Formula: see text] differences along each azimuth angle of the fundamental or higher modes of Rayleigh waves in each shot gather. The S-wave velocity model is updated by the weighted zero-lag crosscorrelation between the weighted source-side wavefield and the back-projected receiver-side wavefield for each azimuth angle. A multiscale 3D WD strategy is provided, which starts from the pseudo-1D S-velocity model, which is then used to get the 2D WD tomogram, which in turn is used as the starting model for 3D WD. The synthetic and field data examples demonstrate that 3D WD can accurately reconstruct the 3D S-wave velocity model of a laterally heterogeneous medium and has much less of a tendency to getting stuck in a local minimum compared with full-waveform inversion.
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Chen, Ji Hua, Ai Hong Zhou, Qiu Jun Wang, and Ying Jiao Xu. "Study on the Influence of Seismic Wave Inputting Interface on the Earthquake Response of Deep Soft Sites." Advanced Materials Research 243-249 (May 2011): 2523–28. http://dx.doi.org/10.4028/www.scientific.net/amr.243-249.2523.
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Earthquake effects of two typical deep soft sites selected from Tianjin(site 1)and Shanghai(site 2) are studied when the vertical inputting earthquake waves are located in different depth of sites. As far as the shear wave velocity of soil layers is concerned, seven kinds of soil layers in site 1 and eight soil layers in site 2 are selected as the vertical imputing interfaces of earthquake waves. Two acceleration waves recorded during Taft earthquake and Northbridge earthquake are selected, and the peak values of two waves are adjusted to be 0.35m/s2、0 70m /s2 and 0 98m /s2, respectively. The earthquake response of sites is calculated by SHAKE91 program. The results are compared to those of site when the input interfaces of earthquake waves are located in bedrock with shear wave velocity larger than 500m/s. The conclusion is as following: With the depth of input position (or shear wave velocity) increasing, the value of the ground acceleration response spectrum gradually closes to the actual data.; For the general building the soil layer with shear wave velocity for 400m/s or so can be chosen as the input interface, and the building with long natural vibration period should be treated seriously, and the soil layer whose shear wave velocity is above 500m/s can be chosen as the input interface.
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Dahl, Elliot J. H., and Kyle T. Spikes. "Local and global fluid effects on sonic wave modes." GEOPHYSICS 82, no. 6 (November 1, 2017): D369—D381. http://dx.doi.org/10.1190/geo2017-0080.1.
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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.
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Solovyev, Victor M., Alexander S. Salnikov, Viktor S. Seleznev, Tatyana V. Kashubina, and Natalya А. Galyova. "TO STUDY THE POSSIBILITIES OF USING THE SEISMOLOGICAL NETWORK OF THE ALTAI-SAYAN REGION FOR REGIME VIBRO-SEISMIC OBSERVATIONS." Interexpo GEO-Siberia 2, no. 2 (May 21, 2021): 289–97. http://dx.doi.org/10.33764/2618-981x-2021-2-2-289-297.
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The results of deep seismic studies based on P - and S-wave data on the East-Stanov fragment of the reference 700-kilometer geophysical profile 8-DV are presented. Deep seismic sections of the upper crust (up to a depth of 20 km) with the distribution of the velocities of longitudinal and transverse waves are constructed. The P - wave velocities in the upper part of the section vary from 4-5 km / s within the Upper Zeya and Amur-Zeya depressions to 5.5-6.0 km/s within mountain ranges and plateaus; at depths of 10-20 km, lenses of high-velocity rocks up to 6.7-7.0 km/s are distinguished in the profile alignment. According to the S - waves in the upper part of the section, the velocity values are generally 3.0-3.2 km/s; reduced velocity values of 2.5-2.6 km / s are observed in the Upper Zey depression. At depths of 5-20 km within the section, according to the transverse wave data, a number of sections with reduced and increased velocity values are distinguished, respectively, up to 3.4-3.5 km/s and 3.75-3.8 km/s. The correlation of the selected anomalies according to the data of P-and S-waves is carried out.
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Jin, Side, G. Cambois, and C. Vuillermoz. "Shear‐wave velocity and density estimation from PS-wave AVO analysis: Application to an OBS dataset from the North Sea." GEOPHYSICS 65, no. 5 (September 2000): 1446–54. http://dx.doi.org/10.1190/1.1444833.
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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.
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Stewart, Robert R., James E. Gaiser, R. James Brown, and Don C. Lawton. "Converted‐wave seismic exploration: Methods." GEOPHYSICS 67, no. 5 (September 2002): 1348–63. http://dx.doi.org/10.1190/1.1512781.
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Multicomponent seismic recording (measurement with vertical‐ and horizontal‐component geophones and possibly a hydrophone or microphone) captures the seismic wavefield more completely than conventional single‐element techniques. In the last several years, multicomponent surveying has developed rapidly, allowing creation of converted‐wave or P‐S images. These make use of downgoing P‐waves that convert on reflection at their deepest point of penetration to upcoming S‐waves. Survey design for acquiring P‐S data is similar to that for P‐waves, but must take into account subsurface VP/VS values and the asymmetric P‐S ray path. P‐S surveys use conventional sources, but require several times more recording channels per receiving location. Some special processes for P‐S analysis include anisotropic rotations, S‐wave receiver statics, asymmetric and anisotropic binning, nonhyperbolic velocity analysis and NMO correction, P‐S to P‐P time transformation, P‐S dip moveout, prestack migration with two velocities and wavefields, and stacking velocity and reflectivity inversion for S‐wave velocities. Current P‐S sections are approaching (and in some cases exceeding) the quality of conventional P‐P seismic data. Interpretation of P‐S sections uses full elastic ray tracing, synthetic seismograms, correlation with P‐wave sections, and depth migration. Development of the P‐S method has taken about 20 years, but has now become commercially viable.
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Gilbert, R. J., and W. J. Dodds. "Effect of selective muscarinic antagonists on peristaltic contractions in opossum smooth muscle." American Journal of Physiology-Gastrointestinal and Liver Physiology 250, no. 1 (January 1, 1986): G50—G59. http://dx.doi.org/10.1152/ajpgi.1986.250.1.g50.
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In this study we examined the role of M1- and M2-muscarinic receptors in the mediation of circular smooth muscle esophageal contractions elicited by pharmacological cholinergic stimulation and during peristalsis in anesthetized opossums. Esophageal-body contractions were induced by bethanechol administration, whereas peristalsis was elicited by pharyngeal stroking or cervical vagal stimulation. Contractions were measured by a low-compliance manometric recording system. The incidence and amplitude of bethanechol-induced contractions were antagonized by 4-diphenylacetoxy-n-methylpiperidine (4-DAMP) and atropine but not pirenzepine. 4-DAMP and atropine caused an increased velocity, decreased amplitude, and preferential reduction of the incidence of primary peristaltic contractions in the proximal smooth muscle esophagus. During long-train vagal stimulation, intra-stimulus A-waves had a velocity similar to primary peristalsis, whereas poststimulus B-waves showed a velocity considerably faster than primary peristalsis. Short-train vagal stimulation produced a contraction sequence, termed an "S-wave," that had a velocity similar to that of the A-wave. At low doses 4-DAMP increased the velocity and decreased the amplitude of A-wave and S-wave contractions, and at high doses 4-DAMP abolished both the A-wave and S-wave contractions. B-wave contractions were minimally affected by 4-DAMP. Pirenzepine had no effect on contractions induced by swallows or vagal stimulation. We conclude that M2-muscarinic receptors mediate esophageal contractions in the circular smooth muscle during primary peristalsis and during A-waves and S-waves induced by vagal stimulation, and M1-receptors do not have any important role in the excitatory neural pathway to the esophagus.(ABSTRACT TRUNCATED AT 250 WORDS)