Extraction of P‐ and S‐waves from the vertical component of the particle velocity at the sea floor

Geophysics ◽  
1995 ◽  
Vol 60 (1) ◽  
pp. 231-240 ◽  
Author(s):  
Lasse Amundsen ◽  
Arne Reitan
Keyword(s):  
Particle Velocity ◽  
Synthetic Data ◽  
Vertical Component ◽  
Transversely Isotropic ◽  
Vertical Axis ◽  
Elastic Stiffness ◽  
P Wave ◽  
S Wave ◽  
Sea Floor ◽  
S Waves

At the boundary between two solid media in welded contact, all three components of particle velocity and vertical traction are continuous through the boundary. Across the boundary between a fluid and a solid, however, only the vertical component of particle velocity is continuous while the horizontal components can be discontinuous. Furthermore, the pressure in the fluid is the negative of the vertical component of traction in the solid, while the horizontal components of traction vanish at the interface. Taking advantage of this latter fact, we show that total P‐ and S‐waves can be computed from the vertical component of the particle velocity recorded by single component geophones planted on the sea floor. In the case when the sea floor is transversely isotropic with a vertical axis of symmetry, the computation requires the five independent elastic stiffness components and the density. However, when the sea floor material is fully isotropic, the only material parameter needed is the local shear wave velocity. The analysis of the extraction problem is done in the slowness domain. We show, however, that the S‐wave section can be obtained by a filtering operation in the space‐frequency domain. The P‐wave section is then the difference between the vertical component of the particle velocity and the S‐wave component. A synthetic data example demonstrates the performance of the algorithm.

Decomposition of multicomponent sea‐floor data into upgoing and downgoing P‐ and S‐waves

Geophysics ◽  
1995 ◽  
Vol 60 (2) ◽  
pp. 563-572 ◽  
Author(s):  
Lasse Amundsen ◽  
Arne Reitan
Keyword(s):  
Particle Velocity ◽  
Layered Medium ◽  
Synthetic Data ◽  
Water Layer ◽  
S Wave ◽  
Sea Floor ◽  
S Waves ◽  
Sea Bottom ◽  
Marine Source ◽  
Horizontal Particle

A method for decomposing multicomponent sea‐floor measurements into upgoing and downgoing P‐ and S‐waves is presented. We assume that a marine survey employing a marine source in the water layer is conducted over a plane‐layered medium. From recordings of the pressure just above the sea floor and the particle velocity vector just below the sea floor, decomposition filters can be determined by plane‐wave analysis. The decomposition filter coefficients depend on the P‐ and S‐wave velocities and the density at the sea bottom. We show how to decompose the multicomponent measurements into upgoing and downgoing P‐ and S‐vertical traction components, vertical‐particle velocity components, and horizontal particle velocity components. The decomposition filters are applied with good results to synthetic data modeled in a plane‐layered medium.

Seismic vertical transversely isotropic parameter inversion from P- and S-wave cross-borehole measurements in an aquifer environment

Geophysics ◽  
2019 ◽  
Vol 84 (3) ◽  
pp. D101-D116
Author(s):  
Julius K. von Ketelhodt ◽  
Musa S. D. Manzi ◽  
Raymond J. Durrheim ◽  
Thomas Fechner
Keyword(s):  
Transversely Isotropic ◽  
P Wave ◽  
Perturbation Equation ◽  
S Wave ◽  
P Waves ◽  
Data Set ◽  
Near Surface ◽  
S Waves ◽  
Wave Measurements ◽  
Wave Splitting

Joint P- and S-wave measurements for tomographic cross-borehole analysis can offer more reliable interpretational insight concerning lithologic and geotechnical parameter variations compared with P-wave measurements on their own. However, anisotropy can have a large influence on S-wave measurements, with the S-wave splitting into two modes. We have developed an inversion for parameters of transversely isotropic with a vertical symmetry axis (VTI) media. Our inversion is based on the traveltime perturbation equation, using cross-gradient constraints to ensure structural similarity for the resulting VTI parameters. We first determine the inversion on a synthetic data set consisting of P-waves and vertically and horizontally polarized S-waves. Subsequently, we evaluate inversion results for a data set comprising jointly measured P-waves and vertically and horizontally polarized S-waves that were acquired in a near-surface ([Formula: see text]) aquifer environment (the Safira research site, Germany). The inverted models indicate that the anisotropy parameters [Formula: see text] and [Formula: see text] are close to zero, with no P-wave anisotropy present. A high [Formula: see text] ratio of up to nine causes considerable SV-wave anisotropy despite the low magnitudes for [Formula: see text] and [Formula: see text]. The SH-wave anisotropy parameter [Formula: see text] is estimated to be between 0.05 and 0.15 in the clay and lignite seams. The S-wave splitting is confirmed by polarization analysis prior to the inversion. The results suggest that S-wave anisotropy may be more severe than P-wave anisotropy in near-surface environments and should be taken into account when interpreting cross-borehole S-wave data.

Separation and enhancement of split S‐waves on multicomponent shot records from the BIRPS WISPA experiment

Geophysics ◽  
1994 ◽  
Vol 59 (1) ◽  
pp. 131-139 ◽  
Author(s):  
M. Boulfoul ◽  
D. R. Watts
Keyword(s):  
Synthetic Data ◽  
P Wave ◽  
Moving Window ◽  
Wave Analysis ◽  
S Wave ◽  
Near Surface ◽  
S Waves ◽  
Wave Velocities ◽  
Wave Splitting ◽  
Explosive Source

Instantaneous rotations are combined with f-k filtering to extract coherent S‐wave events from multicomponent shot records recorded by British Institutions Reflection Profiling Syndicate (BIRPS) Weardale Integrated S‐wave and P‐wave analysis (WISPA) experiment. This experiment was an attempt to measure the Poisson’s ratio of the lower crest by measuring P‐wave and S‐wave velocities. The multihole explosive source technique did generate S‐waves although not of opposite polarization. Attempts to produce stacks of the S‐wave data are unsuccessful because S‐wave splitting in the near surface produced random polarizations from receiver group to receiver group. The delay between the split wavelets varies but is commonly between 20 to 40 ms for 10 Hz wavelets. Dix hyperbola are produced on shot records after instantaneous rotations are followed by f-k filtering. To extract the instantaneous polarization, the traces are shifted back by the length of a moving window over which the calculation is performed. The instantaneous polarization direction is computed from the shifted data using the maximum eigenvector of the covariance matrix over the computation window. Split S‐waves are separated by the instantaneous rotation of the unshifted traces to the directions of the maximum eigenvectors determined for each position of the moving window. F-K filtering is required because of the presence of mode converted S‐waves and S‐waves produced by the explosive source near the time of detonation. Examples from synthetic data show that the method of instantaneous rotations will completely separate split S‐waves if the length of the moving window over which the calculation is performed is the length of the combined split wavelets. Separation may be achieved on synthetic data for wavelet delays as small as two sample intervals.

Azimuthal AVO for tilted TI medium

Geophysics ◽  
2017 ◽  
Vol 82 (1) ◽  
pp. C21-C33 ◽  
Author(s):  
Hongwei Wang ◽  
Suping Peng ◽  
Wenfeng Du
Keyword(s):  
Isotropic Medium ◽  
Symmetry Axis ◽  
Transversely Isotropic ◽  
P Wave ◽  
S Wave ◽  
Transverse Waves ◽  
Propagation Angle ◽  
S Waves ◽  
The Difference ◽  
Dip Angle

With the incident P-wave, we derive approximate formulas for amplitudes and polarizations of waves reflected from and transmitted through a planar, horizontal boundary between an overlying isotropic medium and an underlying tilted transversely isotropic (TTI) medium assuming that the directions of the phase and group velocities are consistent. Provided that the velocities in the isotropic medium are equal to the velocities along the symmetry axis direction, we derive the relational expression between the propagation angle in the TTI medium and the propagation angle in the hypothetical isotropic medium, under the condition that the horizontal slowness is the same, and then we update the approximate formula of the polarization in the TTI medium. Provided that the slow and fast transverse waves (qS and SH) are generated simultaneously in the anisotropic interface, we linearize for a six-order Zoeppritz equation, derive the azimuthal formula of longitudinal and S-waves, and determine their detailed expressions within the symmetry axis plane. According to the derived azimuthal AVO formula, we establish medium models, compare the derived AVO with the precision, and obtain the following conclusions: (1) The dip angle for the symmetry axis with respect to the vertical may have a sufficiently large impact on AVO, and the vertical longitudinal wave can generate an S-wave. (2) For the derived AVO formula, within the symmetry axis plane, the fitting effect of the approximate and exact formulas is good; however, within the other incident planes, taking the azimuth angle 45° as an example, the approximation is suitable for the large impedance contrast if the anisotropic parameters are set properly. (3) The error between the approximation and precision is mainly caused by the difference between the reflected and transmitted angles, the velocities’ derivation with respect to azimuth, and the division of approximation into isotropic and anisotropic parts.

A wavefield-separation-based elastic least-squares reverse time migration

Geophysics ◽  
2018 ◽  
Vol 83 (3) ◽  
pp. S279-S297 ◽  
Author(s):  
Bingluo Gu ◽  
Zhenchun Li ◽  
Jianguang Han
Keyword(s):  
Least Squares ◽  
Synthetic Data ◽  
P Wave ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
S Wave ◽  
S Waves ◽  
Numerical Tests ◽  
Time Migration

Elastic least-squares reverse time migration (ELSRTM) has the potential to provide improved subsurface reflectivity estimation. Compared with elastic RTM (ERTM), ELSRTM can produce images with higher spatial resolution, more balanced amplitudes, and fewer artifacts. However, the crosstalk between P- and S-waves can significantly degrade the imaging quality of ELSRTM. We have developed an ELSRTM method to suppress the crosstalk artifacts. This method includes three crucial points. The first is that the forward and backward wavefields are extrapolated based on the separated elastic velocity-stress equation of P- and S-waves. The second is that the separated vector P- and S-wave residuals are migrated to form reflectivity images of Lamé constants [Formula: see text] and [Formula: see text] independently. The third is that the reflectivity images of [Formula: see text] and [Formula: see text] are obtained by the vector P-wave wavefields achieved in the backward extrapolation of the separated vector P-wave residuals and the vector S-wave wavefields achieved in the backward extrapolation of the separated vector S-wave residuals, respectively. Numerical tests with synthetic data demonstrate that our ELSRTM method can produce images free of crosstalk artifacts. Compared with ELSRTM based on the coupled wavefields, our ELSRTM method has better convergence and higher accuracy.

PERTURBATION OF PHASE VELOCITIES IN ELASTIC ORTHORHOMBIC MEDIA

Geophysics ◽  
2021 ◽  
pp. 1-109
Author(s):  
Alexey Stovas ◽  
Yuriy Roganov ◽  
Vyacheslav Roganov
Keyword(s):  
Seismic Waves ◽  
Transversely Isotropic ◽  
Second Order ◽  
P Wave ◽  
Order Perturbation ◽  
Perturbation Approach ◽  
S Wave ◽  
Anisotropic Models ◽  
S Waves ◽  
Phase Velocities

The parameterization of anisotropic models is very important when focusing on specific signatures of seismic waves and reducing the parameters crosstalk involved in inverting seismic data. The parameterization is strongly dependent on the problem at hand. We propose a new parameterization for an elastic orthorhombic model with on-axes P- and S-wave velocities and new symmetric anelliptic parameters. The perturbation approach is well defined for P waves in acoustic orthorhombic media. In the elastic orthorhombic media, the P-wave perturbation coefficients are very similar to their acoustic counterparts. However, the S-waves perturbation coefficients are still unknown. The perturbation coefficients can be interpreted as sensitivity coefficients, and they are important in many applications. We apply the second-order perturbation in anelliptic parameters for P, S1 and S2 wave phase velocities in elastic orthorhombic model. We show that using the conventional method some perturbation coefficients for S waves are not defined in the vicinity of the singularity point in an elliptical background model. Thus, we propose an alternative perturbation approach that overcomes this problem. We compute the first- and second-order perturbation coefficients for P and S waves. The perturbation-based approximations are very accurate for P and S waves compared with exact solutions, based on a numerical example. The reductions to transversely isotropic and acoustic orthorhombic models are also considered for analysis. We also show how perturbations in anelliptic parameters affect S-wave triplications in an elastic orthorhombic model.

Do dipole sonic logs measure group or phase velocity (revisited)?

Geophysics ◽  
2019 ◽  
Vol 84 (6) ◽  
pp. C311-C322
Author(s):  
Stephen Horne ◽  
Richard T. Coates ◽  
Alexei Bolshakov
Keyword(s):  
Symmetry Axis ◽  
Synthetic Data ◽  
Transversely Isotropic ◽  
Vertical Axis ◽  
Flexural Waves ◽  
S Wave ◽  
Slowness Surface ◽  
Phase Velocities ◽  
Group And Phase Velocities ◽  
Sonic Logs

We have revisited the debate about whether flexural waves from dipole sonic tools and standard processing algorithms measure group or phase velocities in anisotropic formations. We observe that much of the confusion arises from a failure to understand the different meanings of group and phase velocities. Using a transversely isotropic medium with a vertical axis of symmetry that exhibits a triplication in its S-wave group slowness surface, we generate synthetic flexural sonic waveforms corresponding to boreholes at angles of 0°–90° with respect to the anisotropy symmetry axis in 1° increments. We processed these synthetic data using standard time- and frequency-domain semblance methods. The results conclusively demonstrate that dipole sonic logs measure the group slowness for the group angle corresponding to the angle between the borehole and the anisotropic symmetry axis. In addition, data that we have evaluated suggest that current tool geometries and semblance processing may not always be sensitive enough to resolve all branches of the group slowness triplication surface.

scholarly journals Metode Seismik dalam Pemodelan Fisis Letusan Gunung Lumpur Bledug Kuwu

2019 ◽  
Vol 2 (2) ◽  
pp. 61-66
Author(s):  
Ahmad Fauzi Pohan ◽  
Rusnoviandi Rusnoviandi
Keyword(s):  
Wave Velocity ◽  
Physical Modeling ◽  
Vertical Component ◽  
Dominant Frequency ◽  
P Wave ◽  
Physical Parameters ◽  
S Wave ◽  
Interesting Phenomenon ◽  
Central Java ◽  
P Wave Velocity

Aktivitas gunung lumpur Bledug Kuwu di Jawa  Tengah merupakan fenomena yang menarik dikaji menggunakan pemodelan fisis. Tujuan penelitian ini adalah mengetahui parameter dari medium gunung lumpur Bledug Kuwu. Adapun pemodelan fisis yang dilakukan dengan menggunakan media fisis akuarium berukuran 59 × 59 × 37,3 cm yang diisi material dari lumpur Bledug Kuwu. Sumber letusan dihasilkan dari tekanan kompresor yang dapat diatur kedalaman (10.5, 13, dan 15.5 cm) dan sudut (30o, 45o dan 60o) sumbernya. Sensor yang digunakan geophone komponen vertikal sebanyak 3 buah dengan durasi perekaman selama 5 dan 2,5 detik. Data diambil dengan frekuensi sampel 2 dan 4 kHz untuk masing-masing durasi perekaman. Konfigurasi sumber dan geophone dibuat sesuai dengan pemodelan fisisnya. Pengukuran desnsitas lumpur menunjukkan angka sebesar 1200 kg/m3. Berdasarkan hasil analisis seismogram model fisis diperoleh kecepatan perambatan gelombang-P pada medium lumpur Bledug Kuwu adalah sebesar 48,74 m/s,dan gelombang-S sebesar 28,14 m/s dengan frekuensi dominan antara 20 sampai 25 Hz.   Bledug Kuwu mud volcano activity in Central Java is an interesting phenomenon to be studied using both physical  modeling. The objective of this study was to determine the physical parameters of the medium of Bledug Kuwu. The Physical model was an aquarium with a dimension of 59 × 59 × 37.3 cm filled with Bledug Kuwu’s mud. The eruption source is generated by a compressor pressure that can be controled both the depth(10.5, 13, and 15.5 cm) and the angel of the source (30o, 45o and 60o). The resulting seismic signals were recorded by using 3 vertical component geophones for 10 and 5 seconds durations at a frequency of 2 and 4 kHz respectivel, mud density 1200 kg/m3 . The physical modeling shows that the P-wave velocity of the Bledug Kuwu’s medium is 48.7 m/s, S-wave velocity of Bledug Kuwu’s is 28,14 m/s  with a dominant frequency of 20 to 25 Hz.

Numerical simulation of azimuthal acoustic logging in a borehole penetrating a rock formation boundary

Geophysics ◽  
2016 ◽  
Vol 81 (3) ◽  
pp. D283-D291 ◽  
Author(s):  
Peng Liu ◽  
Wenxiao Qiao ◽  
Xiaohua Che ◽  
Xiaodong Ju ◽  
Junqiang Lu ◽  
...  
Keyword(s):  
Domain Model ◽  
P Wave ◽  
S Wave ◽  
Angle Variation ◽  
P Waves ◽  
Acoustic Logging ◽  
S Waves ◽  
Rock Formation ◽  
Logging Tool ◽  
Difference Time

We have developed a new 3D acoustic logging tool (3DAC). To examine the azimuthal resolution of 3DAC, we have evaluated a 3D finite-difference time-domain model to simulate a case in which the borehole penetrated a rock formation boundary when the tool worked at the azimuthal-transmitting-azimuthal-receiving mode. The results indicated that there were two types of P-waves with different slowness in waveforms: the P-wave of the harder rock (P1) and the P-wave of the softer rock (P2). The P1-wave can be observed in each azimuthal receiver, but the P2-wave appears only in the azimuthal receivers toward the softer rock. When these two types of rock are both fast formations, two types of S-waves also exist, and they have better azimuthal sensitivity compared with P-waves. The S-wave of the harder rock (S1) appears only in receivers toward the harder rock, and the S-wave of the softer rock (S2) appears only in receivers toward the softer rock. A model was simulated in which the boundary between shale and sand penetrated the borehole but not the borehole axis. The P-wave of shale and the S-wave of sand are azimuthally sensitive to the azimuth angle variation of two formations. In addition, waveforms obtained from 3DAC working at the monopole-transmitting-azimuthal-receiving mode indicate that the corresponding P-waves and S-waves are azimuthally sensitive, too. Finally, we have developed a field example of 3DAC to support our simulation results: The azimuthal variation of the P-wave slowness was observed and can thus be used to reflect the azimuthal heterogeneity of formations.

Green's function of the Lord–Shulman thermo-poroelasticity theory

2020 ◽  
Vol 221 (3) ◽  
pp. 1765-1776 ◽  
Author(s):  
Jia Wei ◽  
Li-Yun Fu ◽  
Zhi-Wei Wang ◽  
Jing Ba ◽  
José M Carcione
Keyword(s):  
Plane Wave ◽  
Green’S Function ◽  
Green's Function ◽  
Heterogeneous Media ◽  
Numerical Algorithms ◽  
Heat Diffusion ◽  
P Wave ◽  
Wave Analysis ◽  
S Wave ◽  
S Waves

SUMMARY The Lord–Shulman thermoelasticity theory combined with Biot equations of poroelasticity, describes wave dissipation due to fluid and heat flow. This theory avoids an unphysical behaviour of the thermoelastic waves present in the classical theory based on a parabolic heat equation, that is infinite velocity. A plane-wave analysis predicts four propagation modes: the classical P and S waves and two slow waves, namely, the Biot and thermal modes. We obtain the frequency-domain Green's function in homogeneous media as the displacements-temperature solution of the thermo-poroelasticity equations. The numerical examples validate the presence of the wave modes predicted by the plane-wave analysis. The S wave is not affected by heat diffusion, whereas the P wave shows an anelastic behaviour, and the slow modes present a diffusive behaviour depending on the viscosity, frequency and thermoelasticity properties. In heterogeneous media, the P wave undergoes mesoscopic attenuation through energy conversion to the slow modes. The Green's function is useful to study the physics in thermoelastic media and test numerical algorithms.

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