Inversion of P and SV waves from multicomponent offset vertical seismic profiles

Geophysics ◽  
1990 ◽  
Vol 55 (1) ◽  
pp. 39-50 ◽  
Author(s):  
Cengiz Esmersoy
Keyword(s):  
Time Window ◽  
Simple Expression ◽  
P Wave ◽  
Model Parameters ◽  
Separate Analysis ◽  
Angle Of Incidence ◽  
Apparent Velocity ◽  
Event Analysis ◽  
S Wave ◽  
Depth Level

Downgoing waves in multicomponent VSP experiments are used to obtain seismic P- and S-wave velocities as a function of depth and angle of incidence. If P and SV waveforms do not overlap in time at the depth of interest, local velocities of the medium are obtained by separate analysis of these events. The apparent velocity of the event (P or SV) is computed from the moveout across several neighboring depth locations. The angle of incidence of the same event is computed from the particle‐motion hodogram within an appropriately chosen time window. Then, the local medium velocity (P wave or S wave depending on the chosen event) is given by the apparent velocity multiplied by the cosine of the angle of incidence. Layer interfaces with reasonably sharp velocity contrasts are efficient P-wave to SV-wave converters, even at moderate angles of incidence. In offset VSP experiments, converted SV waves are generated with varying strengths at practically all depths. Consequently, the converted SV waveforms partially overlap with the direct P waveforms, making the separate event analysis difficult and inaccurate. These overlapping waveforms can be handled properly by modeling the data in a given time window as a superposition of several events. In particular, the downgoing data at each depth level are modeled as a superposition of a P wave and an SV wave, with local P and S velocities, angles of incidence, and waveforms as model parameters. These parameters are then estimated by minimizing the squared error between the observed data and the model‐generated data. The unknown waveforms are eliminated from the minimization problem, leaving only four nonlinear parameters (velocities and angles) for estimation. Once these four parameters are found, least‐squares estimates of waveforms are obtained by evaluating a simple expression.

scholarly journals Time–frequency windowing in multiparameter elastic FWI of shallow seismic wavefield

2020 ◽  
Vol 222 (2) ◽  
pp. 1164-1177
Author(s):  
Nikolaos Athanasopoulos ◽  
Edgar Manukyan ◽  
Thomas Bohlen ◽  
Hansruedi Maurer
Keyword(s):  
Wave Velocity ◽  
Time Window ◽  
Mass Density ◽  
Waveform Inversion ◽  
P Wave ◽  
S Wave ◽  
Time Frequency ◽  
Full Waveform ◽  
Shallow Seismic ◽  
P Wave Velocity

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.

scholarly journals A new acoustic assumption for orthorhombic media

2020 ◽  
Vol 223 (2) ◽  
pp. 1118-1129
Author(s):  
Mohammad Mahdi Abedi ◽  
Alexey Stovas
Keyword(s):  
Wave Propagation ◽  
Conventional Approach ◽  
P Wave ◽  
Model Parameters ◽  
Governing Equations ◽  
S Wave ◽  
S Waves ◽  
Exploration Seismology ◽  
And Inversion ◽  
Approximate Equations

SUMMARY In exploration seismology, the acquisition, processing and inversion of P-wave data is a routine. However, in orthorhombic anisotropic media, the governing equations that describe the P-wave propagation are coupled with two S waves that are considered as redundant noise. The main approach to free the P-wave signal from the S-wave noise is the acoustic assumption on the wave propagation. The conventional acoustic assumption for orthorhombic media zeros out the S-wave velocities along three orthogonal axes, but leaves significant S-wave artefacts in all other directions. The new acoustic assumption that we propose mitigates the S-wave artefacts by zeroing out their velocities along the three orthogonal symmetry planes of orthorhombic media. Similar to the conventional approach, our method reduces the number of required model parameters from nine to six. As numerical experiments on multiple orthorhombic models show, the accuracy of the new acoustic assumption also compares well to the conventional approach. On the other hand, while the conventional acoustic assumption simplifies the governing equations, the new acoustic assumption further complicates them—an issue that emphasizes the necessity of simple approximate equations. Accordingly, we also propose simpler rational approximate phase-velocity and eikonal equations for the new acoustic orthorhombic media. We show a simple ray tracing example and find out that the proposed approximate equations are still highly accurate.

Thin-bed prestack spectral inversion

Geophysics ◽  
2009 ◽  
Vol 74 (4) ◽  
pp. R49-R57 ◽  
Author(s):  
J. Germán Rubino ◽  
Danilo Velis
Keyword(s):  
Time Window ◽  
A Priori ◽  
Amplitude Spectrum ◽  
Wavelet Spectrum ◽  
Model Parameters ◽  
Data Sets ◽  
S Wave ◽  
P Waves ◽  
S Waves ◽  
Zero Offset

Prestack seismic data has been used in a new method to fully determine thin-bed properties, including the estimation of its thickness, P- and S-wave velocities, and density. The approach requires neither phase information nor normal-moveout (NMO) corrections, and assumes that the prestack seismic response of the thin layer can be isolated using an offset-dependent time window. We obtained the amplitude-versus-angle (AVA) response of the thin bed considering converted P-waves, S-waves, and all the associated multiples. We carried out the estimation of the thin-bed parameters in the frequency (amplitude spectrum) domain using simulated annealing. In contrast to using zero-offset data, the use of AVA data contributes to increase the robustness of this inverse problem under noisy conditions, as well as to significantly reduce its inherent nonuniqueness. To further reduce the nonuniqueness, and as a means to incorporate a priori geologic or geophysical information (e.g., well-log data), we imposed appropriate bounding constraints to the parameters of the media lying above and below the thin bed, which need not be known accurately. We tested the method by inverting noisy synthetic gathers corresponding to simple wedge models. In addition, we stochastically estimated the uncertainty of the solutions by inverting different data sets that share the same model parameters but are contaminated with different noise realizations. The results suggest that thin beds can be characterized fully with a moderate to high degree of confidence below tuning, even when using an approximate wavelet spectrum.

Elastic reflection traveltime inversion with decoupled wave equation

Geophysics ◽  
2018 ◽  
Vol 83 (5) ◽  
pp. R463-R474 ◽  
Author(s):  
Guanchao Wang ◽  
Shangxu Wang ◽  
Jianyong Song ◽  
Chunhui Dong ◽  
Mingqiang Zhang
Keyword(s):  
Wave Equation ◽  
Wave Velocity ◽  
Waveform Inversion ◽  
P Wave ◽  
Model Parameters ◽  
Local Minima ◽  
S Wave ◽  
Traveltime Inversion ◽  
Velocity Models ◽  
Elastic Reflection

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.

Reflection and refraction of elastic waves at a corrugated interface

1966 ◽  
Vol 56 (1) ◽  
pp. 201-221
Author(s):  
Shuzo Asano
Keyword(s):  
Wave Amplitude ◽  
Normal Incidence ◽  
P Wave ◽  
Irregular Waves ◽  
Angle Of Incidence ◽  
S Wave ◽  
Reflected Waves ◽  
S Waves ◽  
Significant Difference ◽  
Almost All

abstract The effect of a corrugated interface on wave propagation is considered by using the method that was first applied to acoustical gratings by Rayleigh. The problem is what happens when a plane P wave is incident on a corrugated interface that separates two semi-infinite media. As is well known, there are irregular (scattered) waves as well as regular waves. By assuming both the amplitude and the slope of a corrugated interface to be small, quantities of the order of the square of corrugation amplitude are taken into account. In the case of normal incidence for three models considered, the effect of corrugation on reflection is larger than the effect of corrugation on refraction; the amplitude of the regularly reflected waves decreases, and that of the regularly refracted waves and of the irregular waves increases, as the corrugation amplitude becomes larger. Generally, the larger the velocity contrast, the larger the variation of wave amplitude with the wavelength and the amplitude of corrugation. The S wave component generally becomes larger as the wavelength of corrugation becomes smaller. Boundary waves exist, depending upon the ratio of wavelength of corrugation to that of the incident wave. For a specified interface, it is possible that there is a significant difference in wave amplitude as a function of the elastic constants. In the case of oblique incidence, computation was carried out for angles of incidence smaller than 15° for one model. For these small angles of incidence, almost all results for the case of normal incidence still hold. Furthermore, it can be concluded that the effect of the angle of incidence on reflected S waves is larger than for the other waves and that large differences in the amplitudes of waves at different angles of incidence may be expected for the irregular waves.

Separation of S‐wave and P‐wave reflections offshore western Florida

Geophysics ◽  
1984 ◽  
Vol 49 (5) ◽  
pp. 493-508 ◽  
Author(s):  
Robert H. Tatham ◽  
Donald V. Goolsbee
Keyword(s):  
Mode Conversion ◽  
Hard Water ◽  
P Wave ◽  
Angle Of Incidence ◽  
Wave Reflections ◽  
S Wave ◽  
Seismic Reflection Data ◽  
Reflection Time ◽  
Processing Techniques ◽  
Independent Confirmation

Hard water‐bottom marine environments, such as offshore western Florida, have presented particular problems in the acquisition and processing of seismic reflection data. One problem has been the limited angle of incidence (less than critical) available to P‐wave penetration into the subsurface. Mode conversion from P‐wave to S‐waves (SV), however, is quite efficient over a broad range of angles of incidence. After the success of a previously reported physical model experiment, an experimental line was acquired offshore western Florida. The 19 mile line, located approximately 100 miles west of Key West, Florida, was shot and processed. Three key factors have contributed to the successful recording of mode‐converted S‐wave reflections: (1) recognition of the effect of the group length on attenuation of energy arriving at large angles of incidence; (2) tau‐p processing techniques that allow separation of energy by angle of incidence; and (3) velocity filtering over a range of hyperbolic normal‐moveout (NMO) velocities as part of the forward tau‐p transform. These three factors, two of them data processing techniques, have allowed separation of P‐ and S‐wave energy in the marine environment. Overall, S‐wave reflections have been unambiguously identified to a reflection time of 2 sec and may be interpreted to a reflection time of 2 sec. Integrating an S‐wave section with P‐wave interpretations of offshore Florida data allows an independent confirmation of structural events. This independent confirmation may be more significant than improvements in the P‐wave data quality alone. Lateraly stable [Formula: see text] values are computed in intervals 1500 to 5000 ft thick and to S‐wave reflection times as great as 3 sec. The opportunity of [Formula: see text], interpretations for lithologic identification, gas thickness estimates, and general stratigraphic trap exploration makes mode‐converted shear waves a new tool in this area.

Source characteristics of small to moderate earthquakes in the Kanto region, Japan: application of a new definition of the S-wave time window length

1996 ◽  
Vol 86 (5) ◽  
pp. 1284-1291
Author(s):  
Kazutoshi Watanabe ◽  
Haruo Sato ◽  
Shigeo Kinoshita ◽  
Masakazu Ohtake
Keyword(s):  
Wave Energy ◽  
Seismic Moment ◽  
Time Window ◽  
P Wave ◽  
Corner Frequency ◽  
Window Length ◽  
S Wave ◽  
S Waves ◽  
Source Characteristics ◽  
Kanto Region

Abstract The S wave from a local earthquake generally consists of several pulses, in contrast to a simple pulse of P wave. This results in a large uncertainty in the estimation of seismic moment and wave energy when the window length for S-wave analysis is not chosen properly. In this study, we propose a new method to define objectively an appropriate time window length of the S wave for estimation of source characteristics based on the S-wave to P-wave energy ratio for a point shear dislocation source. Analyzing waveform data of 97 local earthquakes in the Kanto region, Japan, whose magnitudes M range from 3.3 to 6.0, we obtained simple equations for predicting the time window length of the S-wave TS as a function of earthquake magnitude or pulse width of P-wave TP; we got TS ≈ 1.8 TP for the relation between TP and TS. Applying the S-wave window thus defined, we estimated seismic energy E, seismic moment M0, and corner frequency fc for both P and S waves. Regression analysis of those parameters revealed (1) our method to define TS is confirmed by the fact that the seismic moment determined from P and S waves are consistent; (2) in the range of 1014 < M0 < 1018 (N·m), M0 is almost proportional to f−3c both for P and S waves; (3) the value of E/M0 is 2.7 ∼ 4.0 × 10−5; and (4) breakdown of the scaling relation is seen at M ≦ 4.

AVO inversion and poroelasticity with P- and S-wave moduli

Geophysics ◽  
2012 ◽  
Vol 77 (6) ◽  
pp. N17-N24 ◽  
Author(s):  
Zhaoyun Zong ◽  
Xingyao Yin ◽  
Guochen Wu
Keyword(s):  
Seismic Data ◽  
Real Data ◽  
P Wave ◽  
Model Parameters ◽  
Initial Model ◽  
S Wave ◽  
Data Set ◽  
Statistical Probability ◽  
Avo Inversion ◽  
Poroelasticity Theory

The fluid term in the Biot-Gassmann equation plays an important role in reservoir fluid discrimination. The density term imbedded in the fluid term, however, is difficult to estimate because it is less sensitive to seismic amplitude variations. We combined poroelasticity theory, amplitude variation with offset (AVO) inversion, and identification of P- and S-wave moduli to present a stable and physically meaningful method to estimate the fluid term, with no need for density information from prestack seismic data. We used poroelasticity theory to express the fluid term as a function of P- and S-wave moduli. The use of P- and S-wave moduli made the derivation physically meaningful and natural. Then we derived an AVO approximation in terms of these moduli, which can then be directly inverted from seismic data. Furthermore, this practical and robust AVO-inversion technique was developed in a Bayesian framework. The objective was to obtain the maximum a posteriori solution for the P-wave modulus, S-wave modulus, and density. Gaussian and Cauchy distributions were used for the likelihood and a priori probability distributions, respectively. The introduction of a low-frequency constraint and statistical probability information to the objective function rendered the inversion more stable and less sensitive to the initial model. Tests on synthetic data showed that all the parameters can be estimated well when no noise is present and the estimated P- and S-wave moduli were still reasonable with moderate noise and rather smooth initial model parameters. A test on a real data set showed that the estimated fluid term was in good agreement with the results of drilling.

On the determination of the polarization angle of the S wave

1962 ◽  
Vol 52 (1) ◽  
pp. 95-107
Author(s):  
Otto Nuttli ◽  
John D. Whitmore
Keyword(s):  
Wave Velocity ◽  
Particle Motion ◽  
Poisson’S Ratio ◽  
Epicentral Distance ◽  
Critical Distance ◽  
P Wave ◽  
Poisson's Ratio ◽  
Polarization Angle ◽  
Angle Of Incidence ◽  
S Wave

Abstract This study is concerned with determining the minimum epicentral distance for which it is permissible to obtain the value of the polarization angle of the S wave by measuring the angle between the great circle path at the station and the direction of the horizontal component of the S wave particle motion obtained from the seismograms. This critical distance can be determined by the fact that at smaller distances the particle motion of the earth's surface due to the incidence of S will be nonlinear (the SH and the horizontal and vertical components of SV will be out of phase with respect to one another) while at larger distances the particle motion will be linear. An analysis of the S motion recorded by the Galitzin-Wilip seismographs at Florissant indicates that the critical distance is 42 degrees. The periods of these S waves are of the order of 10 second. The analysis also shows that the effective P wave velocity of teleseismic waves at the earth's free surface is 7.74 km/sec, and the effective value of Poisson's ratio and the effective S wave velocity at the earth's surface are 0.25 and 4.46 km/sec, respectively. By effective values are meant the values of the velocities and Poisson's ratio that govern the angle of incidence of the waves at the earth's surface.

Detection and analysis of naturally fractured gas reservoirs: Multiazimuth seismic surveys in the Wind River basin, Wyoming

Geophysics ◽  
1999 ◽  
Vol 64 (4) ◽  
pp. 1277-1292 ◽  
Author(s):  
Robert E. Grimm ◽  
Heloise B. Lynn ◽  
C. R. Bates ◽  
D. R. Phillips ◽  
K. M. Simon ◽  
...  
Keyword(s):  
P Wave ◽  
Apparent Velocity ◽  
Fracture Density ◽  
S Wave ◽  
High Fracture ◽  
Velocity Anisotropy ◽  
Wind River Basin ◽  
Reflection Data ◽  
Parallel Volume ◽  
Wave Methods

Multiazimuth binning of 3-D P-wave reflection data is a relatively simple but robust way of characterizing the spatial distribution of gas‐producing natural fractures. In our survey, data were divided into two volumes by ray azimuth (approximately perpendicular and parallel (±45° to the dominant fracture strike) and separately processed. Azimuthal differences or ratios of attributes provided a rough measure of anisotropy. Improved imaging was also attained in the more coherent fracture‐parallel volume. A neural network using azimuthally dependent velocity, reflectivity, and frequency attributes identified commercial gas wells with greater than 85% success. Furthermore, we were able to interpret the physical mechanisms of most of these correlations and so better generalize the approach. The apparent velocity anisotropy was compared to that derived from other P- and S-wave methods in an inset three‐component survey. Prestack determination of the azimuthal moveout ellipse will best quantify velocity anisotropy, but simple two‐ or four‐azimuth poststack analysis can adequately identify regions of high fracture density and gas yield.

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