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.

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.

On-axis triplications in elastic orthorhombic media

2020 ◽  
Vol 224 (1) ◽  
pp. 449-467
Author(s):  
Shibo Xu ◽  
Alexey Stovas ◽  
Hitoshi Mikada ◽  
Junichi Takekawa
Keyword(s):  
Group Velocity ◽  
Transversely Isotropic ◽  
Model Complexity ◽  
Model Parameters ◽  
S Wave ◽  
Slowness Surface ◽  
S Waves ◽  
Redundant Signal ◽  
Velocity Surface ◽  
Offset Curve

SUMMARY Triplicated traveltime curve has three arrivals at a given distance with the bowtie shape in the traveltime-offset curve. The existence of the triplication can cause a lot of problems such as several arrivals for the same wave type, anomalous amplitudes near caustics, anomalous behaviour of rays near caustics, which leads to the structure imaging deviation and redundant signal in the inversion of the model parameters. Hence, triplication prediction becomes necessary when the medium is known. The research of the triplication in transversely isotropic medium with a vertical symmetry axis (VTI) has been well investigated and it has become clear that, apart from the point singularity case, the triplicated traveltime only occurs for S wave. On contrary to the VTI case, the triplication behaviour in the orthorhombic (ORT) medium has not been well focused due to the model complexity. In this paper, we derive the second-order coefficients of the slowness surface for two S waves in the vicinity of three symmetry axes and define the elliptic form function to examine the existence of the on-axis triplication in ORT model. The existence of the on-axis triplication is found by the sign of the defined curvature coefficients. Three ORT models are defined in the numerical examples to analyse the behaviour of the on-axis triplication. The plots of the group velocity surface in the vicinity of three symmetry axes are shown for different ORT models where different shapes: convex or the saddle-shaped (concave along one direction and convex along with another) indicates the existence of the on-axis triplication. We also show the traveltime plots (associated with the group velocity surface) to illustrate the effect of the on-axis triplication.

scholarly journals Estimation of radiated energy using the KiK-net downhole records—old method for modern data

2020 ◽  
Vol 221 (2) ◽  
pp. 1029-1042 ◽  
Author(s):  
Hiroo Kanamori ◽  
Zachary E Ross ◽  
Luis Rivera
Keyword(s):  
Site Response ◽  
Source Model ◽  
Synthetic Seismograms ◽  
S Wave ◽  
P Waves ◽  
S Waves ◽  
Radiated Energy ◽  
Time Integral ◽  
Magnitude Range ◽  
Significant Difference

SUMMARY We use KiK-net (NIED) downhole records to estimate the radiated energy, ER, of 29 Japanese inland earthquakes with a magnitude range from Mw = 5.6 to 7.0. The method is based on the work of Gutenberg and Richter in which the time integral of S-wave ground-motion velocity-squared is measured as a basic metric of the radiated energy. Only stations within a distance of 100 km are used to minimize complex path and attenuation effects. Unlike the teleseismic method that uses mainly P waves, the use of S waves which carry more than 95 per cent of the radiated energy allows us to obtain robust results. We calibrate the method using synthetic seismograms to modernize and improve the Gutenberg–Richter method. We compute synthetic seismograms for a source model of each event with a given source function (i.e. known ER), the actual mechanism and the source-station geometry. Then, we compare the given ER with the computed energy metric to correct for the unknown effect of wave propagation and the mechanism. The use of downhole records minimizes the uncertainty resulting from the site response. Our results suggest that the currently available estimates of ER from teleseismic data are probably within a factor of 3, on average, of the absolute value. The scaled energy eR ( = ER/M0) is nearly constant at about 3 × 10−5 over a magnitude range from Mw = 5.6 to 7.0 with a slight increasing trend with Mw. We found no significant difference in eR between dip-slip and strike-slip events.

Robust Empirical Time–Frequency Relations for Seismic Spectral Amplitudes, Part 1: Application to Regional S Waves in Southeastern Iran

2020 ◽  
Author(s):  
Maryam Safarshahi ◽  
Igor B. Morozov
Keyword(s):  
Seismic Waves ◽  
Joint Inversion ◽  
Vertical Component ◽  
Transverse Component ◽  
Model Parameters ◽  
S Wave ◽  
Near Surface ◽  
S Waves ◽  
Time Frequency ◽  
Frequency Independent

ABSTRACT Empirical models of geometrical-, Q-, t-star, and kappa-type attenuation of seismic waves and ground-motion prediction equations (GMPEs) are viewed as cases of a common empirical standard model describing variation of wave amplitudes with time and frequency. Compared with existing parametric and nonparametric approaches, several new features are included in this model: (1) flexible empirical parameterization with possible nonmonotonous time or distance dependencies; (2) joint inversion for time or distance and frequency dependencies, source spectra, site responses, kappas, and Q; (3) additional constraints removing spurious correlations of model parameters and data residuals with source–receiver distances and frequencies; (4) possible kappa terms for sources as well as for receivers; (5) orientation-independent horizontal- and three-component amplitudes; and (6) adaptive filtering to reduce noise effects. The approach is applied to local and regional S-wave amplitudes in southeastern Iran. Comparisons with previous studies show that conventional attenuation models often contain method-specific biases caused by limited parameterizations of frequency-independent amplitude decays and assumptions about the models, such as smoothness of amplitude variations. Without such assumptions, the frequency-independent spreading of S waves is much faster than inferred by conventional modeling. For example, transverse-component amplitudes decrease with travel time t as about t−1.8 at distances closer than 90 km and as t−2.5 beyond 115 km. The rapid amplitude decay at larger distances could be caused by scattering within the near surface. From about 90 to 115 km distances, the amplitude increases by a factor of about 3, which could be due to reflections from the Moho and within the crust. With more accurate geometrical-spreading and kappa models, the Q factor for the study area is frequency independent and exceeds 2000. The frequency-independent and Q-type attenuation for vertical-component and multicomponent amplitudes is somewhat weaker than for the horizontal components. These observations appear to be general and likely apply to other areas.

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.

Transformation to zero offset for mode‐converted waves

Geophysics ◽  
1992 ◽  
Vol 57 (3) ◽  
pp. 474-477 ◽  
Author(s):  
Mohammed Alfaraj ◽  
Ken Larner
Keyword(s):  
Seismic Data ◽  
Constant Velocity ◽  
Reflection Point ◽  
P Waves ◽  
S Waves ◽  
Nmo Correction ◽  
Converted Waves ◽  
Zero Offset ◽  
Correct Data

The transformation to zero offset (TZO) of prestack seismic data for a constant‐velocity medium is well understood and is readily implemented when dealing with either P‐waves or S‐waves. TZO is achieved by inserting a dip moveout (DMO) process to correct data for the influence of dip, either before or after normal moveout (NMO) correction (Hale, 1984; Forel and Gardner, 1988). The TZO process transforms prestack seismic data in such a way that common‐midpoint (CMP) gathers are closer to being common reflection point gathers after the transformation.

A two‐layer stacking procedure to enhance converted waves

Geophysics ◽  
1993 ◽  
Vol 58 (7) ◽  
pp. 997-1001 ◽  
Author(s):  
B. L. N. Kennett
Keyword(s):  
Lower Layer ◽  
Effective Means ◽  
Water Layer ◽  
Physical Models ◽  
S Wave ◽  
P Waves ◽  
S Waves ◽  
Receiver Array ◽  
Sea Bed ◽  
Layer Stacking

For marine seismic sources quite efficient conversion of P‐waves to S‐waves can occur at hard seafloors, e.g., carbonate horizons in tropical waters. The S‐waves are reflected back from structures at depth and are reconverted to P‐waves in the water before detection by the receiver array. Such PSSP reflections can carry useful information on the structure beneath the sea bed but are most significant at large offsets and so are not easily stacked with a conventional normal moveout (NMO) procedure based on a hyperbolic time trajectory. A two‐layer stacking procedure that separates the water layer from the region below the seafloor provides a very effective means of extracting the PSSP arrivals, but also works well for P‐waves. There is no direct analytic form for the stacking trajectories but they can be calculated quite efficiently numerically. A further advantage is that the stacking velocity for S‐waves in the lower layer can be interpreted directly in terms of S‐wave propagation, so that S‐wave interval velocities can be found. Stacking procedures based on such simple physical models are likely to be useful in other cases where attention needs to be focused on a particular aspect of the wavefield.

Focused inversion of vertical radar profile (VRP) traveltime data

Geophysics ◽  
2012 ◽  
Vol 77 (1) ◽  
pp. H9-H18 ◽  
Author(s):  
Giulio Vignoli ◽  
Rita Deiana ◽  
Giorgio Cassiani
Keyword(s):  
Inverse Problem ◽  
Physical Properties ◽  
Reference Model ◽  
A Priori ◽  
S Wave ◽  
Compact Structure ◽  
Arrival Times ◽  
Minimum Support ◽  
Error Amplification ◽  
Zero Offset

The reconstruction of the GPR velocity vertical profile from vertical radar profile (VRP) traveltime data is a problem with a finite number of measurements and imprecise data, analogous to similar seismic techniques, such as the shallow down-hole test used for S-wave velocity profiling or the vertical seismic profiling (VSP) commonly used in deeper exploration. The uncertainty in data accuracy and the error amplification inherent in deriving velocity estimates from gradients of arrival times make this an example of an ill-posed inverse problem. In the framework of Tikhonov regularization theory, ill-posedness can be tackled by introducing a regularizing functional (stabilizer). The role of this functional is to stabilize the numerical solution by incorporating the appropriate a priori assumptions about the geometrical and/or physical properties of the solution. One of these assumptions could be the existence of sharp boundaries separating rocks with different physical properties. We apply a method based on the minimum support stabilizer to the VRP traveltime inverse problem. This stabilizer makes it possible to produce more accurate profiles of geological targets with compact structure. We compare more traditional inversion results with our proposed compact reconstructions. Using synthetic examples, we demonstrate that the minimum support stabilizer allows an improved recovery of the profile shape and velocity values of blocky targets. We also study the stabilizer behavior with respect to different noise levels and different choices of the reference model. The proposed approach is then applied to real cases where VPRs have been used to derive moisture content profiles as a function of depth. In these real cases, the derived sharper profiles are consistent with other evidence, such as GPR zero-offset profiles, GPR reflections and known locations of the water table.

Shear waves, multiple reflections, and converted waves found by a deep vertical wave test (vertical seismic profiling)

Geophysics ◽  
1980 ◽  
Vol 45 (9) ◽  
pp. 1373-1411 ◽  
Author(s):  
C. C. Lash
Keyword(s):  
Traveling Waves ◽  
Wave Energy ◽  
S Wave ◽  
Multiple Reflections ◽  
P Waves ◽  
S Waves ◽  
Seismic Profiling ◽  
Vertical Seismic Profiling ◽  
Converted Waves ◽  
Set Up

Evidence that shear (S) waves are much more important in seismic surveys than currently believed was found in each of two deep well tests conducted some time ago. Wave tests were recorded along vertical lines, following procedures which are now designated “vertical seismic profiling.” The results may be divided into (1) evidence that shear (S) waves are produced by in‐hole dynamite charges and by the resulting compressional (P) waves, and (2) evidence that the S‐waves subsequently produce P‐waves. The proof of S‐wave production is quite conclusive. Even if we say that only P‐waves are set up in the immediate vicinity of the shot, some S‐waves are then generated within a radius of 10 to 100 ft to form what we will call a direct or “source S wave.” Other S‐waves are set up by conversion of P‐wave energy to S‐wave energy at interfaces hundreds and thousands of feet from the dynamite charge. In contrast to the P to S conversion, the evidence for S to P conversion is less conclusive. The source S‐wave generated near the shot was found to have a long‐period character, with many cycles which are believed to be controlled by the layering near the shot. The PS converted waves, which appear later, resemble the P‐waves that produce them. The interference to primary reflections by multiple reflections and/or converted waves produces complex signals at points deep in the well which require directional discrimination to separate up‐traveling waves from down‐traveling waves.

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