Joint inversion of P- and PS-waves in orthorhombic media: Theory and a physical modeling study

Geophysics ◽  
1999 ◽  
Vol 64 (1) ◽  
pp. 146-161 ◽  
Author(s):  
Vladimir Grechka ◽  
Stephen Theophanis ◽  
Ilya Tsvankin
Keyword(s):  
Shear Wave ◽  
Physical Modeling ◽  
Horizontal Plane ◽  
Joint Inversion ◽  
Symmetry Plane ◽  
P Wave ◽  
Simple Relationship ◽  
Converted Wave ◽  
Data Set ◽  
Converted Waves

Reflection traveltimes recorded over azimuthally anisotropic fractured media can provide valuable information for reservoir characterization. As recently shown by Grechka and Tsvankin, normal moveout (NMO) velocity of any pure (unconverted) mode depends on only three medium parameters and usually has an elliptical shape in the horizontal plane. Because of the limited information contained in the NMO ellipse of P-waves, it is advantageous to use moveout velocities of shear or converted modes in attempts to resolve the coefficients of realistic orthorhombic or lower‐symmetry fractured models. Joint inversion of P and PS traveltimes is especially attractive because it does not require shear‐wave excitation. Here, we show that for models composed of horizontal layers with a horizontal symmetry plane, the traveltime of converted waves is reciprocal with respect to the source and receiver positions (i.e., it remains the same if we interchange the source and receiver) and can be adequately described by NMO velocity on conventional‐length spreads. The azimuthal dependence of converted‐wave NMO velocity has the same form as for pure modes but requires the spatial derivatives of two-way traveltime for its determination. Using the generalized Dix equation of Grechka, Tsvankin, and Cohen, we derive a simple relationship between the NMO ellipses of pure and converted waves that provides a basis for obtaining shear‐wave information from P and PS data. For orthorhombic models, the combination of the reflection traveltimes of the P-wave and two split PS-waves makes it possible to reconstruct the azimuthally dependent NMO velocities of the pure shear modes and to find the anisotropic parameters that cannot be determined from P-wave data alone. The method is applied to a physical modeling data set acquired over a block of orthorhombic material—Phenolite XX-324. The inversion of conventional‐spread P and PS moveout data allowed us to obtain the orientation of the vertical symmetry planes and eight (out of nine) elastic parameters of the medium (the reflector depth was known). The remaining coefficient (c12 or δ(3) in Tsvankin’s notation) is found from the direct P-wave arrival in the horizontal plane. The inversion results accurately predict moveout curves of the pure S-waves and are in excellent agreement with direct measurements of the horizontal velocities.

Survey design for coal-scale 3D-PS seismic reflection

Geophysics ◽  
2016 ◽  
Vol 81 (6) ◽  
pp. P57-P70 ◽  
Author(s):  
Shaun Strong ◽  
Steve Hearn
Keyword(s):  
Survey Design ◽  
High Amplitude ◽  
Azimuthal Anisotropy ◽  
Mine Planning ◽  
P Wave ◽  
Depth Range ◽  
Low Velocity ◽  
Converted Wave ◽  
Data Set ◽  
Economic Considerations

Survey design for converted-wave (PS) reflection is more complicated than for standard P-wave surveys, due to raypath asymmetry and increased possibility of phase distortion. Coal-scale PS surveys (depth [Formula: see text]) require particular consideration, partly due to the particular physical properties of the target (low density and low velocity). Finite-difference modeling provides a pragmatic evaluation of the likely distortion due to inclusion of postcritical reflections. If the offset range is carefully chosen, then it may be possible to incorporate high-amplitude postcritical reflections without seriously degrading the resolution in the stack. Offsets of up to three times target depth may in some cases be usable, with appropriate quality control at the data-processing stage. This means that the PS survey design may need to handle raypaths that are highly asymmetrical and that are very sensitive to assumed velocities. A 3D-PS design was used for a particular coal survey with the target in the depth range of 85–140 m. The objectives were acceptable fold balance between bins and relatively smooth distribution of offset and azimuth within bins. These parameters are relatively robust for the P-wave design, but much more sensitive for the case of PS. Reduction of the source density is more acceptable than reduction of the receiver density, particularly in terms of the offset-azimuth distribution. This is a fortuitous observation in that it improves the economics of a dynamite source, which is desirable for high-resolution coal-mine planning. The final-survey design necessarily allows for logistical and economic considerations, which implies some technical compromise. However, good fold, offset, and azimuth distributions are achieved across the survey area, yielding a data set suitable for meaningful analysis of P and S azimuthal anisotropy.

Simultaneous inversion of PP and PS seismic data

Geophysics ◽  
2006 ◽  
Vol 71 (3) ◽  
pp. R1-R10 ◽  
Author(s):  
Helene Hafslund Veire ◽  
Martin Landrø
Keyword(s):  
Seismic Data ◽  
Reservoir Characterization ◽  
Model Building ◽  
Joint Inversion ◽  
P Wave ◽  
Inversion Method ◽  
System Of Equations ◽  
S Wave ◽  
Data Set ◽  
Simultaneous Inversion

Elastic parameters derived from seismic data are valuable input for reservoir characterization because they can be related to lithology and fluid content of the reservoir through empirical relationships. The relationship between physical properties of rocks and fluids and P-wave seismic data is nonunique. This leads to large uncertainties in reservoir models derived from P-wave seismic data. Because S- waves do not propagate through fluids, the combined use of P-and S-wave seismic data might increase our ability to derive fluid and lithology effects from seismic data, reducing the uncertainty in reservoir characterization and thereby improving 3D reservoir model-building. We present a joint inversion method for PP and PS seismic data by solving approximated linear expressions of PP and PS reflection coefficients simultaneously using a least-squares estimation algorithm. The resulting system of equations is solved by singular-value decomposition (SVD). By combining the two independent measurements (PP and PS seismic data), we stabilize the system of equations for PP and PS seismic data separately, leading to more robust parameter estimation. The method does not require any knowledge of PP and PS wavelets. We tested the stability of this joint inversion method on a 1D synthetic data set. We also applied the methodology to North Sea multicomponent field data to identify sand layers in a shallow formation. The identified sand layers from our inverted sections are consistent with observations from nearby well logs.

scholarly journals Methodology for dense spatial sampling of multicomponent recording of converted waves in shallow marine environments

Geophysics ◽  
2010 ◽  
Vol 75 (6) ◽  
pp. WB29-WB37 ◽  
Author(s):  
Nihed Allouche ◽  
Guy G. Drijkoningen ◽  
Joost van der Neut
Keyword(s):  
Spatial Sampling ◽  
Danube River ◽  
Converted Wave ◽  
Data Set ◽  
Shallow Marine ◽  
Spatial Aliasing ◽  
Receiver Array ◽  
Effective Manner ◽  
Processing Step ◽  
Converted Waves

A widespread use of converted waves for shallow marine applications is hampered by spatial aliasing and field efficiency. Their short wavelengths require dense spatial sampling which often needs to be achieved by receivers deployed on the seabed. We adopted a new methodology where the dense spatial sampling is achieved in the common-receiver domain by reducing the shot spacing. This is done by shooting one track multiple times and merging the shot lines in an effective manner in a separate processing step. This processing step is essential because positioning errors introduced during the field measurement can become significant in the combined line, particularly when they exceed the distance between two adjacent shot positions. For this processing step, a particular shot line is used as a reference line and relative variations in source and receiver positions in the other shot lines are corrected for using crosscorrelation. The combined shot line can subsequently be regularized for further processing. The methodology is adopted in a field experiment conducted in the Danube River in Hungary. The aim of the seismic experiment was to acquire properly sampled converted-wave data using a multicomponent receiver array. The dense spatial sampling was achieved by sailing one track 14 times. After correcting for the underwater receiver positions using the direct arrival, the crosscorrelation step was applied to merge the different shot lines. The successfully combined result is regularized into a densely sampled data set free of visible spatial aliasing and suitable for converted-wave processing.

Shallow crustal structure in the northwestern Iranian Plateau and its tectonic implications

2021 ◽  
Author(s):  
Xu Wang ◽  
Ling Chen ◽  
Morteza Talebian ◽  
Yinshuang Ai ◽  
Mingming Jiang ◽  
...  
Keyword(s):  
Shear Wave ◽  
Crustal Structure ◽  
Joint Inversion ◽  
Receiver Functions ◽  
Causal Link ◽  
Passive Margin ◽  
P Wave ◽  
Iranian Plateau ◽  
Systematic Analysis ◽  
Study Region

<p>The crustal structure of the Iranian Plateau bears important information about the details of the tectono-magmatic processes associated with the Neo-Tethys subduction and subsequent Arabia-Eurasia collision. Using a newly developed method of joint inversion of multi-frequency waveforms around and horizontal-to-vertical (H/V) ratios of the direct P arrivals in teleseismic P-wave receiver functions, we construct the shear-wave velocity image of the shallow crust (from surface up to 10-km depth below sea level) along a dense seismic array across the Zagros suture in the northwest Iranian Plateau. The most striking structural feature of the study region is the presence of low- and high-velocity anomalies (LVAs and HVAs) beneath the Zagros fold-and-thrust belt and the Iranian continent, respectively, indicating strong structural differences on the two sides of the suture. Systematic analysis on the velocity estimates and comparison with laboratory measurements and regional geology suggest that the LVAs and HVAs are representatives of Zagros sedimentary rocks and arc to intraplate magmatic rocks, respectively. The LVAs (1.3-2.0 km/s) are characterized by a series of faulted anti-form structures at ~1-7 km depths beneath Zagros. They are likely dominantly composed of shales and mudstones, and could have acted as mechanically weaknesses to accommodate different deformations of surroundings and give rise to the present-day depth-dependent seismicity. The HVAs beneath the central domain and Alborz in the Iranian continent present large ranges in both velocity (3.2-3.9 km/s) and depth (0-10 km), probably suggesting strong lithological variations in these areas. Most of the HVAs above 5-km depth have shear-wave velocities of 3.2 to 3.6 km/s, comparable to those of andesites and basalts dominated in the northwestern Iranian plateau. The deeper HVAs (below 5-km depth), which generally have greater velocities ~3.6-3.9 km/s falling into the velocity range of intrusive rocks such as granodiorites, diorites and diabases, appear to have much larger volumes at depth than that exposed on the surface in the study region. Moreover, the surface projections of the HVAs are spatially coincident with the major faults or tectonic boundaries of the region, suggesting a causal link. Our observations provide evidence for not only the lithology-controlled layering in both sedimentary structure and deformation in the Zagros passive margin but also the much more substantial magma generation and emplacement at depth than faulting-facilitated eruption and exposure on the surface in the Iranian active margin during the subduction and collision processes.</p>

Variation of P-wave reflectivity with offset and azimuth in anisotropic media

Geophysics ◽  
1998 ◽  
Vol 63 (3) ◽  
pp. 935-947 ◽  
Author(s):  
Andreas Rüger
Keyword(s):  
Reflection Coefficient ◽  
Shear Wave ◽  
Wave Reflection ◽  
Symmetry Plane ◽  
Anisotropic Media ◽  
Shear Wave Splitting ◽  
P Wave ◽  
Reflection Coefficients ◽  
Wave Splitting ◽  
Splitting Parameter

P-wave amplitudes may be sensitive even to relatively weak anisotropy of rock mass. Recent results on symmetry‐plane P-wave reflection coefficients in azimuthally anisotropic media are extended to observations at arbitrary azimuth, large incidence angles, and lower symmetry systems. The approximate P-wave reflection coefficient in transversely isotropic media with a horizontal axis of symmetry (HTI) (typical for a system of parallel vertical cracks embedded in an isotropic matrix) shows that the amplitude versus offset (AVO) gradient varies as a function of the squared cosine of the azimuthal angle. This change can be inverted for the symmetry‐plane directions and a combination of the shear‐wave splitting parameter γ and the anisotropy coefficient [Formula: see text]. The reflection coefficient study is also extended to media of orthorhombic symmetry that are believed to be more realistic models of fractured reservoirs. The study shows the orthorhombic and HTI reflection coefficients are very similar and the azimuthal variation in the orthorhombic P-wave reflection response is a function of the shear‐wave splitting parameter γ and two anisotropy parameters describing P-wave anisotropy for near‐vertical propagation in the symmetry planes. The simple relationships between the reflection amplitudes and anisotropic coefficients given here can be regarded as helpful rules of thumb in quickly evaluating the importance of anisotropy in a particular play, integrating results of NMO and shear‐wave‐splitting analyses, planning data acquisition, and guiding more advanced numerical amplitude‐inversion procedures.

Identifying, removing, and imaging P‐S conversions at salt‐sediment interfaces

Geophysics ◽  
2003 ◽  
Vol 68 (3) ◽  
pp. 1052-1059 ◽  
Author(s):  
Richard S. Lu ◽  
Dennis E. Willen ◽  
Ian A. Watson
Keyword(s):  
P Wave ◽  
Time Interval ◽  
S Wave ◽  
Converted Wave ◽  
Prestack Depth Migration ◽  
Depth Migration ◽  
Time Migration ◽  
Wave Imaging ◽  
Wave Image ◽  
Converted Waves

The large velocity contrast between salt and the surrounding sediments generates strong conversions between P‐ and S‐wave energy. The resulting converted events can be noise on P‐wave migrated images and should be identified and removed to facilitate interpretation. On the other hand, they can also be used to image a salt body and its adjacent sediments when the P‐wave image is inadequate. The converted waves with smaller reflection and transmission angles and much larger critical angles generate substantially different illumination than does the P‐wave. In areas where time migration is valid, the ratio between salt thickness in time and the time interval between the P‐wave and the converted‐wave salt base on a time‐migrated image is about 2.6 or 1.3, depending upon whether the seismic wave propagates along one or both of the downgoing and upcoming raypaths in salt as the S‐wave, respectively. These ratios can be used together with forward seismic modeling and 2D prestack depth migration to identify the converted‐wave base‐of‐salt (BOS) events in time and depth and to correctly interpret the subsalt sediments. It is possible to mute converted‐wave events from prestack traces according to their computed arrival times. Prestack depth migration of the muted data extends the updip continuation of subsalt sedimentary beds, and improves the salt–sediment terminations in the P‐wave image. Prestack and poststack depth‐migrated examples illustrate that the P‐wave and the three modes of converted waves preferentially image different parts of the base of salt. In some areas, the P‐wave BOS can be very weak, obscured by noise, or completely absent. Converted‐wave imaging complements P‐wave imaging in delineating the BOS for velocity model building.

Joint inversion of Rayleigh-wave dispersion and P-wave refraction data for laterally varying layered models

Geophysics ◽  
2014 ◽  
Vol 79 (4) ◽  
pp. EN49-EN59 ◽  
Author(s):  
Daniele Boiero ◽  
Laura Valentina Socco
Keyword(s):  
Rayleigh Wave ◽  
Joint Inversion ◽  
A Priori ◽  
P Wave ◽  
Inversion Method ◽  
Model Parameters ◽  
Data Set ◽  
Wave Refraction ◽  
Velocity Models ◽  
Refraction Data

We implemented a joint inversion method to build P- and S-wave velocity models from Rayleigh-wave and P-wave refraction data, specifically designed to deal with laterally varying layered environments. A priori information available over the site and any physical law to link model parameters can be also incorporated. We tested and applied the algorithm behind the method. The results from a field data set revealed advantages with respect to individual surface-wave analysis (SWA) and body wave tomography (BWT). The algorithm imposed internal consistency for all the model parameters relaxing the required a priori assumptions (i.e., Poisson’s ratio level of confidence in SWA) and the inherent limitations of the two methods (i.e., velocity decreases for BWT).

Examining the processing differences between P and P-S waves in a Rocky Mountain Foothills model

2014 ◽  
Vol 54 (2) ◽  
pp. 504
Author(s):  
Sanjeev Rajput ◽  
Michael Ring
Keyword(s):  
Rocky Mountain ◽  
P Wave ◽  
S Wave ◽  
Converted Wave ◽  
Wave Source ◽  
Depth Migration ◽  
S Waves ◽  
Full Waveform ◽  
Fluid Saturation ◽  
Converted Waves

For the past two decades, most of the shear-wave (S-wave) or converted wave (P-S) acquisitions were performed with P-wave source by making the use of downgoing P-waves converting to upgoing S-waves at the mode conversion boundaries. The processing of converted waves requires studying asymmetric reflection at the conversion point, difference in geometries and conditions of source and receiver, and the partitioning of energy into orthogonally polarised components. Interpretation of P-S sections incorporates the identification of P-S waves, full waveform modeling, correlation with P-wave sections and depth migration. The main applications of P-S wave imaging are to obtain a measure of subsurface S-wave properties relating to rock type and fluid saturation (in addition to the P-wave values), imaging through gas clouds and shale diapers, and imaging interfaces with low P-wave contrast but significant S-wave changes. This study examines the major differences in processing of P and P-S wave surveys and the feasibility of identifying converted mode reflections by P-wave sources in anisotropic media. Two-dimensional synthetic seismograms for a realistic rocky mountain foothills model were studied. A Kirchhoff-based technique that includes anisotropic velocities is used for depth migration of converted waves. The results from depth imaging show that P-S section help in distinguishing amplitude associated with hydrocarbons from those caused by localised stratigraphic changes. In addition, the full waveform elastic modeling is useful in finding an appropriate balance between capturing high-quality P-wave data and P-S data challenges in a survey.

scholarly journals Advantages of Shear Wave Seismic in Morrow Sandstone Detection

2011 ◽  
Vol 2011 ◽  
pp. 1-16 ◽  
Author(s):  
Paritosh Singh ◽  
Thomas Davis
Keyword(s):  
Shear Wave ◽  
Pure Shear ◽  
High Amplitude ◽  
Compressional Wave ◽  
Side Lobe ◽  
P Wave ◽  
S Wave ◽  
Converted Wave ◽  
P Waves ◽  
Wave Data

The Upper Morrow sandstones in the western Anadarko Basin have been prolific oil producers for more than five decades. Detection of Morrow sandstones is a major problem in the exploration of new fields and the characterization of existing fields because they are often very thin and laterally discontinuous. Until recently compressional wave data have been the primary resource for mapping the lateral extent of Morrow sandstones. The success with compressional wave datasets is limited because the acoustic impedance contrast between the reservoir sandstones and the encasing shales is small. Here, we have performed full waveform modeling study to understand the Morrow sandstone signatures on compressional wave (P-wave), converted-wave (PS-wave) and pure shear wave (S-wave) gathers. The contrast in rigidity between the Morrow sandstone and surrounding shale causes a strong seismic expression on the S-wave data. Morrow sandstone shows a distinct high amplitude event in pure S-wave modeled gathers as compared to the weaker P- and PS-wave events. Modeling also helps in understanding the adverse effect of interbed multiples (due to shallow high velocity anhydrite layers) and side lobe interference effects at the Morrow level. Modeling tied with the field data demonstrates that S-waves are more robust than P-waves in detecting the Morrow sandstone reservoirs.

Reflectivity inversion for attenuated seismic data: Physical modeling and field data experiments

Geophysics ◽  
2016 ◽  
Vol 81 (1) ◽  
pp. T11-T24 ◽  
Author(s):  
Xintao Chai ◽  
Shangxu Wang ◽  
Jianxin Wei ◽  
Jingnan Li ◽  
Hanjun Yin
Keyword(s):  
Physical Model ◽  
Seismic Data ◽  
Physical Modeling ◽  
P Wave ◽  
Ratio Method ◽  
Blind Test ◽  
Data Set ◽  
Text Input ◽  
Text Filtering ◽  
Reflectivity Inversion

We have developed a method of nonstationary sparse reflectivity inversion (NSRI) that directly retrieves the reflectivity series from nonstationary seismic data without the intrinsic instability associated with inverse [Formula: see text] filtering methods. We have investigated the NSRI performance in the presence of input error (e.g., the phase shift and the peak frequency of the wavelet), which determined that NSRI results are reasonable in the case of moderate error. NSRI was then applied to data collected from a laboratory physical model made of highly attenuating media, for which true reflectivities were known, but the wave propagation and the [Formula: see text] filtering mechanism were not. Analysis of data from the physical model, therefore, represented a blind test for evaluating the effectiveness and accuracy of NSRI. The physical model had a specified spatial scale of 1:5000 (relative to the field scale) and an approximate 1:1 velocity scale. Because the [Formula: see text] input is required by NSRI, attenuation of the P-wave was measured in the laboratory at ultrasonic frequencies with a pulse transmission technique and the spectral ratio method. Although multiples, side reflections from the model boundaries, diffractions, and other event types were clearly observed from the raw data, no preprocessing was done to avoid affecting the [Formula: see text] filtering effects. Results from the physical modeling data demonstrated that the derived formula for an attenuated seismogram was correct and estimated [Formula: see text] values were reliable. The functions and advantages of NSRI were confirmed. The [Formula: see text] compensated seismogram generated by NSRI was superior to that generated using gain-limited inverse [Formula: see text] filtering. We have also investigated NSRI’s capabilities in analyzing a marine data set from the Gulf of Suez. These examples provided a basis for discussing assumptions and limitations of NSRI.

Sign in / Sign up

Export Citation Format

Share Document