scholarly journals Effect of errors in the migration velocity model of PS-converted waves on traveltime accuracy in prestack Kirchhoff time migration in weak anisotropic media

Geophysics ◽  
2008 ◽  
Vol 73 (5) ◽  
pp. S195-S205 ◽  
Author(s):  
Hengchang Dai ◽  
Xiang-Yang Li
Keyword(s):  
Wave Velocity ◽  
Vertical Velocity ◽  
Velocity Ratio ◽  
Anisotropic Media ◽  
Horizontal Distance ◽  
Converted Wave ◽  
Anisotropic Parameter ◽  
Effective Velocity ◽  
Time Migration ◽  
Converted Waves

We investigated the effect of errors in the migration-velocity model of PS-converted waves on the traveltime calculated in prestack Kirchhoff time migration in weak anisotropic media. The prestack-Kirchhoff-time-migration operator contains four parameters: the PS-converted-wave velocity, the vertical velocity ratio, the effective velocity ratio, and the anisotropic parameter. We derived four error factors that correspond to those parameters. Theoretical and numerical analyses of the error factors show them all to be inversely proportional to the velocity and to traveltime. Traveltime errors for shallow events usually are larger than for deep events. Error in PS-converted-wave velocity causes the largest traveltime error, and error in the vertical velocity ratio causes the smallest traveltime error. For a small horizontal-distance/depth ratio, the error in the effective velocity ratio affects traveltime more than does the anisotropic-parameter error. However, the anisotropic-parameter error affects traveltime more when the horizontal-distance/depth ratio is larger. Traveltime errors caused by errors in effective velocity ratio and the anisotropic parameter mainly stem from the converted-S-wave raypath of the PS-converted waves. To save processing time and cost, PS-wave velocity can be estimated accurately without an accurate vertical velocity ratio, effective velocity ratio, and anisotropic parameter. These findings are useful for understanding PS-wave behavior and for PS-wave imaging in anisotropic media.

Anisotropic velocity updating for converted-wave prestack time migration

Geophysics ◽  
2007 ◽  
Vol 72 (2) ◽  
pp. D29-D32 ◽  
Author(s):  
Xiaogui Miao ◽  
Torre Zuk
Keyword(s):  
Wave Velocity ◽  
Velocity Ratio ◽  
Anisotropy Parameter ◽  
Estimation Method ◽  
P Wave ◽  
Converted Wave ◽  
Anisotropic Parameter ◽  
Wave Data ◽  
Time Migration ◽  
Prestack Time Migration

The conventional method used to estimate velocities for converted-wave (C-wave) prestack time migration is awkward because the P-wave velocity [Formula: see text] comes from P-wave processing, the velocity ratio gamma [Formula: see text] is estimated from C-wave data, and the S-wave velocity [Formula: see text] is then derived from [Formula: see text] and gamma. Instead, by using the C-wave velocity [Formula: see text], effective gamma [Formula: see text], and anisotropy parameter [Formula: see text], velocity updating becomes straightforward and more reliable. To update [Formula: see text] for converted-wave time migration, one can carry out hyperbolic moveout analysis on the hyperbolic-moveout-migrated-common-midpoint (HMO-MCMP) gathers. However, the errors in initial [Formula: see text] and anisotropy parameter [Formula: see text] can only be corrected by trial and error. In this article, we propose to remove the effects of initial [Formula: see text] and [Formula: see text] in the HMO-MCMP gathers by inverting the moveout related to the initial [Formula: see text] and [Formula: see text]. This enables a full nonhyperbolic velocity analysis to update not only [Formula: see text] but also [Formula: see text] and [Formula: see text]. To obtain reliable [Formula: see text], we also develop a simultaneous PP/PS anisotropic-parameter estimation method so the [Formula: see text] estimated from P-wave data is compared immediately with the [Formula: see text] derived from [Formula: see text] by using C-wave data. This provides a better constraint for estimating anisotropy parameters. The method has been tested and shows consistent improvement in converted-wave prestack time-migration velocity estimations.

Explicit expressions for prestack map time migration in isotropic and VTI media and the applicability of map depth migration in heterogeneous anisotropic media

Geophysics ◽  
2006 ◽  
Vol 71 (1) ◽  
pp. S13-S28 ◽  
Author(s):  
Huub Douma ◽  
Maarten V. de Hoop
Keyword(s):  
Closed Form ◽  
Anisotropic Media ◽  
Velocity Model ◽  
Pure Mode ◽  
Anisotropic Parameter ◽  
Depth Migration ◽  
Time Migration ◽  
Isotropic Media ◽  
The Common ◽  
Vti Media

We present 3D prestack map time migration in closed form for qP-, qSV-, and mode-converted waves in homogeneous transversely isotropic media with a vertical symmetry axis (VTI). As far as prestack time demigration is concerned, we present closed-form expressions for mapping in homogeneous isotropic media, while for homogeneous VTI media we present a system of four nonlinear equations with four unknowns to solve numerically. The expressions for prestack map time migration in VTI homogeneous media are directly applicable to the problem of anisotropic parameter estimation (i.e., the anellipticity parameter η) in the context of time-migration velocity analysis. In addition, we present closed-form expressions for both prestack map time migration and demigration in the common-offset domain for pure-mode (P-P or S-S) waves in homogeneous isotropic media that use only the slope in the common-offset domain as opposed to slopes in both the common-shot and common-receiver (or equivalently the common-offset and common-midpoint) domains. All time-migration and demigration equations presented can be used in media with mild lateral and vertical velocity variations, provided the velocity is replaced with the local rms velocity. Finally, we discuss the condition for applicability of prestack map depth migration and demigration in heterogeneous anisotropic media that allows the formation of caustics and explain that this condition is satisfied if, given a velocity model and acquisition geometry, one can map-depth-migrate without ambiguity in either the migrated location or the migrated orientation of reflectors in the image.

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.

The effects of migration velocity errors on traveltime accuracy in prestack Kirchhoff time migration and the image of PS converted waves

Geophysics ◽  
2006 ◽  
Vol 71 (2) ◽  
pp. S73-S83 ◽  
Author(s):  
Hengchang Dai ◽  
Xiang-Yang Li
Keyword(s):  
Wave Velocity ◽  
Velocity Ratio ◽  
Real Data ◽  
Velocity Model ◽  
Image Point ◽  
Analysis Tool ◽  
Model Errors ◽  
Time Migration ◽  
Dip Angle ◽  
Wave Migration

We analyze prestack PS migration images and their focusing sensitivity to errors in the computed PS traveltimes. The key analysis tool is a formula that defines PS traveltimes errors as explicit functions of velocity model errors. The most important factors in this formula are the PS velocity and the P-to-S velocity ratio. Analysis shows that the error in PS traveltime for shallow events is usually larger than that for deep events for a given error in the velocity model. Also the PS traveltime is affected more severely by errors in the PS-velocity model than in the P-to-S velocity ratio. The effect of traveltime errors increases with dip angle of reflectors. Numerical analysis shows that, for a fixed scatterpoint, the effect of the PS-wave velocity error is several times larger than the effect of the error in the P-to-S velocity ratio. Examples from field data show that the PS-wave velocity must be estimated accurately with errors less than 1% in order perfectly flatten the events in common-image-point (CIP) gathers. In contrast, an error in the PS-velocity ratio of up to several percent is allowed. This suggests that for acceptable PS-wave migration, only the PS-velocity model and a rough estimate of the P-to-S velocity ratio is needed. This finding is useful for processing PS-wave data because it is difficult and time consuming to estimate the velocity ratio accurately from the real data. This finding is also useful for our understanding of PS-wave behavior and for PS-wave imaging.

Converted‐wave reflection seismology over inhomogeneous, anisotropic media

Geophysics ◽  
1999 ◽  
Vol 64 (3) ◽  
pp. 678-690 ◽  
Author(s):  
Leon Thomsen
Keyword(s):  
Velocity Ratio ◽  
Anisotropic Media ◽  
P Wave ◽  
Image Point ◽  
Physical Parameters ◽  
Pure Mode ◽  
Good Precision ◽  
Converted Wave ◽  
Wave Data ◽  
Conversion Point

Converted‐wave processing is more critically dependent on physical assumptions concerning rock velocities than is pure‐mode processing, because not only moveout but also the offset of the imaged point itself depend upon the physical parameters of the medium. Hence, unrealistic assumptions of homogeneity and isotropy are more critical than for pure‐mode propagation, where the image‐point offset is determined geometrically rather than physically. In layered anisotropic media, an effective velocity ratio [Formula: see text] (where [Formula: see text] is the ratio of average vertical velocities and γ2 is the corresponding ratio of short‐spread moveout velocities) governs most of the behavior of the conversion‐point offset. These ratios can be constructed from P-wave and converted‐wave data if an approximate correlation is established between corresponding reflection events. Acquisition designs based naively on γ0 instead of [Formula: see text] can result in suboptimal data collection. Computer programs that implement algorithms for isotropic homogeneous media can be forced to treat layered anisotropic media, sometimes with good precision, with the simple provision of [Formula: see text] as input for a velocity ratio function. However, simple closed‐form expressions permit hyperbolic and posthyperbolic moveout removal and computation of conversion‐point offset without these restrictive assumptions. In these equations, vertical traveltime is preferred (over depth) as an independent variable, since the determination of the depth is imprecise in the presence of polar anisotropy and may be postponed until later in the flow. If the subsurface has lateral variability and/or azimuthal anisotropy, then the converted‐wave data are not invariant under the exchange of source and receiver positions; hence, a split‐spread gather may have asymmetric moveout. Particularly in 3-D surveys, ignoring this diodic feature of the converted‐wave velocity field may lead to imaging errors.

Some comments on common-asymptotic-conversion-point (CACP) sorting of converted-wave data in isotropic, laterally inhomogeneous media

Geophysics ◽  
2005 ◽  
Vol 70 (3) ◽  
pp. U29-U36 ◽  
Author(s):  
Mirko van der Baan
Keyword(s):  
Wave Velocity ◽  
Velocity Ratio ◽  
P Wave ◽  
Pure Mode ◽  
S Wave ◽  
Converted Wave ◽  
Wave Data ◽  
Conversion Point ◽  
Isotropic Media ◽  
Zero Offset

Common-midpoint (CMP) sorting of pure-mode data in arbitrarily complex isotropic or anisotropic media leads to moveout curves that are symmetric around zero offset. This greatly simplifies velocity determination of pure-mode data. Common-asymptotic-conversion-point (CACP) sorting of converted-wave data, on the other hand, only centers the apexes of all traveltimes around zero offset in arbitrarily complex but isotropic media with a constant P-wave/S-wave velocity ratio everywhere. A depth-varying CACP sorting may therefore be required to position all traveltimes properly around zero offset in structurally complex areas. Moreover, converted-wave moveout is nearly always asymmetric and nonhyperbolic. Thus, positive and negative offsets need to be processed independently in a 2D line, and 3D data volumes are to be divided in common azimuth gathers. All of these factors tend to complicate converted-wave velocity analysis significantly.

Determination of Depth of Surface Cracks in Asphalt Pavements

2003 ◽  
Vol 1853 (1) ◽  
pp. 143-149 ◽  
Author(s):  
Shane Underwood ◽  
Y. Richard Kim
Keyword(s):  
Surface Wave ◽  
Wave Velocity ◽  
Ultrasonic Testing ◽  
Kernel Method ◽  
Direct Method ◽  
Velocity Ratio ◽  
Crack Depth ◽  
Asphalt Pavements ◽  
Quantitative Prediction ◽  
Processing Techniques

Nondestructive measurement of crack depths of asphalt pavements in situ could be a valuable tool for engineers in rehabilitation planning. Such measurements currently must be made by first coring or trenching a pavement and then measuring the crack by hand. Two methods for performing this task nondestructively are presented. The two methods, surface wave and ultrasonic, use the slowing effect that a crack has on a wave. Two signal-processing techniques were used to analyze the surface wave method—the fast Fourier transform (FFT) and the short kernel method (SKM). The FFT method provided a frequency spectrum that was used to find the energy carried by specific frequencies. The percent energy reduction (PER) was computed and plotted at each crack depth; this plot revealed that PER values increase as crack depth increases. The SKM method showed the wave velocity to decrease as the crack depth in creased. By comparing the wave velocity of the cracked pavement with that of the undamaged pavement, a phase velocity ratio plot was developed and was shown to be adequate for predicting crack depth. Ultrasonic testing proved to be a simpler and more direct method than surface wave testing. It was not necessary to know the wave properties of an undamaged pavement with this method, and a quantitative prediction of crack depth was obtained. While encouraging results were observed with both methods, ultrasonic testing showed the most promise for application because of the commercial availability of ultrasonic meters and the direct prediction of crack depth.

Vector-based elastic reverse time migration based on scalar imaging condition

Geophysics ◽  
2017 ◽  
Vol 82 (2) ◽  
pp. S111-S127 ◽  
Author(s):  
Qizhen Du ◽  
ChengFeng Guo ◽  
Qiang Zhao ◽  
Xufei Gong ◽  
Chengxiang Wang ◽  
...  
Keyword(s):  
Alternative Methods ◽  
Polarity Reversal ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
S Wave ◽  
Converted Wave ◽  
Imaging Condition ◽  
Time Migration ◽  
Wavefield Separation ◽  
Wave Modes

The scalar images (PP, PS, SP, and SS) of elastic reverse time migration (ERTM) can be generated by applying an imaging condition as crosscorrelation of pure wave modes. In conventional ERTM, Helmholtz decomposition is commonly applied in wavefield separation, which leads to a polarity reversal problem in converted-wave images because of the opposite polarity distributions of the S-wavefields. Polarity reversal of the converted-wave image will cause destructive interference when stacking over multiple shots. Besides, in the 3D case, the curl calculation generates a vector S-wave, which makes it impossible to produce scalar PS, SP, and SS images with the crosscorrelation imaging condition. We evaluate a vector-based ERTM (VB-ERTM) method to address these problems. In VB-ERTM, an amplitude-preserved wavefield separation method based on decoupled elastic wave equation is exploited to obtain the pure wave modes. The output separated wavefields are both vectorial. To obtain the scalar images, the scalar imaging condition in which the scalar product of two vector wavefields with source-normalized illumination is exploited to produce scalar images instead of correlating Cartesian components or magnitude of the vector P- and S-wave modes. Compared with alternative methods for correcting the polarity reversal of PS and SP images, our ERTM solution is more stable and simple. Besides these four scalar images, the VB-ERTM method generates another PP-mode image by using the auxiliary stress wavefields. Several 2D and 3D numerical examples are evaluated to demonstrate the potential of our ERTM method.

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