Transverse isotropy versus lateral heterogeneity in inversion of P‐wave reflection traveltimes

1996 ◽  
Author(s):  
Vladimir Grechka ◽  
Jack K. Cohen
Keyword(s):  
Wave Reflection ◽  
Transverse Isotropy ◽  
P Wave ◽  
Lateral Heterogeneity

Transverse isotropy versus lateral heterogeneity in the inversion of P-wave reflection traveltimes

Geophysics ◽  
1998 ◽  
Vol 63 (1) ◽  
pp. 204-212 ◽  
Author(s):  
Vladimir Y. Grechka
Keyword(s):  
Wave Reflection ◽  
Transverse Isotropy ◽  
Transversely Isotropic ◽  
Numerical Differentiation ◽  
Linear Functions ◽  
P Wave ◽  
Lateral Heterogeneity ◽  
Anisotropic Parameter ◽  
Single Plane ◽  
Ti Media

Nonelliptic transverse isotropy may cause pronounced nonhyperbolic moveout of long‐spread P-wave reflection data. Lateral heterogeneity may alter the moveout in much the same way, and one can expect that a given P-wave reflection moveout may be interpreted equally well in terms of parameters of homogeneous transversely isotropic (TI) or laterally heterogeneous (LH) isotropic models. Here, the common‐midpoint (CMP) moveout of a P-wave reflected from a horizontal interface beneath a weakly laterally heterogeneous medium that is also weakly transversely isotropic is represented analytically in the form similar to that in homogeneous TI media. Both the normal‐moveout (NMO) velocity and the quartic moveout coefficient contain derivatives of the zero‐ offset traveltime t0 and the NMO velocity Vnmo with respect to the lateral coordinate. Despite the presence of heterogeneity, nonhyperbolic velocity analysis can be performed in the same way as in homogeneous TI models. If all parameters of the medium are linear functions of the lateral coordinate, heterogeneity does not influence the results of inversion for the anisotropic parameter η. However, to find η in the case of general lateral heterogeneity, the second derivative of Vnmo and the fourth derivative of t0 are needed. Since these high‐order derivatives are calculated from the data measured at discrete points by numerical differentiation, stability of η estimation is further reduced as compared to that in homogeneous TI media. Consequently, the trade‐off between anisotropy and heterogeneity significantly complicates the inversion of P-wave reflection traveltimes, even in the simplest model of a single plane layer.

Reflection moveout approximations for P-waves in a moderately anisotropic homogeneous tilted transverse isotropy layer

Geophysics ◽  
2017 ◽  
Vol 82 (5) ◽  
pp. C175-C185 ◽  
Author(s):  
Ivan Pšenčík ◽  
Véronique Farra
Keyword(s):  
Transverse Isotropy ◽  
Transversely Isotropic ◽  
P Wave ◽  
Weak Anisotropy ◽  
P Waves ◽  
3D Space ◽  
Axis Of Symmetry ◽  
Relative Errors ◽  
Symmetry Tests ◽  
Ti Media

We have developed approximate nonhyperbolic P-wave moveout formulas applicable to weakly or moderately anisotropic media of arbitrary anisotropy symmetry and orientation. Instead of the commonly used Taylor expansion of the square of the reflection traveltime in terms of the square of the offset, we expand the square of the reflection traveltime in terms of weak-anisotropy (WA) parameters. No acoustic approximation is used. We specify the formulas designed for anisotropy of arbitrary symmetry for the transversely isotropic (TI) media with the axis of symmetry oriented arbitrarily in the 3D space. Resulting formulas depend on three P-wave WA parameters specifying the TI symmetry and two angles specifying the orientation of the axis of symmetry. Tests of the accuracy of the more accurate of the approximate formulas indicate that maximum relative errors do not exceed 0.3% or 2.5% for weak or moderate P-wave anisotropy, respectively.

Amplitude Variations of P-wave Reflection from Thinly Layered Porous Medium

2008 ◽  
Author(s):  
H. Ren ◽  
G.M. Goloshubin ◽  
F.J. Hilterman
Keyword(s):  
Porous Medium ◽  
Wave Reflection ◽  
P Wave

Nonlinear Waves in Strings: The Barrage Balloon Problem

1998 ◽  
Vol 65 (1) ◽  
pp. 141-149
Author(s):  
J. F. Hall
Keyword(s):  
World War Ii ◽  
Nonlinear Waves ◽  
Wave Reflection ◽  
Wave Theory ◽  
P Wave ◽  
Linear Wave ◽  
Geometrically Nonlinear ◽  
World War ◽  
Linear Wave Theory ◽  
Important Solution

This paper develops a theory for geometrically nonlinear waves in strings and presents analytical solutions for a traveling kink, generation of a geometric wave with its accompanying P wave, reflection of a kink at a fixed support and at a smooth sliding support, and interaction of a P wave and a kink. Conditions that must be satisfied for linear wave theory to hold are derived. The nonlinear theory is demonstrated by extending an historically important solution of the barrage balloon problem that was obtained during World War II.

Migration velocity analysis for TI media in the presence of quadratic lateral velocity variation

Geophysics ◽  
2012 ◽  
Vol 77 (6) ◽  
pp. U87-U96 ◽  
Author(s):  
Mamoru Takanashi ◽  
Ilya Tsvankin
Keyword(s):  
Migration Velocity ◽  
P Wave ◽  
Velocity Variation ◽  
Small Scale ◽  
Velocity Analysis ◽  
Lateral Heterogeneity ◽  
Lateral Velocity ◽  
Symmetry Direction ◽  
Migration Velocity Analysis ◽  
Ti Media

One of the most serious problems in anisotropic velocity analysis is the trade-off between anisotropy and lateral heterogeneity, especially if velocity varies on a scale smaller than the maximum offset. We have developed a P-wave MVA (migration velocity analysis) algorithm for transversely isotropic (TI) models that include layers with small-scale lateral heterogeneity. Each layer is described by constant Thomsen parameters [Formula: see text] and [Formula: see text] and the symmetry-direction velocity [Formula: see text] that varies as a quadratic function of the distance along the layer boundaries. For tilted TI media (TTI), the symmetry axis is taken orthogonal to the reflectors. We analyzed the influence of lateral heterogeneity on image gathers obtained after prestack depth migration and found that quadratic lateral velocity variation in the overburden can significantly distort the moveout of the target reflection. Consequently, medium parameters beneath the heterogeneous layer(s) are estimated with substantial error, even when borehole information (e.g., check shots or sonic logs) is available. Because residual moveout in the image gathers is highly sensitive to lateral heterogeneity in the overburden, our algorithm simultaneously inverts for the interval parameters of all layers. Synthetic tests for models with a gently dipping overburden demonstrate that if the vertical profile of the symmetry-direction velocity [Formula: see text] is known at one location, the algorithm can reconstruct the other relevant parameters of TI models. The proposed approach helps increase the robustness of anisotropic velocity model-building and enhance image quality in the presence of small-scale lateral heterogeneity in the overburden.

Low‐cost geophysical investigations of a paleochannel aquifer in the Eastern Goldfields, Western Australia

Geophysics ◽  
2002 ◽  
Vol 67 (3) ◽  
pp. 690-700 ◽  
Author(s):  
Josef Holzschuh
Keyword(s):  
Water Table ◽  
Western Australia ◽  
Seismic Reflection ◽  
Wave Reflection ◽  
Gravity Data ◽  
P Wave ◽  
Gravity Modeling ◽  
S Wave ◽  
Sand And Gravel ◽  
Gravel Aquifer

Compressional (P) wave and shear (S) wave seismic reflection techniques were used to delineate the sand and gravel aquifer within a highly saline clay‐filled paleochannel in the Eastern Goldfields of Western Australia. The seismic refraction and gravity methods were also used to investigate the paleochannel. The unsaturated loose fine‐grained sand up to 10 m in depth at the surface is a major factor in degrading subsurface imaging. The seismic processing needed to be precise, with accurate static corrections and normal moveout corrections. Deconvolution enhanced the aquifer and other paleochannel reflectors. P‐wave reflection and refraction layer depths had good correlation and showed a total of six boundaries: (1) water table, (2) change in velocity (compaction) in the paleochannel sediments, (3) sand and gravel aquifer, (4) red‐brown saprolite and green saprolite boundary, (5) weathered bedrock, and (6) unweathered bedrock. P‐wave explosive and hammer sources were found to have similar signal characteristics, and the aquifer and bedrock were both imaged using the hammer source. The deep shots below the water table have the most broadband frequency response for reflections, but stacking clear reflections was difficult. The S‐wave reflection results showed high lateral and vertical resolution of the basal saprolite clay, the sand and gravel aquifer, and very shallow clays above the aquifer. The S‐wave reflection stacking velocities were 10–20% of the P‐waves, increasing the resolution of the S‐wave section. The gravity data were modelled to fit the known drilling and P‐wave seismic reflection depths. The refraction results did not identify the top of bedrock, so refraction depths were not used for the gravity modeling in this highly weathered environment. The final gravity model mapped the bedrock topography beyond the lateral extent of the seismic and drilling data.

Sign in / Sign up

Export Citation Format

Share Document