Waveform‐based AVO inversion and AVO prediction‐error

Geophysics ◽  
1996 ◽  
Vol 61 (6) ◽  
pp. 1575-1588 ◽  
Author(s):  
James L. Simmons ◽  
Milo M. Backus
Keyword(s):  
Reflection Coefficient ◽  
Thin Layer ◽  
Shear Wave ◽  
Prediction Error ◽  
Wave Reflection ◽  
A Priori ◽  
Normal Incidence ◽  
Strong Increase ◽  
Time Range ◽  
Zoeppritz Equations

A practical approach to linear prestack seismic inversion in the context of a locally 1-D earth is employed to use amplitude variation with offset (AVO) information for the direct detection in hydrocarbons. The inversion is based on the three‐term linearized approximation to the Zoeppritz equations. The normal‐incidence compressional‐wave reflection coefficient [Formula: see text] models the background reflectivity in the absence of hydrocarbons and incorporates the mudrock curve and Gardner’s equation. Prediction‐error parameters, [Formula: see text] and [Formula: see text], represent perturbations in the normal‐incidence shear‐wave reflection coefficient and the density contribution to the normal incidence reflectivity, respectively, from that predicted by the mudrock curve and Gardner’s equation. This prediction‐error approach can detect hydrocarbons in the absence of an overall increase in AVO, and in the absence of bright spots, as expected in theory. Linear inversion is applied to a portion of a young, Tertiary, shallow‐marine data set that contains known hydrocarbon accumulations. Prestack data are in the form of angle stack, or constant offset‐to‐depth ratio, gathers. Prestack synthetic seismograms are obtained by primaries‐only ray tracing using the linearized approximation to the Zoeppritz equations to model the reflection amplitudes. Where the a priori assumptions hold, the data are reproduced with a single parameter [Formula: see text]. Hydrocarbons are detected as low impedance relative to the surrounding shales and the downdip brine‐filled reservoir on [Formula: see text], also as positive perturbations (opposite polarity relative to [Formula: see text]) on [Formula: see text] and [Formula: see text]. The maximum perturbation in [Formula: see text] from the normal‐incidence shear‐wave reflection coefficient predicted by the a priori assumptions is 0.08. Hydrocarbon detection is achieved, although the overall seismic response of a gas‐filled thin layer shows a decrease in amplitude with offset (angle). The angle‐stack data (70 prestack ensembles, 0.504–1.936 s time range) are reproduced with a data residual that is 7 dB down. Reflectivity‐based prestack seismograms properly model a gas/water contact as a strong increase in AVO and a gas‐filled thin layer as a decrease in AVO.

A simplification of the Zoeppritz equations

Geophysics ◽  
1985 ◽  
Vol 50 (4) ◽  
pp. 609-614 ◽  
Author(s):  
R. T. Shuey
Keyword(s):  
Reflection Coefficient ◽  
Elastic Properties ◽  
Critical Angle ◽  
Wave Reflection ◽  
Normal Incidence ◽  
Compressional Wave ◽  
Zoeppritz Equations ◽  
The Third ◽  
Reflection Data ◽  
Simplified Formula

The compressional wave reflection coefficient R(θ) given by the Zoeppritz equations is simplified to the following: [Formula: see text] The first term gives the amplitude at normal incidence (θ = 0), the second term characterizes R(θ) at intermediate angles, and the third term describes the approach to critical angle. The coefficient of the second term is that combination of elastic properties which can be determined by analyzing the offset dependence of event amplitude in conventional multichannel reflection data. If the event amplitude is normalized to its value for normal incidence, then the quantity determined is [Formula: see text] [Formula: see text] specifies the normal, gradual decrease of amplitude with offset; its value is constrained well enough that the main information conveyed is [Formula: see text] where [Formula: see text] is the contrast in Poisson’s ratio at the reflecting interface and [Formula: see text] is the amplitude at normal incidence. This simplified formula for R(θ) accounts for all of the relations between R(θ) and elastic properties first described by Koefoed in 1955.

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.

scholarly journals Subglacial seismic reflection strategies when source amplitude and medium attenuation are poorly known

2009 ◽  
Vol 55 (193) ◽  
pp. 931-937 ◽  
Author(s):  
Charles W. Holland ◽  
Sridhar Anandakrishnan
Keyword(s):  
Reflection Coefficient ◽  
Physical Properties ◽  
Seismic Data ◽  
Seismic Reflection ◽  
A Priori ◽  
Normal Incidence ◽  
A Priori Knowledge ◽  
New Methods ◽  
Attenuation Profile ◽  
Lack Of Knowledge

AbstractSeismic reflection techniques are a powerful way to probe physical properties of subglacial strata. Inversion of seismic data for physical properties may be hampered, however, by lack of knowledge of the source amplitude as well as lack of knowledge of the compressional and shear attenuation in the ice. New methods are described to measure the source signature that require no a priori knowledge of the ice attenuation profile. Another new method is described to obtain the angular dependence of the subglacial bed reflection coefficient that is relatively insensitive to knowledge of the ice attenuation. Finally, a correction is provided to a long-standing error in the literature regarding measurement of the bed normal incidence reflection coefficient.

AVO modeling and the locally converted shear wave

Geophysics ◽  
1994 ◽  
Vol 59 (8) ◽  
pp. 1237-1248 ◽  
Author(s):  
James L. Simmons ◽  
Milo M. Backus
Keyword(s):  
Shear Wave ◽  
Transmission Loss ◽  
Real Data ◽  
Normal Incidence ◽  
Synthetic Seismograms ◽  
Thin Layers ◽  
Reflection Coefficients ◽  
Zoeppritz Equations ◽  
Short Period ◽  
Ray Trace

The locally converted shear wave is often neglected in ray‐trace modeling when reproduction of the AVO response of potential hydrocarbon reservoirs is attempted. Primaries‐only ray‐trace modeling in which the Zoeppritz equations describe the reflection amplitudes is most common. The locally converted shear waves, however, often have a first‐order effect on the seismic response. This fact does not appear to be widely recognized, or else the implications are not well understood. Primaries‐only Zoeppritz modeling can be very misleading. Interference between the converted waves and the primary reflections from the base of the layers becomes increasingly important as layer thicknesses decrease. This interference often produces a seismogram that is very different from one produced under the primaries‐only Zoeppritz assumption. For primaries‐only modeling of thin layers, synthetic seismograms obtained by use of a linearized approximation to the Zoeppritz equations to describe the reflection coefficients are more accurate than those obtained by use of the exact Zoeppritz reflection coefficients. A real‐data example consisting of an assemblage of very thin layers has recently been discussed in the literature. Inferences as to the true earth properties based on the predicted amplitude variation with offset are in error because the primaries‐only assumption is invalid. For one of the models, primaries‐only modeling predicts an amplitude increase of approximately a factor of three from the near trace to the far trace. Reflectivity modeling predicts an amplitude decrease with offset. The O’Doherty‐Anstey effect suggests that transmission loss for primary reflections should not be included in normal‐incidence synthetic seismograms if the short‐period reverberations are not also included. The same principle holds for prestack modeling. Similarly, the Zoeppritz equations should not be used for synthetic seismograms without including the locally converted shear wave.

ESTIMATION FORMULAS FOR WAVE REFLECTION COEFFICIENT OF LONG-PERIOD WAVE ABSORBING MOUND STRUCTURES

2019 ◽  
Vol 75 (2) ◽  
pp. I_787-I_792
Author(s):  
Jun MITSUI ◽  
Iwao HASEGAWA ◽  
Masashi TANAKA ◽  
Akira MATSUMOTO
Keyword(s):  
Reflection Coefficient ◽  
Wave Reflection ◽  
Long Period ◽  
Period Wave
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