Anisotropic multimode joint Rayleigh- and Love-wave inversion
Edan Gofer
1
, Scott Leaney
2
, Ranjan Dash
3
, and Hermes Malcotti
3
, Jim DiSiena
4
1
Schlumberger,
2
SLRDC,
3
Chevron Energy Technology Corporation,
4
formerly with Chevron Energy
Technology Corporation
Summary
Obtaining anisotropic near surface elastic properties is of
interest for engineering, environmental, and geophysical
exploration purposes. State of the art depth imaging
workflows are anisotropic. While surface-wave inversion
has been used for building near surface velocity models for
depth imaging, by itself and jointly with first arrival analysis,
it is being carried out assuming the subsurface is isotropic.
There is a need to incorporate anisotropy in surface-wave
inversion and to pursue joint estimation of VS and
transversely isotropic parameters. In this study, we
demonstrate multimode joint estimation of VS and
transversely isotropic parameters, which can provide near
surface anisotropy for different applications.
Introduction
The accuracy of the near-surface velocity model is one of the
main factors that impacts the quality of the seismic image at
the depth of interest, a few kilometers into the subsurface
(Keho and Kelamis, 2012). While surface-waves are
routinely attenuated in seismic processing as they overlay
the reflections (Strobbia et al., 2011), inversion of surface-
wave dispersion curves has been used in near surface
velocity model building for the purposes of depth imaging
and static corrections (Boiero et al. 2013). In general,
Rayleigh-, Scholte-, and Love-wave dispersion curves are
inverted assuming the subsurface is isotropic (Socco et al.,
2010).
In an isotropic media, Rayleigh/Scholte-wave and Love-
wave phase velocities are a function of the vertical and
horizontal S-wave velocities, respectively (Aki and
Richards, 1980). As a result, when seismic data is measured
with multicomponent source and acquisition system,
dispersion curves of the two wave types are inverted
separately (Socco et al. 2011). Results of two separate
inversions may not always be consistent. Moreover, the
isotropic assumption may be invalid as the near subsurface
can be anisotropic. For example, vertical loading will cause
stress induced anisotropy in soft unconsolidated sediments
(Nur and Simmons, 1969; Walton, 1987; Sayers, 2002). Fine
scale layering can induce vertical transverse isotropy (VTI)
(Backus, 1962) and fractured rocks can exhibit azimuthal
anisotropy (Schoenberg and Sayers, 1995). To characterize
these rocks accurately, the anisotropy must be taken into
consideration.
In this paper, we present an anisotropic multimode joint
Rayleigh- and Love-wave inversion. We analyze the effect
of elastic anisotropy on surface wave phase velocities, the
sensitivity of different surface wave modes to model
parameters and show inversion results from a field example.
Model parameterization
A VTI media is defined by five independent elastic constants
C11, C33, C55, C66, and C13 with C12=C11–2C66. To assist in
analyzing seismic reflection normal moveout (NMO)
velocities and amplitude versus offset (AVO), several
notations have been employed. Herein, we use Schoenberg
et al. (1996):
≡√
33
;
≡√
55
(1)
≡
11
−
33
11
+
33
;
≡
66
−
55
66
+
55
≡
(
11
−
55
)(
33
−
55
) − (
13
+
55
)
2
(
11
−
55
)(
33
−
55
)
where Cij are the elastic stiffness constants and is the
density. In a VTI media, Rayleigh-wave phase velocity can
be written in implicit form as (, ,
11
,
33
,
55
,
13
, , ℎ)
and the Love-wave phase velocity as (, ,
55
,
66
, , ℎ),
where f and k are the frequency and wavenumber. Cij, , and
h are the elastic stiffness constants, the density, and the
thickness of an individual layer in the media, respectively,
(Anderson, 1961). Note, Rayleigh-wave phase velocities are
a function of four out of the five independent elastic VTI
constants and Love-wave phase velocities are a function of
two out of the five. Implicit form with Schoenberg et al.
(1996) notations is:
• Rayleigh-wave phase velocity:
(, ,
,
,
,
, , ℎ)
• Love-wave phase velocity: (, ,
,
, , ℎ)
Phase velocity sensitivity to model parameters
To better understand the effect of elastic anisotropy on
surface wave dispersion curves and how it changes as a
function of depth, we calculated sensitivity of both
Rayleigh- and Love-wave phase velocities of different
modes to model parameter perturbation. Figure 1 shows the
VTI model and the modeled fundamental mode and two
higher modes. Rayleigh-wave dispersion curves were
analyzed with respect to vertical S-wave velocity (VS), EP,
and EA (Figure 2) and Love-wave dispersion curves were
10.1190/segam2021-3590447.1
Page 1856
© 2021 Society of Exploration Geophysicists
First International Meeting for Applied Geoscience & Energy
Downloaded 09/22/21 to 54.80.106.143. Redistribution subject to SEG license or copyright; see Terms of Use at http://library.seg.org/page/policies/terms
DOI:10.1190/segam2021-3590447.1