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Z-99 Estimating and correcting of tilted multicomponent receivers
JIANCHAO LI AND SHUKI RONEN
Veritas DGC, 10300 Town Park Drive, Houston, TX 77072, USA
Abstract
We developed a new and simple algorithm for multi-component receiver tilt correction. We
estimate the receiver tilt and orientation angles using seismic data by finding such angles that
best make the data from all the shots consistent. It has been successfully applied in tilt angle
estimation on VSP and tilt correction on seabed field data.
Introduction
Correction of tilted multi-component (MC) receivers has become a routine and must-do
process in MC data processing because it is impossible to plant all MC receivers perfectly
vertical on both land and seafloor. Unless corrected, the tilted receivers will cause vector
infidelity and seismic energy cross mixing; for example shear waves may be recorded on the
Z-component and the P-wave energies are on the X- and Y-components. Some major
manufacturers of MC receivers, like Input/Output and Sercel, have developed their own tilt
angle measurement technologies and unpublished correction algorithms. Other multicomponent receivers do not provide tilt information and this has to be estimated from the
data. We have developed and presented a data-driven method to estimate tilt angles (Li et al,
2004). In this paper, we show more details about the tilt correction algorithm that we use and
application to VSP and seabed field data.
Theory
Mathematically, receiver tilt correction is rotation of coordinate systems. We assume that the
three components of a tilted receiver are (x, y, z). After tilt correction, three components (x, y,
z) will become (X, Y, V) (Figure 1). So the operation of receiver tilt correction can be
expressed as
⎛ X ⎞ ⎛ l1
⎜ ⎟ ⎜
⎜ Y ⎟ = ⎜ m1
⎜V ⎟ ⎜
⎝ ⎠ ⎝ n1
l l ⎞⎟⎛⎜ x ⎞⎟
m m ⎟⎟⎜ y ⎟
n n ⎠⎜⎝ z ⎟⎠
2
3
2
3
2
3
(1)
The rotation matrix consists of the direction cosines of the tilt corrected X-, Y- and Vcomponents in the tilted receiver coordinate (x, y, z), respectively. Equation (1) involves nine
tilt angles, and it is not practical to be used for tilt correction.
Keeping the azimuth of the projection of the x-component on the horizontal plane, we only
need three tilt angles defined in Figure 2 and Equation (1) becomes,
EAGE 67th Conference & Exhibition — Madrid, Spain, 13 - 16 June 2005
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⎛
⎜ sin α
⎜
⎛X⎞ ⎜
⎜ ⎟
⎜Y ⎟ = ⎜ 0
⎜V ⎟ ⎜
⎝ ⎠ ⎜
⎜⎜
⎝ cos α
−
cos α cos β
sin α
cos γ
sin α
cos β
−
cos α cos γ ⎞
⎟
sin α ⎟
⎟⎛⎜ x ⎞⎟
cos β ⎟⎜ y ⎟
−
sin α ⎟⎜ z ⎟
⎟⎝ ⎠
⎟⎟
cos γ
⎠
(2)
Equation (2) is used to rotate three-component seismic data recorded with tilted receivers to
ones which is equivalent to the data collected with vertically planted receivers. The tilt angles
(α, β, γ) may be measured in the field with accelerometers measuring the earth gravity, or
they can also be estimated by analyzing MC data. Tilt correction is the core in tilt angle
estimation. The aim in tilt angle estimation is to obtain a set of angles that are the best to
remove the tilt effect from the seismic data. In order to find the best tilt angles, a lot of sets of
angles (αi, βi, γi) have to be used to tilt correct the MC data. The best tilt angles would make
the estimated receiver orientation distributions over all shots more consistent. By measuring
the consistency, the estimated tilt angles and orientation of a receiver can be found. The
receiver orientation θ is measured from the north to the direction of X component.
Applications
Figure 3 is an example for tilt correction. Figure 3a shows the z-component data of a seabed
MC receiver gather. It can be seen that not only P waves, but also shear wave energies have
been recorded on the z-component due to the receiver tilt deployment. Velocity filtering can
be used to remove those shear waves from the z-component data. Velocity filtering, however,
just simply throws away the shear wave energies that are useful signals in MC data processing
and may also hurt P-wave energies of similar dips. The tilt correction of MC receivers will
move shear waves from z-component to two horizontal components accordingly, not throw
away them. Figure 3b is the result after applying tilt correction. The tilt correction has moved
most part of shear wave energies out of the z-component and enhanced P-wave events.
For estimating tilt angles, our previous paper (Li et al, 2004) has shown the land and seabed
data examples. Here we present a 3D MC VSP field data set. Figure 4a is the display of a
common receiver gather of the x-, y- and z-components. Figure 4b shows the hodograms of
the x-y, the z-y and the z-x components. Figure 4c is the measurement of consistency used for
picking the estimated tilt angles. Figure 4d shows the receiver orientation distributions with
shot-to-receiver azimuths for all shots. The analysis shows that the tilt angles of this receiver
are α=89.75o, β=89.5o, γ =0.56o, and the orientation angle is θ=–50.49o.
Conclusions
It is impossible to plant all MC receivers perfectly vertically on either land or seafloor.
Seismic data from tilted receivers must be corrected using receiver tilt angles. We present a
new and simple algorithm for MC receiver tilt correction and have successfully applied the
algorithm in the tilt correction and the tilt angle estimation.
Acknowledgments
The authors thank Side Jin for the contribution to implementation of interactive tilt angle
estimation based on the new algorithm.
Reference
Li, J., Jin, S., and Ronen, S., 2004, Data-driven tilt angle estimation of multi-component
receivers: 74th Ann. Internat. Mtg., Soc. Expl. Geophys., Expended Abstracts, MC 3.5.
3
X
x
x
α
Y
y
β
γ
y
z
z
V
V
Figure 1. Receiver tilt correction is
coordinate rotation from the tilted
three components (x, y, z) to the tilt
corrected (X, Y, V).
(a)
Figure 2. The definition of tilt
angles for a three-component
receiver.
(b)
Figure 3. Tilt angle correction of a seabed common-receiver-gather z-component data: (a) before
and (b) after tilt correction. The tilt correction has moved shear waves out of the z-component.
EAGE 67th Conference & Exhibition — Madrid, Spain, 13 - 16 June 2005
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(a)
x-y
z-x
z-y
(b)
θ
(c)
(d)
Figure 4. Tilt angle estimation for a 3D MC VSP data: (a) the display of a common receiver gather of x-,
y- and z-component data; (b) the hodograms of x-y, z-y and z-x components; (c) the measurement of
consistency used to pick the tilt angles; (d) the receiver orientation cross plotted against shot-receiver
azimuth and histogram after applying the tilt correction.