Download Shear-wave statics using receiver functions

Shear-wave statics using receiver functions
Dirk-Jan van Manen1 , Johan Robertsson2 , Andrew Curtis3 , Ralf Ferber3 and Hanneke Paulssen1
Dept. of Geophysics, Utrecht University, The Netherlands
2
WesternGeco Oslo Technology Centre, Asker, Norway
3
Schlumberger Cambridge Research, Cambridge, United Kingdom
1
Summary
We extend the seismological receiver function method to
the exploration seismic domain to solve the problem of
shear-wave statics for multicomponent data. The method
relies on crosscorrelation or deconvolution of vertical with
radial component traces in the common-receiver domain
followed by a stacking step. This procedure is repeated
for each receiver, resulting in a profile of high-resolution
stacked receiver functions; events corresponding to
shallow mode-converted waves constrain the shear-wave
static. The method is applied to a line of commercial
multicomponent seabed seismic data and gives results
in good agreement with a conventional statics method,
although results on some other lines require additional
interpretation.
In contrast to seismological receiver
function analysis, the main converted wave energy in the
receiver functions originates from reflection at shallow
interfaces rather than conversion of upgoing wavefields.
Introduction
The use of multicomponent receivers for commercial
seismic data acquisition in marine (i.e., seafloor) environments has gradually been accepted and multicomponent
technology is receiving new interest on land as well.
The advantages of multicomponent recordings are well
known and reside in the ability to record mode-converted
waves with the horizontal components. Although there is
consensus that multicomponent technology will play an
important role in the future of seismic data acquisition,
several issues must be resolved before its potential is
fully realized.
One problem that the industry experiences applying multicomponent technology is the distortive effect the near
surface has on the deeper reflected wavefield, better
known as the statics problem. The near surface, both
in seabed and in land acquisition, is generally associated
with low, laterally varying shear-wave velocities. On land,
the P-wave velocity can also be low. These properties
often lead to large P- and S-wave traveltime perturbations in the deeper reflected wavefield, which vary from
receiver-to-receiver. These perturbations, when they remain uncorrected, can lead to a significant loss of high
frequencies in subsequent processing.
In this paper, we extend the seismological receiver function method to the exploration and production seismic
domain to solve the shear-wave statics problem for multicomponent data. We start by reviewing the receiver
SEG International Exposition and 72nd Annual Meeting
function method. We then propose a new data processing flow to estimate the S-statics and apply this to a line
of commercial multicomponent (4C) seabed seismic data.
Finally, we discuss the observations and give some potential applications beyond shear-wave statics estimation, to
end with some conclusions. Although we focus our discussion on the seabed seismic case, the proposed method
should also work for land multicomponent data.
Receiver functions in seismology
The receiver function method is a well-known seismological method to investigate the structure of the earth’s
crust and upper mantle. It relies on the observation of
shear-waves in the coda of a teleseismic P-wave resulting
from mode conversion of the P-wave at major crustal
or upper-mantle discontinuities. The receiver function
method exploits the recording of these phases on separate
components; P-waves on the vertical and S-waves on the
radial (Figure 1). By deconvolving the vertical from the
radial component the receiver function is formed, containing events related to crust and upper-mantle structure
only (Langston, 1979). In a typical receiver function
study, receiver functions are inverted for a horizontally
layered model using the Thomson-Haskell propagator
matrix formalism (Paulssen et al., 1993). In the simplest
implementation, however, the receiver function provides
a measure of the difference in traveltime between the
main phase and the mode-converted branches through
the upper mantle or crust. The tangential receiver
function, when it contains significant energy, provides
information on dip of the main convertors or anisotropy
within the crust and upper mantle (Levin and Park,
1997).
Statics using receiver functions
When strong contrasts in material properties exist in
the shallow subsurface (e.g., 250 m) at a seismic
survey location, significant mode-conversion of up- and
downgoing wavefields will take place at these interfaces.
Moreover, the natural separation of P-waves on the
vertical and S-waves on the horizontal components is also
well known for industrial multicomponent seismic data.
This suggests that, by applying the receiver function
method to exploration seismic data, information about
the compressional- and shear-wave properties of the near
surface can be obtained.
We focus on seabed seismic data because source and P-
Main Menu
Shear-wave statics using receiver functions
air
water
seabed
the natural domain because all energy arriving at the
same receiver probes the same near-surface structure.
Preprocessing also typically includes muting or gaining
part of the input data.
crust
PS
PSconverted
P
P-transmitted
P
Moho
upper-mantle
shallow interface
deeper regions
P-upgoing
P-transmitted
P-projection
dt=ts-tp
MODEL
DATA
radial
vertical
component component
PS-projection
PS-converted
Fig. 1: Schematic illustration of the receiver function method.
Up- and downgoing waves partially mode convert upon transmission or reflection at shallow interfaces. By calculating receiver functions, information about near surface structure is
obtained.
II. Receiver function calculation
The second step is the calculation of receiver functions
for the full or a restricted range of source-receiver offsets
in a common receiver gather. The receiver functions
are calculated using a stabilized deconvolution technique
known as the water level method. This method has
been described in detail in connection with the receiver
function method by Langston (1979). It works in the
frequency domain by filling the troughs of the denominator in the spectral division up to a fraction, c, of
its maximum to prevent the division from exploding.
Typically, we use a value c = 0.05 when calculating the
receiver functions for real data.
III. Stacking
wave statics are considered insignificant for this environment. This allows us to deal with the S-statics directly.
More importantly, since the shear-wave velocities in the
seabed are extremely low, the events in the receiver function are dominated by the shear-wave traveltime and,
hence, a direct measure of the S-static. When the P-wave
traveltime through the near surface cannot be neglected,
the P-statics must be found separately and added to the
traveltime differences given by the receiver functions.
In this step, the receiver functions obtained for a common
receiver gather are stacked. The stacked trace amplitude
is normalized by the number of input receiver functions.
Note that no moveout correction is applied before
stacking the receiver functions; we explicitly rely on the
signal to be static as a function of offset.
Furthermore, we assume that the difference in P- and
S-wave traveltime through the near surface at a given receiver location is constant and independent of reflection
depth or offset (i.e., slowness). In contrast to the receiver
function method in seismology, this gives the opportunity
to use long time windows for receiver function calculation,
containing not a single event, but a range of reflections.
Moreover, we can take advantage of the large amount of
data present in a typical seismic survey by stacking receiver functions obtained for different offsets, resulting in
a single, high signal-to-noise (S/N) ratio receiver function
per receiver.
The process of calculating and stacking receiver functions
is repeated for all receivers. Because the stacked receiver
functions only contain events related to near surface
structure, shallow mode-converted waves measuring the
shear-wave static will be visible in a profile of these
stacked receiver functions and can subsequently be
picked.
Data processing
We now propose a seismic processing flow to find the
shear-wave statics based on the receiver function methodology. The approach is divided in four main steps, each
described briefly below.
I. Preprocessing
Before the receiver functions are calculated, the data
must be rotated into radial-transverse coordinates to
maximize the projection of the shear-waves on the radial
component. Furthermore, the data must be sorted to the
common receiver gather domain. Although the receiver
function calculation can be done in any domain, this is
SEG International Exposition and 72nd Annual Meeting
IV. Plotting and picking
Results
To test the approach, several shot lines of commercial
multi-component seabed seismic data were available. We
show the results on one of them. The data were recorded
on the North Sea continental shelf. The sampling rate
was 2 ms and the source and receiver intervals were 50 m
and 25 m, respectively. The line consisted of 180 shot
positions, inline with and directly over a cable of 174
receivers.
In Figure 2 top and middle panels, the pressure and radial components are shown for a typical common receiver
gather. We calculate the receiver functions using the pressure instead of the vertical component. The main results
that will be shown, however, have also been obtained using the vertical component, although at a slightly higher
noise level. The result of calculating the receiver functions
is shown in the bottom panel. We have restricted the
range of lag times in the receiver functions to [-0.4,0.4] s.
Main Menu
Shear-wave statics using receiver functions
0
This range should be chosen in accordance with shearwave static delays expected. Note the complicated behavior in the central part of the receiver function gather.
At large offsets, however, some approximately flat events
can be seen. Next, the traces are stacked to form a single
receiver function for this receiver gather.
We have also tested crosscorrelation of the vertical and
pressure with the radial component, because our main
interest is in phase information only. The results were
similar to those obtained using stabilized deconvolution,
however inferior in resolution and are not shown here.
Discussion
In contrast with the receiver function method in seismology, mode conversion of the upgoing wavefields does
not seem to play a significant role in the formation of
the events observed in the receiver function profile. We
attribute the lack of such energy to the small incidence
angles, and hence, small conversion coefficients involved
with the central cone of reflection data. In other survey
areas, however, such energy may result in a significant
signal. We explain the signal observed in the receiver
function profile by PS-waves, mode-converted upon
reflection at shallow interfaces and the corresponding
P-reflections. We also consider the possibility of headwaves propagating along shallow interfaces, emitting
both P- and S-waves upward into the near surface. Such
waves would also explain the static traveltime differences
SEG International Exposition and 72nd Annual Meeting
0.6
Time [s]
0.8
1
1.2
1.4
1.6
1.8
2
−3000
−2000
−1000
0
1000
2000
3000
1000
2000
3000
Offset [m]
0
0.2
0.4
0.6
0.8
Time [s]
To test which part of the input data contributes most
to the statics event observed in the receiver functions, a
simple muting experiment was done. The central cone
of reflection data is muted from the input data. The
black solid lines in Figure 2 indicate the top mute boundary. Subsequently, the whole processing was repeated.
The profile of stacked receiver functions is shown in Figure 3, middle panel. Note that the results have an even
higher S/N ratio, although the general features remain
unchanged. We have concluded that the central cone
of reflection data does not contribute significantly to the
shear-wave statics event in the stacked receiver function
profile. This was also confirmed by the inverse muting
experiment for which the results are shown in the bottom panel. Note that the shear-wave statics signature is
faintly visible, however the S/N ratio is significantly lower
and the receiver functions are much more low frequency.
0.4
1
1.2
1.4
1.6
1.8
2
−3000
−2000
−1000
0
Offset [m]
−0.4
−0.3
−0.2
−0.1
Time lag [s]
In Figure 3 (top) the results are shown when the process
of calculating and stacking receiver functions is repeated
for all common receiver gathers. The profile contains only
a few events and has a very high S/N ratio. Note how the
events at 0.1 s and 0.3 s, already visible in Figure 2 (bottom), are amplified through the stacking. A shear-wave
statics solution available for this line, obtained independently using a residual statics method, is plotted on top
of the profile in blue. This profile serves as a reference solution. In green, the maximum of the event in the receiver
functions is picked automatically. Note the good agreement between the events in the receiver function profile
and the reference solution.
0.2
0
0.1
0.2
0.3
0.4
−3000
−2000
−1000
0
1000
2000
3000
Offset [m]
Fig. 2: Typical common receiver gather input data with a t2
gain applied. (Top) Pressure recording. (Middle) Radial
component of particle velocity. (Bottom) Receiver function
gather calculated by deconvolution of the pressure from the
respective radial component traces. The gather is scaled uniformly.
observed at far offsets, contributing most to the signal.
We have repeated the processing on several other lines of
data for which residual statics profiles were available, with
mixed results. For some lines, the long wavelength match
Main Menu
Shear-wave statics using receiver functions
0
Residual statics
Receiver function statics
0.05
0.1
Time lag [s]
0.15
0.2
0.25
0.3
0.35
0.4
0
500
1000
1500
2000
2500
3000
3500
4000
Offset [m]
neglected. Further research is needed to resolve this.
Finally, it is interesting to consider additional applications
of the receiver function method to exploration seismic
data, given the results that we have obtained. Calculation
of tangential receiver functions, or stacking radial receiver
functions for a narrow azimuthal range, could provide information about shallow anisotropy. Another aspect that
we have not considered here is amplitude information.
Because the receiver function combines information on
both P- and S-waves having propagated through the near
surface, the amplitude is a measure of the differential attenuation in the near surface, and hence, seems to offer
a possibility of inverse-Q filtering horizontal component
data. The shortest wavelength amplitude variations could
be diagnostic of receiver coupling effects.
0
Residual statics
Receiver function statics
0.05
0.1
Time lag [s]
0.15
0.2
0.25
0.3
0.35
0.4
0
500
1000
1500
2000
2500
3000
3500
4000
Offset [m]
Conclusion
We have demonstrated the potential of the receiver function method in an exploration and production seismic
setting to investigate the near surface and the distortive
effect it has on the deeper reflected wavefield. In the
simplest approach, the receiver function method can
give information about the shear-wave statics. These
traveltime perturbations generally limit multi component
seismic data quality. A data processing approach was
proposed and tested on a line of commercial multicomponent seabed seismic data. The processing gave results
consistent with a conventional statics solution, although
results on some other lines require further investigation.
0
Residual statics
Acknowledgments
0.05
We thank Everhard Muyzert and Valerie le Mezo for
valuable input. The first author thanks WesternGeco and
Schlumberger for hospitality during stays in which most
of this work was done. We acknowledge the permission
to publish these results.
0.1
Time lag [s]
0.15
0.2
0.25
References
0.3
0.35
0.4
0
500
1000
1500
2000
2500
3000
3500
4000
Offset [m]
Fig. 3: Profiles of stacked receiver functions. In blue an Sstatics solution is shown, obtained independently using a conventional statics method. (Top) Unmuted input data (Middle) reflection data mute (Bottom) Direct wave and shallow
reflections mute.
Langston, C., 1979, Structure under Mount Rainier,
Washington, inferred from teleseismic body waves: J.
Geophys. Res., 84, 4749–4762.
Levin, V., and Park, J., 1997, P-SH conversions in a flatlayered medium with anisotropy of arbitrary orientation: Geophys. J. Int., 131, 253–266.
Paulssen, H., Visser, J., and Nolet, G., 1993, The crustal
structure from teleseismic P-wave coda–I. Method:
Geophys. J. Int., 112, 15–25.
between the events in the receiver functions and the conventional shear-wave statics solution was poor. One explanation for more complicated results is the fact that
the shallow P-waves involved reflect at different locations
than the PS-converted waves, leading to lateral averaging
or significant P-wave traveltimes that can no longer be
SEG International Exposition and 72nd Annual Meeting
Main Menu