Seismic imaging for near-surface problems in complex areas
Jiangping Liu, Ting Gong, Yinhe Luo, and Xi Yixian*
Institute of Geophysics and Geomatics, China University of Geosciences, Wuhan, 430074 China.
Summary
Two methods have been presented to improve near surface
seismic imaging for near-surface geophysical surveys. (1)
Common Focus Point (CFP) technology. Aiming at the
shortcomings of tomographic velocity inversion of
common reflection point gathers, CFP is applied to extract
transmitted wave information along horizon and the multiinterface information constrained tomographic inversion
method is proposed. It is feasible to apply CFP technology
to get the transmission time of the traces from the focus
points to the area shot windows and can greatly improve
the precision of the vertical interfaces fuzzed by
tomographic inversion and build velocity structures with
high accuracy. (2) Floating datum for elevation and NMO
corrections. In practice, seismic reflected raypaths are
assumed to be almost vertical through the near-surface
layers because they have much lower velocities than layers
below. This assumption is acceptable in most cases since it
results in little residual error for small elevation changes
and small offsets in reflection events. Although static
algorithms based on choosing a floating datum related to
common midpoint gathers or residual surface-consistent
functions are available and effective, errors caused by the
assumption of vertical raypaths often generate pseudoindications of structures. We provide an approach of
combining elevation and NMO corrections to improve the
accuracy of velocity structure and quality of stacked
seismic profile.
CFP technology
Step of chromatographic velocity inversion of
transmitting wave with lateral CFP technology
①According to the acquired echo duration of multiinterface, carry out the lateral CFP imaging respectively to
acquire the transmission time of the traces from the focus
points to the face-source windows.
② Carry out BPT algorithm reconstruction for the
transmission time of each interface respectively to acquire
the velocity structure of the medium on the interface and
form the iterative initial value of iterative reconstruction
SIRT through weighted array so as to restrict the iterative
reconstruction SIRT.
③ At the same time, use the multi-interface lateral
CFP imaging information to carry out the iterative
reconstruction SIRT inversion, which settles the problems
such as insufficient data projection angle and uneven data
overlaying and so on, and enhancing the chromatographic
velocity inversion precision and resolution.
Chromatographic velocity inversion of model
In order to make up the disadvantages such as
insufficient data projection angle, uneven data overlaying
and lack of amount of information and so on, the
transmission time information of multi-interface lateral
CFP imaging is applied in the chromatographic imaging
process so as to enhance the effect and the precision of the
chromatographic velocity inversion.
Meanwhile, the results of the chromatographic
imaging carried out with the transmission time of the traces
from the imaging points to the corresponding face-source
windows on interface B, C and D are shown in Figure 1
and 2. It can be seen that since restricted by interface B and
C synchronously, the interval velocity of the third and
fourth layer is basically coincident with the theoretical
model value（1000, 1250m/s）, the max. absolute errors
of the third and the fourth layer are respectively 75 and
50m/s, and it lies in both ends of the section and the lowest
place of interface C (400~550m); the inversion result over
interface B is represented as the average characteristics of
the interval velocity of the first and the second layer of the
overlaid medium. The main factor causing the above errors
is the lock of the face-source record at both ends of the
section and the fuzzification of vertical interface by the
chromatographic velocity inversion.
To sum up, the lateral CFP imaging technology can
accurately put the wave field into place as well as
accurately acquire the transmission time of the traces from
the imaging points to the corresponding face-source
windows. With this time information, the average velocity
of the medium on the imaging point can be acquired; the
ground chromatographic velocity inversion of the
transmitting wave can be realized with the established
crosshole chromatographic imaging technology and the
velocity structure (or model) of the medium on the
interface can be acquired with high precision.
Velocity inversion
Meanwhile, carry out the chromatographic imaging of
the transmitting wave with the transmission information of
the traces from the imaging points to the corresponding
face-source windows on T1, T2 and T4 interface and the
chromatographic imaging results are shown in Figure 3. It
can be seen that it is well-stratified; the horizon composed
of T1 and T2 interface has obvious transverse variablespeed of the lamination and the difference of the interval
velocity is about 100m/s; since the lamination composed of
T2 and T4 interface also has obvious transverse variable
speed and the local abnormality exists in the layer and the
difference of the layer velocity reaches up to 150m/s.
Floating datum for elevation and NMO corrections
Seismic imaging for near-surface problems in complex areas
Reflection time-distance equation on an uneven surface
The exact t-x equation for a source-receiver pair of a
CMP gather from an uneven observation surface (Fig. 4)
can be written as
S *R
~
tx 

v
x 2  [( hs  hreflector )  (hr  hreflector )] 2
, (1)
v2
where hreflector is the reflector elevation, and hs and hr are the
source and receiver elevations, respectively. In the right
side of equation (1) the terms (hs － hreflector) and (hr －
hreflector) indicate elevation differences from source and
receiver stations to the reflector. They can be replaced by
[(hs－hm)＋(hr－hm)＋2(hm－hreflector)], in which hm is the
elevation of the midpoint of a source-receiver pair on the
surface. Defining dm = (hm － hreflector) as the elevation
difference from the midpoint of a source-receiver pair to
the reflector shown in Fig. 4, and Δhsm = (hs－hm) and Δhrm
= (hr － hm) as elevation differences from source and
receiver to midpoint, respectively, the travel-time may be
described by
h  hrm  2d m
~
tx  sm
v
x2
 1 (2)
(hsm  hrm  2d m ) 2
.
Supposing (Δhsm+Δhrm+2dm) >> x and expanding the
square-root expression on the right side of equation (2) by
Taylor-series and ignoring the 2-order and higher terms, we
have an approximate form
(3)
h  hrm  2d m
x2
1
~
tx  sm


v
4vdm
 hsm  hrm 
 .
1  
2d m


If (Δhsm+Δhrm) << 2dm , the last term of the right side can
also be written approximately by its Taylor-series
expansion , that
h  hrm
x2
x2
~
t t 
 sm

(h  h ) (4)
x
m0
2t m 0 v 2
v
2t m2 0 v 3
sm
rm
,
where tm0 = 2dm/v is the normal-incidence reflection time
from the ground surface at the midpoint of the CMP gather.
The second term on the right side of equation (4) is the
NMO.
According to the discussion above, we should use the
accurate expression of time shifts (NMO plus elevation
correction) from an irregular observation surface, that is
~
t 
h  hrm 

  t m 0  sm
  t m0 .
2
v
v


2
x2
(5)
For comparison, the conventional time shift expression is
t 
x2
v
2
 t d20 
hsd  hrd
 td 0 ,
v
(6)
where Δhsd and Δhrd are height differences from a source
and a receiver, respectively, to the uniform datum plane of
h
o
i
h
n
an entire seismic survey, and td0 is the vertical travel-time
from the datum to reflector. For a horizontal subsurface,
equation (5) gives a true description of NMO instead of an
approximation.
Equation (6) indicates that time-shift (NMO and the
elevation correction) depends not only on the elevations of
source and receiver, but also on the choice of datum. An
inappropriate choice of datum can generate an aberrant
x
elevation correction,
x i and the larger the absolute value of
(Δhsd+Δhrd),oi thei larger the possibility
hm of aberrance.
k
Reducing the elevation
differences between
datum and
m
source-receiver pairs as muchs as possible is one way to
h for multi-coverage
i
restrain the error. Nevertheless,
s h
observation,
any
inappropriate
elevation
correction can
i
h
m
cause problems
for subsequent data processing, such as
velocity analysis.
α α static correction in the model
Results from conventional
As examples, all stacked CMP traceshwill
refle still need to
ctor survey for the
be shifted to the datum of the whole seismic
purpose of mapping since the moveout corrections for each
CMP gather are computed relative to its midpoint level
(Fig. 5a). A static correction is needed to shift the stacked
section to a horizontal datum, which is accomplished by
applying the simple elevation correction to each stacked
CMP gather at its midpoint. Fig. 5b shows an almost
perfectly stacked section after shifting all stacked CMP
traces to the datum of the whole seismic survey.
A real-world example
To further study the feasibility of the NMO plus
elevation correction, a shallow reflection survey was
conducted at a highway construction site in PRC.
Objectives of the project were to map the interface between
the weathered surface layer and bedrock and possible
faults. Fig 6a shows the results of using a fixed datum at
the level of h = 625m with the conventional processing
equation. Fig. 6b is the results processed by the new
approach discussed in the paper--NMO plus elevation
correction with a floating datum. Coherence of the
reflection due to the interface between the top weathered
layer and bedrock is much better than the corresponding
event in Fig. 6a. Accounting to Fig 6b, it also is relatively
easy to determine several faults within bedrock based on
their reflection continuity and frequency contents. Finally,
we noticed that the signal to noise ratio of Fig. 6b is higher
than Fig. 6a because a correct moveout calculated by
equation (5) was applied to data.
On uneven topographic surfaces, the time-distance
(5)
curve of a common-midpoint reflection after conventional
elevation correction is not a hyperbola. The reflection
events exhibit a smaller moveout on raised surfaces and a
larger moveout on sunken surfaces, so that reflection events
(6)
may cross each other. This leads to misunderstanding to the
existence of structures. In this case, conventional static
correction methods fail to find accurate time shifts owing to
overcorrection or undercorrection. Accurate moveout,
Seismic imaging for near-surface problems in complex areas
which is based on the bias raypaths, can find accurate
stacking velocities. Theoretically, the inversed velocities
from the velocity spectrum analysis are not related to the
topography. In other words, rugged topography has no
effect on determination of stacking velocities. The synthetic
and real-world examples demonstrated accuracy of
moveout of seismic reflection data on a rugged topography
with the algorithm discussed in the paper. It should be
pointed out that the problems we are dealing with are the
elevation and NMO corrections. The refraction statics that
accounts for delays due to near surface geology often need
to be applied to data in practice.
0
0
50
100
150
200
250
References
Berkhout A.J., 2000, CFP technology, new opportunities in
seismic processing: 70th Ann. Internat. Mtg., Soc.
Expl. Geophys., Expanded Abstracts, 778-781.
Berkhout A.J., Pushing the limits of seismic imaging, Part
I: Prestack migration in terms of double dynamic
focusing: Geophysics, 62(3), pp937-953, 1997.
Marsden, D., 1993a, Static corrections — a review Part I.
The Leading Edge 1: 43-49.
Marsden, D., 1993b, Static corrections — a review Part III.
The Leading Edge 3: 210-216.
Mayne, W.H., 1962, Horizontal data stacking techniques.
Supplement to Geophysics 27: 927-937.
distance/m
350
400
300
450
500
550
600
650
700
750
A
1300m/s
0
1200m/s
B
30
30
depth/m
1100m/s
60
60
C
90
120
1000m/s
90
900m/s
800m/s
120
D
150
700m/s
150
600m/s
Figure 1 chromatographic imaging velocity distribution chart synchronously using the transmission time information of
the imaging points on three interfaces (interface B, C and D)
0
0
50
100
150
200
250
300
distance/m
350
400
450
500
550
600
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700
750
A
300m/s
0
250m/s
200m/s
B
30
30
150m/s
depth/m
100m/s
60
60
50m/s
0m/s
C
90
90
-50m/s
-100m/s
120
120
150
-150m/s
-200m/s
D
150
-250m/s
-300m/s
Figure 2 Chromatographic imaging velocity error distribution chart of the transmission time at the imaging points on
three interfaces (interface B, C and D)
1000
0
2000
4000
6000
distance/m
8000
ZK
10000
12000
14000
3600m/s
3540m/s
3480m/s
1000
3420m/s
3360m/s
3300m/s
3240m/s
depth/m
1250
1250
3180m/s
3120m/s
3060m/s
3000m/s
1500
1500
1750
1750
2000
2000
2940m/s
2880m/s
2820m/s
2760m/s
2700m/s
2640m/s
2580m/s
2520m/s
2460m/s
2400m/s
Figure 3 Velocity section of chromatographic imaging layer (for conveniently analyzing it, zoom it out by four times of
the original in longitudinal direction), ZK is the boring position.
Seismic imaging for near-surface problems in complex areas
Fig. 4 The reflection raypath from source S to receiver R. The geometrical relationship between raypath and the
elevations of source, receiver and reflector, is shown through use of the imaged source S*.
a
b
Fig. 5a Stacked section when using time shift equation (5) tofind stacking velocities and calculate NMO. Because the
corrections are applied to each CMP gather relative to the elevation of the midpoint, events take the inverse shape of the
topography. 2b The Stacked section with corrections completed. These correction included NMO and elevation (equation
5), and time shift to reduce stacked CMP gathers to the flat datum. Events (reflectors) are clearly indicated.
a
b
Fig. 6 An example of mapping bedrock and faults. (a) The stacked section in depth domain after NMO and elevation
corrections using a fixed datum at level h = 625 m with equation (10). (b) The stacked section in depth domain after NMO
and elevation corrections with equation (10) using a floating datum. (c) is an interpreted section of (b). A solid line is a
bedrock surface and dash lines are faults.