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7/25/2019 Static Corrections Methods in the Processing Seismic
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Journal of Earth Science, Vol. 25,No. 2,p. 299308,April 2014 ISSN 1674-487X
Printed in ChinaDOI: 10.1007/s12583-014-0422-x
Zhu, X. S., Gao, R., Li, Q. S., et al., 2014. Static Corrections Methods in the Processing of Deep Reflection Seismic Data. Journal of
Earth Science, 25(2): 299308, doi:10.1007/s12583-014-0422-x
Static Corrections Methods in the Processing of
Deep Reflection Seismic Data
Xiaosan Zhu*,Rui Gao,Qiusheng Li,Ye Guan,Zhanwu Lu,Haiyan Wang
Institute of Geology,Chinese Academy of Geological Sciences,Beijing 100037,China
ABSTRACT: Statics are big challenges for the processing of deep reflection seismic data. In this paper
several different statics solutions have been implemented in the processing of deep reflection seismic
data in South China and their corresponding results have been compared in order to find proper statics
solutions. Either statics solutions based on tomographic principle or combining the low-frequency
components of field statics with the high-frequency ones of refraction statics can provide reasonable
statics solutions for deep reflection seismic data in South China with very rugged surface topography,
and the two statics solutions can correct the statics anomalies of both long spatial wavelengths and
short ones. The surface-consistent residual static corrections can serve as the good compensations to the
several kinds of the first statics solutions. Proper statics solutions can improve both qualities and reso-
lutions of seismic sections, especially for the reflections of Moho in the upmost mantle.
KEY WORDS: deep reflection seismic data, static correction, field static, refraction static, tomographic
static, residual static correction.
1 INTRODUCTION
Correcting near-surface velocity and elevation variations
with statics is an essential step and static corrections are very
important in the processing of land data, which can improve the
qualities of subsequent processing steps and are related to the
quality and resolution of final imaged section (Li L et al., 2011;
Deere, 2009; Laak and Zaghloul, 2009; Li P et al., 2009a; Raef,2009; Stein et al., 2009; Han et al., 2008; Vossen and Trampert,
2007; Yan et al., 2006; Criss and Cunningham, 2001). Static
corrections are defined as (Cox, 1999; Sheriff, 1991): correc-
tions applied to seismic data to compensate for the effects of
variations in elevation, weathering thickness, weathering veloc-
ity, or reference to a datum. The objective is to determine the
reflection arrival times which would have been observed if all
measurements had been made on a (usually) flat plane with no
weathering or low-velocity material present. Hence it leads to
the concept of surface-consistent corrections, which are de-
pendent on the location of the source (or receiver) but are in-
dependent of the source to receiver offset or time of the record
data (Deere, 2009; Cox, 1999).
There are many issues which are associated with the near
surface and related with the variations of velocity and thickness
in the near-surface layers. Field statics can compensate the data
with some of the problems mentioned above and there are
many papers which are focus on it (Luo et al., 2010; Li et al.,
2009b; Huang et al., 2008). There are lots of static correction
*Corresponding author: [email protected]
China University of Geosciences and Springer-Verlag Berlin
Heidelberg 2014
Manuscript received August 21, 2013.Manuscript accepted January 15, 2014.
methods based on seismic refraction principle, which can be
used to resolve velocities of shallow layers using head waves,
such as slope (or intercept) method (Knox, 1967), delay time
method (Coppens, 1985), reciprocal method (Palmer, 1980),
least square method (Chang et al., 2002; Simmons and Backus,
1992) and turn-rays method (Henley, 2009; Criss and Cun-
ningham, 2001). Tomographic static correction methods havebeen developed by many researchers (Liu et al., 2010; Li et al.,
2009b; Yordkayhun et al., 2009; Zhu et al., 2008; Taner et al.,
1998) to obtain the static corrections, which use the tomo-
graphic velocity models based on the first-arrival information
to predict static corrections. These statics methods require a
large number of rays going through the model areas evenly
with different ray angles. Ray tomography methods have been
used to build near-surface velocity models using first-arrival
information and to estimate the static corrections (Zhang et al.,
2009; Ke et al., 2007). Many residual static correction methods
have been developed in order to compensate for the time delays
during the last several decades, such as traveltime inversion
based method (Hatherly et al., 1994), stack-power maximiza-
tion method (Ronen and Claerbout, 1985), nonstationary resid-
ual statics method (Henley, 2012) and sparsity maximization
method (Gholami, 2013).
In real world, there are many factors which cause the static
corrections and residual static corrections difficult to be han-
dled. These factors are including rugged surface acquisition
topography, non-planar refractors, near-surface low-velocity
layers, lateral variant velocities of weathering layers and varia-
tions of underground water tables (Li et al., 2009b; Wang,
1999). Errors in static corrections lead to the losses of seismic
resolutions, both temporal and spatial, and bring the difficulties
and confusions during the interpretations of seismic sections.In this paper, we study the static correction methods using
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Xiaosan Zhu, Rui Gao, Qiusheng Li, Ye Guan, Zhanwu Lu and Haiyan Wang300
the deep reflection seismic data (Liu et al., 2010; Xu et al.,
2005; Huang and Gao, 2001) along a long survey in South
China (Fig. 1) and compare the statics solutions of different
methods in order to find the proper statics solutions for the
processing of deep reflection seismic data. The outline of the
paper is the following. Firstly, we briefly summarize the theo-
ries of field statics, refraction statics, tomographic statics andresidual static corrections, separately. We then study on the
statics solutions of deep reflection seismic data based on these
methods mentioned above and compare the results of different
statics solutions in detail. Finally, we summarize this study.
2 METHODOLOGY OF STATIC CORRECTIONS
In this section, the brief summarizations of four static cor-
rection methods have been presented and these methods are
field statics, refraction statics, tomographic statics and residual
static corrections.
2.1 Field StaticsThe source and receiver can be replaced on a reference
datum with the datum static corrections according to the infor-
mation of both elevation and near-surface velocity distribution
from the uphole survey and the near-surface refraction data
(Cox, 1999). The datum static corrections are including the
weathering corrections for removing the effects of near-surface
layers and the elevation corrections for moving from the base
of these near-surface layers up to (or down to) a reference da-
tum. The assumption of static corrections is that a simple time
shift of an entire seismic trace which will yield the seismic
record being observed if the geophone had been displaced ver-
tically downward to the reference datum and the assumption is
not strictly true in most cases. Strictly, the elevation correction
can be used only in those areas there are no weathered layers
and lateral velocity changes in low-velocity layers (Luo et al.,
2010). If the velocity variations only affect the high-frequency
components of the datum static corrections, then the elevation
corrections can be used companying with residual static correc-
tions.
2.2 Refraction Statics
Refraction methods allow us to derive estimates of the
thicknesses and velocities of the near-surface layers by analyz-
ing the first-breaks of the seismic records (Luo et al., 2010; Wu
et al., 2009; Duan, 2006; Lin et al., 2006; Pan et al., 2003).According to the Huygens Principle, that is, every point on an
advancing wavefront can be regarded as the source of a secon-
dary wave and that a later wavefront is the envelope tangent to
all the secondary waves (Cox, 1999). The important concept in
seismic refraction is that when a seismic ray crosses a boundary
between two formations of different velocities, then the ray is
bent according to Snells law which defines that the sine of
refracted angle is equal to the ratio of the velocities of the two
formations. Therefore, the static correction based on refraction
survey acquires the information of the first-arrival time of
wavefield from refractor and the refractor velocity. Hence,
there are two basic conditions for refraction survey, that is, a
relative stable refraction interface between the two formations
and the acknowledged near-surface velocity distribution (Bridle
and Aramco, 2009; Liu, 1998).
Applying the static corrections based on refraction survey
can ensure structural integrity in the processed section. Refrac-
tion statics are effective for correcting long spatial wavelength
anomalies and compensating for the weathering layers. Actually,
refraction statics are also effective against short spatial wave-
length anomalies (Liu, 1998).
2.3 Tomographic Statics
Tomographic statics are commonly used during the proc-
essing of seismic data, especially in the areas with rapid veloc-
ity variations in laterally (Hao et al., 2011; Luo et al., 2010;
Han et al., 2008; Wang, 2005; Yang et al., 2005). The definition
of tomography is that (Sheriff, 1991) a method for finding the
velocity and reflectivity distribution from a multitude of obser-
vations using combinations of source and receiver locations.
The tomographic inversion approaches use the first arrival in-
formation of wavefront to inverse the velocity distribution of
near-surface without the assumption of layer structure in orderto produce a near-surface velocity model which best fits the
observed minimum arrival times. Space is divided into cells
and the data are expressed as line integrals along raypaths
through the cells. Iterated adjusting and updating the
near-surface velocity model, until the differences between arri-
val times of model and those of the observed data reach ac-
ceptable levels or are unchanged between iterations (Becerra et
al., 2009; Henley, 2009; Li et al., 2009b; Vossen and Trampert,
2007; Chang et al., 2002). Tomographic methods include the
algebraic reconstruction technique (ART) (Henley, 2009), the
simultaneous reconstruction technique (SIRT) (Aster et al.,
2005; Emily and Bradford, 2002) and Gauss-Seidel method
(Taner et al., 1998).
The static solutions based on tomography principle need a
large number of different ray paths which go through each of
cells with a wide-angle coverage and constrains of indirect
regularization during the inversion. The methods provide
proper corrections for long and middle spatial wavelength
components under most of situations with rugged surface to-
pography and rapidly changed velocities in near-surface layers.
However, there are still some disadvantages of static correc-
tions based on tomographic techniques and the uncertainties in
tomographic velocity models have also been qualified from a
2D seismic line acquired in Colombia through a variety of nu-
merical techniques (Becerra et al., 2009).
2.4 Residual Static Corrections
The residual static corrections are time shifts applied to
traces in order to compensate for time delays and the statics
model is a function of time and space (Henley, 2012; Li et al.,
2011; Sheriff, 1991). Residual static corrections are defined as
a subset of the static corrections (Cox, 1999). Data-smoothing
statics methods assume that patterns of irregularities which
most events have in common result from near-surface varia-
tions and hence static correction trace shifts should be such as
to minimize those irregularities. Sheriff (1991) describes that
the concept of static correction is the assumption that a simple
time shift of an entire seismic trace will yield the seismic re-
cords which would have been observed if the geophones had
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Static Corrections Methods in the Processing of Deep Reflection Seismic Data 301
been displaced vertically downward to a reference datum. The
time shift approximation means that static corrections are
surface-consistent and independent of reflection times and trace
offsets.
Due to the near-surface model for statics solutions is a
simplification of the geology resulting in a tradeoff between
thicknesses and velocities which result in inexact static correc-tions and these corrections are the approximations for more
complex problems, the applications of field statics, or refraction
statics, never leave the seismic data completely free of static
anomalies (Yin et al., 2004; Jing, 2003). Therefore, its definite
necessary that the residual static anomalies should be handled
properly. In reality, residual static anomalies are compensated
for using statistical correlation techniques. Usually the residual
static corrections are extracted from integrated seismic sections
and designed to correct small inaccuracies in the near-surface
velocity model, which seek to enhance the qualities and resolu-
tions of stacked seismic sections.
3 STATIC CORRECTIONS OF DEEP REFLECTION
SEISMIC DATA
The deep reflection seismic data used in this paper are
along a two-dimensional survey in South China (Fig. 1). There
are very rugged surface topographies and rapid variant veloci-
ties of near-surface layers in both laterally and vertically due to
the variations of compaction and lithology along the survey.
The acquisition line is very long (around 550 km) and the ele-
vation along the acquisition line of survey is shown in Fig. 2a.
Its difficult to deal with the static solutions of the deep reflec-
tion seismic data from this area and the velocity model of
near-surface layers along the survey (Fig. 2b) is obtained using
a ray-tracing method during the procedure of tomographic stat-
ics. If static corrections are not properly handled during the
processing of seismic data, then a whole catalog of problems
will affect the interpretations of the seismic sections, including
lines with variable elevations, false structural anomalies re-
maining in the sections, false events being created out of noises
and the data qualities not being optimized. Therefore, proper
statics solutions are definite desirable for obtaining
high-resolution sections which can be used for both strati-
graphic and lithologic interpretations. As for the deep reflection
seismic data, proper statics solutions are very important in or-
der to obtain the final clear and accurate images of the crust andupper mantle.
Several static correction methods including field statics,
refraction statics, tomographic statics and in the wave of resid-
ual statics are used during the data processing of deep reflection
seismic data. We also combine the low-frequency components
of field statics solutions with the high-frequency ones of refrac-
tion statics solutions in order to obtain more reasonable statics
solutions and this procedure is shown in Fig. 3a. In order to
compare the results of these different statics solutions, a raw
shot profile and those profiles applied with different statics
solutions are shown in Figs. 3b3f. The static corrections of
these methods for all receivers and sources of the survey areshown in Figs. 4a and 4b, respectively. Four common middle
point (CMP) stacked profiles of deep reflection seismic data
corresponding to applying these statics solutions, that is, field
statics, refraction statics, tomogrpahic statics and combining of
the former two statics solutions, are shown in Figs. 5a, 5b, 6a
and 6b, respectively. Comparing these solutions shown in Figs.
3c3f, the results of refraction statics (Fig. 3d) are slightly bet-
ter than those of field ones (Fig. 3c). Both the results of tomo-
graphic statics solutions (Fig. 3e) and those of the combining
solutions of field statics with those of refraction ones (Fig. 3f)
can provide good qualities of shot profiles, and the reflection
events have better continuities than those in the other two pro-
files. The similar conclusions can be derived from the CMP
stacked profiles after applied the four kinds of statics solutions
mentioned above which are shown in Figs. 5 and 6. Comparing
the three kinds of statics solutions using separately for both
receivers (Fig. 4a) and sources (Fig. 4b), the field static
Figure 1. Location map showing the deep reflection seismic profile in South China. The red line indicates the location of sur-
vey and its length is around 550 km. The red square at the right upper corner shows the location of study area and the black
lines indicate the locations of faults. The survey is a symmetric survey with 700 receivers distributed at two sides of sourceand the total source number is 2 269, receiver spacing is every 40 m and source spacing is every 280 m, near offset is 140 m
from the source, 7 499 time gates are recorded with 4 ms spacing.
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Xiaosan Zhu, Rui Gao, Qiusheng Li, Ye Guan, Zhanwu Lu and Haiyan Wang302
Figure 2. (a) Elevation along the survey line of the deep reflection seismic profile in South China. (b) Velocity model of
near-surface layers along the survey which is obtained using ray-tracing method (the black line indicates the ray bottom and
the velocity below the line is not creditable).
Figure 3. (a) Static corrections of all the receivers of the survey by combining the low-frequency components of field statics
solutions with the high-frequency components of refraction ones; (b) raw shot profile; (c) field static corrections applied; (d)
refraction static corrections applied; (e) tomographic static corrections applied; (f) applying the combining low spatial wave-
length components of field statics solutions with the high ones of refraction statics solutions. The white rectangles show the
areas with great improvements after applied statics solutions.
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Static Corrections Methods in the Processing of Deep Reflection Seismic Data 303
Figure 4. Profiles of static corrections of all the receivers (a) and sources (b) of the survey for field statics, refraction statics,
tomographic statics and combining field statics with refraction ones.
Figure 5. CMP stacked sections illustrating the results of field static corrections (a) and those of refraction static corrections (b).
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Xiaosan Zhu, Rui Gao, Qiusheng Li, Ye Guan, Zhanwu Lu and Haiyan Wang304
Figure 6. CMP stacked sections illustrating the results of tomographic static corrections (a) and those of combining the
low-frequency components of field statics solutions with the high-frequency ones of refraction statics solutions (b).
corrections are slightly big and the refraction ones are some-
what small, however the tomographic ones are the best solu-
tions among them. The combining statics solutions of the for-
mer two can also provide reasonable solutions in this case.
Implement of field statics is very fast and need only small
amount of computation time. During the processing of seismic
data, field static corrections are usually served as a basic stan-
dard of quality control in order to obtain some basic informa-
tion for both the parameters of static corrections and its pre-
liminary stack section of the deep reflection seismic data. The
statics solutions based on refraction principles work well in the
region with mild topography and well behaved weathering
layers. However, the refraction model does not match the geo-
logic reality of complex terrains in most cases and the refrac-
tion statics cannot properly handle the conditions with inverse
velocity distribution layers where the low-velocity layers locate
under the high-velocity ones and hidden layers which are too
thin to be recognized. Its a good choice that combing the ad-
vantages of both field statics and refraction ones, which is
shown in Fig. 3a. The reason is that the combining statics solu-
tions can correct the statics anomalies of both long spatial
wavelengths and short ones. However, the problem for this
procedure is that it's difficult to handle the ratios of the static
corrections of field statics versus those of refraction ones be-cause the velocity distributions of near-surface layers varying
strongly. The statics solutions based on tomographic techniques
can provide proper corrections for long and middle spatial
wavelengths components in most cases and work well for those
areas with rapidly changed thicknesses, strong velocity varia-
tions in laterally and vertically of near-surface layers and com-
plex subsurface geology as long as enough first-arrival infor-
mation from the relative small offset has been used during in-
version procedure. Tomographic statics can be used to obtain
the model of near-surface low-velocity layers (Fig. 2b) and it is
very useful for the velocity updating in the subsequent proc-
essing steps. However, there are still some shortcomings of this
method. The solution of tomographic inversion is not unique
and unstable usually, and it is sensitive to the initial velocity
model and the picking accuracies of first-arrivals. Zhang et al.
(2005) have developed a hybrid optimization inversion method
to calculate large statics by integrating stack-power maximiza-
tion, simulated annealing and genetic algorithm in complex
terrains. In this method, large statics are corrected using a spe-
cial smooth filtering operator which can eliminate the
pseudo-static corrections from long spatial wavelengths com-
ponents to short ones iteratively. Therefore, the method has
some combined abilities of field statics, refraction statics and
tomographic statics.
Due to the complex geological structures and most of
static correction methods are based on simplified models, itsdifficult to obtain the accurate velocity model of near-surface
layers no matter what kinds of methods being used, and there
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Static Corrections Methods in the Processing of Deep Reflection Seismic Data 305
are always some residual statics anomalies remaining in seis-
mic sections. Residual static corrections can enhance the quali-
ties of stacked traces using statistical correlation methods after
applying those first statics solutions (i.e., field statics, refraction
statics, tomographic statics and combining of the former two
statics solutions). In reality, the residual static corrections are
used iteratively for obtaining close to free of statics anomalies
of stacked traces. In this implement, we iteratively apply the
residual static corrections three times. The first and third resid-
ual static corrections for all the receivers and sources of the
survey are shown in Figs. 7a7d. From these figures, we see
that both the residual statics solutions of receivers and source
Figure 7. Profiles of the first residual statics solutions of both receivers (a) and sources (b) after applying those first static
corrections (i.e., field static corrections, refraction static corrections, tomographic static corrections and combining the
low-frequency components of field statics solutions with the high-frequency ones of refraction statics solutions). Profiles of
the third residual statics solutions of both receivers (c) and sources (d) of the survey after applying the second residual statics
solutions.
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Xiaosan Zhu, Rui Gao, Qiusheng Li, Ye Guan, Zhanwu Lu and Haiyan Wang306
Figure 8. CMP stacked sections illustrating the changes
in apparent structure after residual static corrections
applied. (a) Field static corrections applied; (b) residual
static corrections applied after field static corrections; (c)
refraction static corrections applied; (d) residual static
corrections applied after refraction static corrections.
The white rectangles show the areas with great im-
provements of the reflections of Moho after applied re-
sidual statics solutions.
Figure 9. CMP stacked sections illustrating the changes
in apparent structure after residual static corrections
applied. (a) Tomographic static corrections applied; (b)
residual static corrections applied after tomographic
static corrections; (c) combining the statics solutions of
field statics solutions with those of refraction statics solu-
tions applied; (d) residual static corrections applied after
the combining statics solutions. The white rectangles
show the areas with great improvements of the reflec-tions of Moho after applied residual statics solutions.
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Static Corrections Methods in the Processing of Deep Reflection Seismic Data 307
become smaller and smaller with the iterated applying the re-
sidual statics corrections. Therefore, we can reduce the statics
anomalies in the deep reflection seismic sections iterated using
the same procedure.
In order to compare the results of residual statics solutions,
four CMP stacked profiles of deep reflection seismic data are
shown in Figs. 8 and 9. Due to the reflections of Moho are veryimportant for deep reflection seismic profiles, these profiles are
shown corresponding to the special time sections of these re-
flections of Moho in CMP stacked profiles. Figures 8 and 9
show that most of the reflections of Moho in those profiles
applied residual statics solutions have better continuities than
those without applying this procedure, and the resolutions of
them have been greatly improved after applying residual static
corrections. The residual static corrections are represented usu-
ally by the short spatial wavelength components of the profiles
and not the long ones (Li et al., 2011). However, the serious
shortcoming of residual static corrections is that there will exit
cycle skipping in the sections when the statics errors aregreater than half the length of seismic wavelet, which looks like
faults in the data and may be misaligned by a whole cycle of
the seismic wavelet.
Theoretically, all the first static corrections (i.e., field stat-
ics, refraction statics, tomographic statics and combining the
former two) and residual static corrections should be treated as
not only frequency dependent time shifts but also time and
phase components. Therefore, the challenging rugged surface
topography and large magnitude statics need the processing
procedures with iterative statics calculations, noises attenuation
and the velocity updating of near-surface model for obtaining
high-resolution seismic section.
4 CONCLUSIONS
In this paper, both the field statics solutions and refraction
ones used separately in the processing of deep reflection seis-
mic data along the long survey in South China cannot derive
reasonable statics solutions anymore due to the rugged surface
topography, low-velocity layers and the velocities of
near-surface layers varying strongly in laterally and vertically
along the survey. However, statics solutions based on tomo-
graphic principle can provide proper solutions for this kind of
situation. Combining the low-frequency components of field
statics solutions with the high-frequency ones of refraction
statics solutions can also provide reasonable solutions for thedeep reflection seismic data in South China. The surface-
consistent residual static corrections are good compensations to
the procedures of the first statics solutions studied in the paper
and can leave the deep reflection seismic data close to free of
statics anomalies.
ACKNOWLEDGMENTS
This work was supported by the Foundation of Institute of
Geology, Chinese Academy of Geological Sciences (No.
J1315), the 3D Geological Mapping Project (No. D1204) and
the SinoProbe-02 project of China. The authors thank
Hongqiang Li and Gong Deng for providing wonderful com-
ments and suggestions.
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