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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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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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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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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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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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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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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