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 resolutions of seismic sections, especially for the reflections of Moho in the upmost mantle.
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): corrections applied to seismic data to compensate for the effects of variations in elevation, weathering thickness, weathering velocity, 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 dependent on the location of the source (or receiver) but are independent 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 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 Cunningham, 2001). Tomographic static correction methods have been 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 tomographic 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 maximization method (Ronen and Claerbout, 1985), nonstationary residual 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 handled. These factors are including rugged surface acquisition topography, non-planar refractors, near-surface low-velocity layers, lateral variant velocities of weathering layers and variations 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 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 theories of field statics, refraction statics, tomographic statics and residual 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.
Figure
1.
Location map showing the deep reflection seismic profile in South China. The red line indicates the location of survey 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 source and 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.
In this section, the brief summarizations of four static correction methods have been presented and these methods are field statics, refraction statics, tomographic statics and residual static corrections.
2.1
Field Statics
The source and receiver can be replaced on a reference datum with the datum static corrections according to the information 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 datum. 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 vertically 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 corrections.
2.2
Refraction Statics
Refraction methods allow us to derive estimates of the thicknesses and velocities of the near-surface layers by analyzing 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 secondary 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 Snell's 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. Refraction statics are effective for correcting long spatial wavelength anomalies and compensating for the weathering layers. Actually, refraction statics are also effective against short spatial wavelength anomalies (Liu, 1998).
2.3
Tomographic Statics
Tomographic statics are commonly used during the processing of seismic data, especially in the areas with rapid velocity 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 observations using combinations of source and receiver locations. The tomographic inversion approaches use the first arrival information of wavefront to inverse the velocity distribution of near-surface without the assumption of layer structure in order to 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 arrival times of model and those of the observed data reach acceptable 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 topography and rapidly changed velocities in near-surface layers. However, there are still some disadvantages of static corrections 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 numerical 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 variations 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 records which would have been observed if the geophones had 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 corrections 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, it's 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 resolutions 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 velocities 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 elevation along the acquisition line of survey is shown in Fig. 2a. It's difficult to deal with the static solutions of the deep reflection 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 statics. 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 remaining 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 stratigraphic and lithologic interpretations. As for the deep reflection seismic data, proper statics solutions are very important in order to obtain the final clear and accurate images of the crust and upper mantle.
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).
Several static correction methods including field statics, refraction statics, tomographic statics and in the wave of residual 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 refraction 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. 3b–3f. The static corrections of these methods for all receivers and sources of the survey are shown 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. 3c–3f, the results of refraction statics (Fig. 3d) are slightly better than those of field ones (Fig. 3c). Both the results of tomographic 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 profiles. 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 corrections are slightly big and the refraction ones are somewhat small, however the tomographic ones are the best solutions among them. The combining statics solutions of the former two can also provide reasonable solutions in this case.
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 wavelength 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.
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.
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 standard of quality control in order to obtain some basic information for both the parameters of static corrections and its preliminary 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 geologic reality of complex terrains in most cases and the refraction 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. It's a good choice that combing the advantages of both field statics and refraction ones, which is shown in Fig. 3a. The reason is that the combining statics solutions 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 because 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 variations in laterally and vertically of near-surface layers and complex subsurface geology as long as enough first-arrival information from the relative small offset has been used during inversion 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 processing 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 maximization, simulated annealing and genetic algorithm in complex terrains. In this method, large statics are corrected using a special smooth filtering operator which can eliminate the pseudo-static corrections from long spatial wavelengths components 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, it's difficult to obtain the accurate velocity model of near-surface layers no matter what kinds of methods being used, and there are always some residual statics anomalies remaining in seismic sections. Residual static corrections can enhance the qualities 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 residual static corrections for all the receivers and sources of the survey are shown in Figs. 7a–7d. From these figures, we see that both the residual statics solutions of receivers and source become smaller and smaller with the iterated applying the residual statics corrections. Therefore, we can reduce the statics anomalies in the deep reflection seismic sections iterated using the same procedure.
Figure
7.
CMP stacked sections illustrating the results of field static corrections (a) and those of refraction static corrections (b).
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 very important for deep reflection seismic profiles, these profiles are shown corresponding to the special time sections of these reflections 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 usually 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 are greater 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.
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 improvements of the reflections of Moho after applied residual 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 solutions applied; (d) residual static corrections applied after the combining statics solutions. The white rectangles show the areas with great improvements of the reflections of Moho after applied residual statics solutions.
Theoretically, all the first static corrections (i.e., field statics, 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 seismic 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 tomographic 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 the deep reflection seismic data in South China. The surfaceconsistent 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 comments and suggestions.
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Figure 1. Location map showing the deep reflection seismic profile in South China. The red line indicates the location of survey 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 source and 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.
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 wavelength 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.
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).
Figure 6. CMP stacked sections illustrating the results of field static corrections (a) and those of refraction static corrections (b).
Figure 7. CMP stacked sections illustrating the results of field static corrections (a) and those of refraction static corrections (b).
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 improvements of the reflections of Moho after applied residual 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 solutions applied; (d) residual static corrections applied after the combining statics solutions. The white rectangles show the areas with great improvements of the reflections of Moho after applied residual statics solutions.
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