Journal of Earth Science, Vol. 25, No. 1, p. 146–151, February 2014
Printed in China
DOI: 10.1007/s12583-014-0407-9 ISSN 1674-487X
Inversion of Moho Interface in Northeastern China with
Prior Information
Runhai Feng, Ping Dong*, Liangshu Wang, Bin Sun, Yongjing Wu, Changbo Li
School of Earth Sciences and Engineering, Nanjing University, Nanjing 210093, China
ABSTRACT: Non-uniqueness is always, by nature, the problem we face in inversion processes, and it
is caused by the phenomenon of equivalence in field, erroneous, discrete, and finite features in observation and the influence of other sources. Many authors have done lots of researches in this field in
order to get more reliable outcomes, and joint inversion is a thriving one where different kinds of
data are combined to derive certain information simultaneously or sequentially. One of these studies
is that the prior information such as the geological, drilling and seismic data will be used as constraints, while the inversion procedure can be controlled. In this article we use a new method with
the goal of better obtaining the three-dimensional density contrast interface. This prior seismic data
integrated in the inversion can play a constrained role in the procedure which means that the depth
of the Moho interface at the seismic location will be restricted. It thus can provide a credible result.
In order to test its effect, this program is applied in a field example―derivation of Moho geometry in
Northeast China.
KEY WORDS: prior information, inversion, Moho, seismic data.
1 INTRODUCTION
Many authors have done lots of researches in the gravity
inversion studies, and have presented different algorithms to
derive the geometry related to a known anomaly (Tarantola,
2005, 1987; Cordell and Handerson, 1968; Bott, 1960; Talwani
et al., 1959). The most frequently used method is put forward
by Parker (1994, 1973) and Oldenburg (1974). The whole
scheme is based on the Fourier transform of the gravitational
anomaly as a result of the sum of the Fourier transform of the
powers of the surface causing the anomaly and the theory that
the Parker’s expression could be rearranged in order to determine the geometry of the density interface from the gravity
anomaly (Gόmez-Ortiz and Agarwal, 2005).
However, because we always want the flexibility of explaining as much of the true complexity of the 3D Earth as
possible, non-uniqueness is a pervasive characteristic of solving
the geophysical inverse problem (Ellis, 2010; Yin, 2003). Since
an infinite number of models or solutions are possible, alternative information must be used to constrain the models so that
one can be chosen in favor of all the rest. That is where prior
information—what we already know about the problem, comes
in. Usually, geological, geophysical or logical information constitutes the prior knowledge (Scales and Tenorio, 2001).
But all of the algorithms mentioned above are performed
without integrating the prior information such as the seismic
*Corresponding author: [email protected]
© China University of Geosciences and Springer-Verlag Berlin
Heidelberg 2014
Manuscript received September 28, 2012.
Manuscript accepted January 20, 2013.
data, even if they do, only the average depth is used such as in
the Parker—Oldenburg method (Gόmez-Ortiz and Agarwal,
2005; Nagendra et al., 1996).
So here, we use a new method put forward by Wang and
Hao (2008) to derive the Moho density interface in which the
prior information—usually the seismic data, will be incorporated, since this value enjoys a highly vertical resolution (Liu et
al., 1996).
2 THEORY
First, it is supposed that the depth of several points on the
density interface is already known. Controlled by this prior
value, the initial depth of the interface can be obtained by the
Bouguer slab approximation (Chenot and Debeglia, 1990) with
the implicit hypothesis that the amplitude of the gravity anomaly at any station is in direct proportion to the thickness of the
rectangular prism below it (Rao et al., 1999). The thickness of
these prisms is corrected by assuming a ratio between the improvement to the thickness and the difference in the observed
and calculated anomalies. The iterative process is performed
until some criterion is met or a maximum number of iterations
have been accomplished. The whole procedure is organized in
six main steps (Fig. 1), combining alternately computations in
spatial-domain―the initialization and depth adjustment, and
wavenumber-domain—the model effect (Gerard and Debeglia,
1975).
The detailed mathematical steps are described in the following (Wang and Hao, 2008; Zeng, 2005; Wang et al., 1991;
Ling and Yang, 1985).
(1) Give the observed gravity anomaly—gi (i=1, 2, …, N;
N is the total number of the observation points), the position
and depth of the known points—z j (j=1, 2, …, M; M is
Feng, R. H., Dong, P., Wang, L. S., et al., 2014. Inversion of Moho Interface in Northeastern China with Prior Information. Journal
of Earth Science, 25(1): 146–151, doi:10.1007/s12583-014-0407-9 Inversion of Moho Interface in Northeastern China with Prior Information 1. Pre-processing
z ( k 1)  z ( k ) 
4. Initial depth conversion of interface
5. Computation of the interface
residual model effect
Test
6. Iterative depth computation
(3)
End
Figure 1. Diagram showing main steps of the inversion procedure (after Chenot and Debeglia, 1990).
total number of the known points), the average depth of the
interface—z0, the density contrast―ρ and other necessary parameters.
(2) Compute the calculated anomaly ∆gj of the known
points by the infinite plate formula approximately
(1)
(3) Subtract the calculated anomaly ∆gj from the observed
gravity value gi of the known points, and calculate the regional
anomaly equation by polynomial fitting method defining the
subtracted result as a constraint.
(4) Utilizing the polynomial equation derived in step 3,
compute the regional anomaly of each point—∆gr, then subtract the observed gravity anomaly with the regional one, thus
the local value of every point—∆gi' can be acquired.
(5) Calculate the initial depth of the interface according to
Eq. (2)
Δg i'
z i(1)  z 0 
(2)
2πG
(6) Forward compute the calculated anomaly ∆gi of the interface modeled by the initial depth―zi and the mean depth―z0
in the frequency domain.
(7) Same with step 3, compute the regional anomaly equation by using the subtracted result of the observed gravity
anomaly with the calculated one which is obtained in step 6.
(8) Calculate the regional anomaly of each point by the
equation derived in step 7, and the local anomaly―∆gi' can be
computed by the same procedure in step 4.
(9) δgi is obtained by subtracting the local anomaly ∆gi'
with the calculated anomaly ∆gi.
(10) Adjust the depth of the interface according to Eq. (3)
3 APPLICATION EXAMPLE
In order to test the effect of this methodology, we apply it
to inverse the Moho geometry in northeastern China. It is located in the east of East Asia orogen between the Siberia Plate
and the North China Plate, as an overlapping region of an EWtrending paleo-Asian Ocean and a NE-trending marginal Pacific domain, with the former having a longer history, controlled the formation and evolvement of the Meso–Cenozoic
basins in this area (Sun et al., 2012; Lin et al., 2008; Jia et al.,
2004; Xie, 2000; Ren et al., 1980).
All the gravity data are from China Aerogeophysical Survey & Remote Senging Center (AGRS). After the multi-scaled
wavelet decomposition processing and the analysis of power
spectrum (Fig. 2) (Albora and Ucan, 2001; Ucan et al., 2000;
Fedi and Quarta, 1998; Spector and Grant, 1970), the slope of
the best-fit straight lines of spectrum segments of logarithm
power spectrum versus radial wavenumber plot indicates the
average depth of the sources which can reflect the upliftdepression features of the Bouguer anomaly associated with the
crust-mantle boundary (Sun et al., 2012; Wu et al., 2012; Dolmaz et al., 2005) (Fig. 3).
In Fig. 3, we can see that the general trend is NNE-SSW
with a clear characteristic of partition which vividly reflects the
A 4G
0
LnPower (F)
3. Initialization
δg i
2πG
where z(k+1) and z(k) are the (k+1)th and kth iterated processes of
the interface depth.
(11) The RMS of δgi will be computed, and if it is lower
than a pre-assigned value, i.e., the convergence criterion, the
procedure stops, otherwise the steps 6 to 11 will be cycled until
the criterion is met or a maximum number of iteration is
reached.
In steps 2 and 5, it can be observed that the initial depth of
the known points is the given depth, and will not change during
the iterative process from steps 7–10. So the given points can
play a very good role in the inversion, and the undulation of the
density interface will be controlled. In the computation of the
regional equation, the least square theory will be applied to
derive the polynomial (Liu et al., 2012; Zeng, 2005).
2. Optional constraint input
∆gj=2πGρ(z0–zj)
147
-10
Z=39.7 km
-20
-30
-40
0
0.1
0.2
0.3
0.4
0.5
Wavenumber (Radians/km)
0.6
Figure 2. Power spectrum analysis of the 4th-order approximation anomaly.
148
Runhai Feng, Ping Dong, Liangshu Wang, Bin Sun, Yongjing Wu and Changbo Li assembling of microplates during the pre-Mesozoic Period (Xie,
2000).
Applying the program illustrated, we derive the Moho interface shown in Fig. 4. All the colored circles in this map
represents the control points from the Global Geoscience Transect (GGT) (Xiong et al., 2011; Fu et al., 1998; Yang et al.,
1998; Jin and Yang, 1994; Lu and Xia, 1993) and the colored
triangles are the 9 Chinese National Digital Seismic Network
(CNDSN) stations where the crustal thickness could be calcu-
lated using the receiver function (Chen et al., 2010) (Table 1).
In the inversion map, it is shown that the depth of Moho
fluctuates in the range of 25–50 km, and becomes deeper from
center to west and east generally. In the center, there is an obvious uplift in the interface, where Songliao Basin lies. It also
clearly demonstrates a linear characteristic of NE-NNE trend
which approximately corresponds to the faults’ feature.
Here it can be seen that the prior knowledge―depth of the
control points, can play a good role in the inversion process.
Figure 3. Bouguer gravity anomaly attributed to Moho interface in Northeast China.
Figure 4. Moho interface derived from the application of the method presented in this article.
Inversion of Moho Interface in Northeastern China with Prior Information Two more pieces of information are provided by the program. Figure 5 is the gravity anomaly map obtained by means
of the forward modeling algorithm demonstrated by Parker
(1994, 1973) and Gόmez-Ortiz and Agarwal (2005). Figure 6
149
shows the difference between the original and computed anomaly maps. It can be observed that this difference is insignificant
and is in the range of -0.6–0.8 mGal.
Table 1 Coordinates and depth of the control points
Coordinates (º)
119.49
40.08
Depth (m)
32.00
Coordinates (º)
123.33
42.10
Depth (m)
34.00
Coordinates (º)
129.50
44.78
117.04
40.41
36.00
111.22
42.20
48.00
129.08
44.92
39.00
123.98
40.41
36.00
128.60
42.20
35.00
128.42
45.02
38.00
110.93
40.51
43.00
119.19
42.29
36.00
128.00
45.11
35.00
115.06
40.51
41.00
116.62
42.39
42.00
127.52
45.39
32.00
119.01
40.51
34.00
124.82
42.39
33.00
126.62
45.58
31.00
120.03
40.60
33.00
121.05
42.48
38.00
126.20
46.00
30.00
118.29
40.69
33.00
117.57
42.62
39.00
125.90
46.10
32.00
114.22
41.02
43.00
123.62
42.62
35.00
125.00
46.71
34.00
117.99
41.02
36.00
119.19
42.72
34.00
124.52
47.08
35.00
120.21
41.02
34.00
129.02
42.72
33.00
122.79
48.21
40.00
115.48
41.21
41.00
124.04
42.81
35.00
121.29
48.96
42.00
110.03
41.31
46.00
128.48
42.81
34.00
122.01
48.59
41.00
120.69
41.40
35.00
120.51
42.90
37.00
111.56
40.85
44.00
115.06
41.49
41.00
120.09
43.00
36.00
116.17
40.02
39.10
117.51
41.49
39.00
124.28
43.00
34.00
116.08
43.90
35.40
110.03
41.92
47.00
129.97
43.00
35.00
123.58
41.83
31.60
116.02
41.92
42.00
119.97
43.19
37.00
125.26
43.48
29.30
128.48
41.92
38.00
119.19
43.70
36.00
127.40
45.74
31.00
111.11
42.01
48.00
118.77
44.22
40.00
129.59
44.62
37.70
116.98
42.01
41.00
117.99
44.59
39.00
119.36
49.13
35.10
121.83
42.10
36.00
129.97
44.69
39.00
127.41
50.25
32.30
Figure 5. The forward gravity anomaly of the 3D Moho relief map.
Depth (m)
40.00
150
Runhai Feng, Ping Dong, Liangshu Wang, Bin Sun, Yongjing Wu and Changbo Li Figure 6. Difference between calculated gravity map of Fig. 5 and Bouguer gravity map presented in Fig. 3.
4 CONCLUSIONS
In this article a new way has been introduced to invert the
Moho geometry with the prior knowledge to be used as a constraint. The whole theory is based on the separation of the regional and local anomalies, and the depth adjustment is according to the assumption of a ratio between the improvement to the
thickness and the difference in the observed and calculated
anomalies. The iterative process is performed until some criterion is met or a maximum number of iterations have been accomplished.
In calculation of the regional anomaly equation, the prior
data—usually the seismic information which depends primarily
on the fact that the waves enjoy a higher vertical resolution,
will be used. Since we always consider that the regional gravity
has the intrinsic feature of smoothness and steadiness, a
second-order polynomial will be sufficient to represent it.
The Parker methodology is utilized to forward compute
the effect of the interface modeled by the initial or iterative
depth and the mean one.
By comparison between the Bouguer gravity and calculated one, we can see this method is a reliable and alternative
way to derive the Moho interface.
ACKNOWLEDGMENTS
This study was financially supported by the National
Natural Science Foundation of China (No. 41074084) and the
National Science and Technology Major Project of China (No.
2011ZX05009). We thank the editors and two anonymous reviewers for their constructive reviews that improved the manuscript significantly.
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