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Volume 25 Issue 1
Feb.  2014
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Runhai Feng, Ping Dong, Liangshu Wang, Bin Sun, Yongjing Wu, Changbo Li. Inversion of Moho Interface in Northeastern China with Prior Information. Journal of Earth Science, 2014, 25(1): 146-151. doi: 10.1007/s12583-014-0407-9
Citation: Runhai Feng, Ping Dong, Liangshu Wang, Bin Sun, Yongjing Wu, Changbo Li. Inversion of Moho Interface in Northeastern China with Prior Information. Journal of Earth Science, 2014, 25(1): 146-151. doi: 10.1007/s12583-014-0407-9

Inversion of Moho Interface in Northeastern China with Prior Information

doi: 10.1007/s12583-014-0407-9
More Information
  • Corresponding author: Ping Dong, dongp@nju.edu.cn
  • Received Date: 2012-09-28
  • Accepted Date: 2013-01-20
  • Publish Date: 2014-02-01
  • 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.
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Inversion of Moho Interface in Northeastern China with Prior Information

doi: 10.1007/s12583-014-0407-9

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.

Runhai Feng, Ping Dong, Liangshu Wang, Bin Sun, Yongjing Wu, Changbo Li. Inversion of Moho Interface in Northeastern China with Prior Information. Journal of Earth Science, 2014, 25(1): 146-151. doi: 10.1007/s12583-014-0407-9
Citation: Runhai Feng, Ping Dong, Liangshu Wang, Bin Sun, Yongjing Wu, Changbo Li. Inversion of Moho Interface in Northeastern China with Prior Information. Journal of Earth Science, 2014, 25(1): 146-151. doi: 10.1007/s12583-014-0407-9
  • 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 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).

  • 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).

    Figure 1.  Diagram showing main steps of the inversion procedure (after Chenot and Debeglia, 1990).

    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—zj (j=1, 2, …, M; M is 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 Δgj of the known points by the infinite plate formula approximately

    (3) Subtract the calculated anomaly Δgj 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—Δgr, then subtract the observed gravity anomaly with the regional one, thus the local value of every point—Δg'i can be acquired.

    (5) Calculate the initial depth of the interface according to Eq. (2)

    (6) Forward compute the calculated anomaly Δgi 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-Δg'i can be computed by the same procedure in step 4.

    (9) δgi is obtained by subtracting the local anomaly Δg'i with the calculated anomaly Δgi.

    (10) Adjust the depth of the interface according to Eq. (3)

    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).

  • 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).

    Figure 2.  Power spectrum analysis of the 4th-order approximation anomaly.

    Figure 3.  Bouguer gravity anomaly attributed to Moho interface in Northeast China.

    In Fig. 3, we can see that the general trend is NNE-SSW with a clear characteristic of partition which vividly reflects the 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 calculated using the receiver function (Chen et al., 2010) (Table 1).

    Figure 4.  Moho interface derived from the application of the method presented in this article.

    Table 1.  Coordinates and depth of the control points

    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.

    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 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.

    Figure 5.  The forward gravity anomaly of the 3D Moho relief map.

    Figure 6.  Difference between calculated gravity map of Fig. 5 and Bouguer gravity map presented in Fig. 3.

  • 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.

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