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SCIENCE CHINA Earth Sciences, Volume 62, Issue 7: 1110-1124(2019) https://doi.org/10.1007/s11430-018-9341-9

Crustal structure study based on principal component analysis of receiver functions

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  • ReceivedAug 9, 2018
  • AcceptedFeb 22, 2019
  • PublishedMar 27, 2019

Abstract

The receiver function (RF) technique is an effective method for studying crustal structure. For a single station, the average 1-D crustal structure is usually derived by stacking the radial RFs from all back-azimuths, whereas structural variations (such as dipping discontinuities or anisotropy) can be constrained through analysis of waveform dependence on the back-azimuth of both the radial and tangential RFs. However, it is often difficult to directly extract information about structural variations from the waveform of RF, due to the common presence of noise in real data. In this study, we proposed a new method to derive structural variation information for individual stations by applying principal component analysis (PCA) to RFs sorted by back-azimuth. In this method (termed as RF-PCA), a set of principal components (PCs), which are uncorrelated with each other and reflect different characteristics of the RF data, were extracted and utilized separately to reconstruct new RFs. Synthetic tests show that the first PC of the radial RFs contains the average structural information of the crust beneath the corresponding station, and the second PC of the radial RFs and the first PC of the tangential RFs both reflect the variations of the crustal structure. Our synthetic modeling results indicate that the new RF-PCA method is valid for a variety of synthetic models with intra-crustal dipping discontinuities and/or anisotropy. We applied this method to the real data from a broadband temporary seismic station (s233) in the central part of the Sichuan Basin. The results suggest that the RF data can be best explained by the presence of two nearly parallel dipping discontinuities within the crust. Combining with previous logging data, seismic exploration and deep sounding observations, we interpret the shallow dipping discontinuity as the top boundary of the Precambrian crystalline basement of the Sichuan Basin and the deep one corresponding to the Conrad interface between the upper and lower crust, consistent with the geological feature of the study area. In this work, both synthetic tests and real data application results demonstrate the effectiveness of the RF-PCA method for studying crustal structures.


Funded by

the National Natural Science Foundation of China(Grant,No.,4188103)

the independent project of the State Key Laboratory of the Lithospheric Evolution

IGGCAS(Grant,No.,SKL-Z201704-11712180)


Acknowledgment

We acknowledge the participants of the Seismic Array Laboratory of IGGCAS for collecting the data (doi: 10.12129/IGGSL.Data.Observation, http://www.seislab.cn/). We thank Prof. Frederiksen and Prof. Bostock for providing the Raysum package and Prof. Qingju Wu for providing the time domain maximum entropy spectral deconvolution algorithm. We thank reviewers for their constructive comments and suggestions, as well as the help of Yiming Bai, Zimu Wu, and Yujing Lai. This project was supported by the National Natural Science Foundation of China (Grant No. 41688103) and the independent project of the State Key Laboratory of the Lithospheric Evolution, IGGCAS (Grant No. SKL-Z201704-11712180).


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  • Figure 1

    RF waveforms of the three theoretical models. The cartoons correspond to the three models, i.e., the isotropic model with a horizontal discontinuity (Model 1) and a dipping discontinuity (Model 2), and the anisotropic model with a horizontal symmetry axis (Model 3), from left to right. (a), (b), and (c) are the waveforms of the R-RFs corresponding to Models (1), (2), and (3), respectively. (d), (e), and (f) are the waveforms of the T-RFs (the amplitude is amplified by a factor of three). Red waveforms indicate positive polarity signals.

  • Figure 2

    RF-PCA results from three crustal models. The cartoons are the model diagrams (same as Figure 1). Cartoon in rows represent the results of the same model. In the icons (1a), (2a), and (3a), Models 1, 2, and 3 are represented by 1, 2, and 3, respectively. The first column is the eigenvalue distribution of the covariance matrix. The x-axis is the sequence of eigenvalues, and the y-axis is the percentage of each eigenvalue, indicating the contribution rate of the corresponding PC. The amplitudes of the third and fourth columns are amplified by a factor of five. And the reconstructed results for the T-RF are also amplified by a factor of five. The positive and negative signals are shaded in red and blue, respectively.

  • Figure 3

    RF-PCA results at various noise levels. In figure 3, the first and second columns show the original RF waveforms and the PC reconstructed results for the isotropic dipping discontinuity model (with 10% noise) and the azimuthal anisotropic model (with 10% noise), respectively. The amplitudes of T-RFs are amplified by a factor of three. (3a) and (3b) show the original R-RF waveforms and the reconstructed results for the second PC of the isotropic dipping discontinuity model (with 25% noise). (3c) and (3d) show that of the azimuthal anisotropic model (with 25% noise), respectively. The amplitudes of the reconstructed results are amplified by a factor of five.

  • Figure 4

    R-RF-PCA reconstructed results for complex models. The cartoons correspond to three models, i.e., the anisotropic model with a dipping symmetry axis (Model 4), the coexistent model with a dominant dipping discontinuity and anisotropy (Model 5), and the coexistent model with a dominant anisotropy and dipping discontinuity (Model 6). The amplitudes are amplified by a factor of five.

  • Figure 5

    R-RF-PCA results for the two dipping discontinuities model. The cartoons in the right panel correspond to different models, i.e., (1) and (2) are the same isotropic model with two nearly parallel dipping discontinuities (Model 8), (3) and (4) are the same isotropic model with two dipping discontinuities which are very different in dip angle (Model 9), and (5) is an isotropic model with a dipping discontinuity (Model 7). The model parameters are shown in Table 1. The strike parameters of each model can be found at the bottom of the R-RF waveforms. The amplitudes of the reconstructed results are amplified by a factor of five.

  • Figure 6

    Topography of Sichuan Basin and its adjacent areas, position of s233 seismic station, and distribution of telesimic earthquake events. Abbreviations, SGB: Songpan-Ganzi block; HYF: Huayin fault, LQF: Longquan fault, LFB: Longmenshan fault belt.

  • Figure 7

    Observed R-RFs of s233, as well as synthetic R-RFs with Models A, B, and C, and reconstructed results for the second and third PCs. The first row is the results of the observed data. The cartoons depict the corresponding models A, B, and C, respectively. The amplitude of the reconstructed results is amplified by a factor of five.

  • Table 1   Theoretical model parameters

    Model

    N

    Thick (km)

    ρ

    (kg/m³)

    Vp (km/s)

    Vs (km/s)

    %P

    %S

    Trend (°)

    Plunge (°)

    Strike (°)

    Dip (°)

    1

    1

    40

    2.7

    6.4

    3.5

    0

    0

    0

    0

    0

    0

    2

    3.29

    8.15

    4.55

    0

    0

    0

    0

    0

    0

    2

    1

    40

    2.7

    6.4

    3.5

    0

    0

    0

    0

    0

    0

    2

    3.29

    8.15

    4.55

    0

    0

    0

    0

    0

    5

    3

    1

    40

    2.7

    6.4

    3.5

    5

    5

    0

    0

    0

    0

    2

    3.29

    8.15

    4.55

    0

    0

    0

    0

    0

    0

    4

    1

    40

    2.7

    6.4

    3.5

    5

    5

    0

    65

    0

    0

    2

    3.29

    8.15

    4.55

    0

    0

    0

    0

    0

    0

    5

    1

    40

    2.7

    6.4

    3.5

    5

    5

    0

    0

    0

    0

    2

    3.29

    8.15

    4.55

    0

    0

    0

    0

    0

    25

    6

    1

    40

    2.7

    6.4

    3.5

    10

    10

    0

    0

    0

    0

    2

    3.29

    8.15

    4.55

    0

    0

    0

    0

    0

    5

    7

    1

    6

    2.65

    5.8

    2.76

    0

    0

    0

    0

    0

    0

    2

    2.83

    6.45

    3.7

    0

    0

    0

    0

    0

    5

    8

    1

    6

    2.65

    5.8

    2.76

    0

    0

    0

    0

    0

    0

    2

    17

    2.7

    6.4

    3.6

    0

    0

    0

    0

    0

    5

    3

    2.83

    7

    3.97

    0

    0

    0

    0

    0

    6

    9

    1

    6

    2.65

    5.8

    2.76

    0

    0

    0

    0

    0

    0

    2

    17

    2.7

    6.4

    3.6

    0

    0

    0

    0

    0

    15

    3

    2.83

    7

    3.97

    0

    0

    0

    0

    0

    5

    N represents the number of model layers. “Thick” represents the thickness of the layer. The terms Vp, Vs, and ρ represent the P-wave velocity, S-wave velocity, and density, respectively. The terms %P and %S represent the percentage of maximum velocity change of the P-wave and S-wave, respectively. “Trend” represents the angle between the horizontal projection of the anisotropic symmetry axis (fast axis) and north. “Plunge” represents the angle between the anisotropic symmetry axis (fast axis) and the horizontal plane. “Strike” represents the strike of the dipping discontinuity, for example, 0° indicates that the discontinuity’s strike is north-south and its down dip direction is east. “Dip” represents the dip angle of the discontinuity.

  • Table 2   Model parameters for the station s233

    Model

    N

    Thick (km)

    ρ

    (kg/m³)

    Vp (km/s)

    Vs (km/s)

    %P

    %S

    Trend (°)

    Plunge (°)

    Strike (°)

    Dip (°)

    A

    1

    6.0

    2.65

    5.56

    2.66

    0

    0

    0

    0

    0

    0

    2

    41.05

    2.83

    6.45

    3.7

    0

    0

    0

    0

    210

    5

    3

    3.298

    8.15

    4.55

    0

    0

    0

    0

    210

    4

    B

    1

    6.0

    2.65

    5.8

    2.76

    0

    0

    0

    0

    0

    0

    2

    17.0

    2.7

    6.4

    3.6

    0

    0

    0

    0

    210

    5

    3

    24.24

    2.83

    7.0

    3.97

    0

    0

    0

    0

    210

    6

    4

    3.298

    8.15

    4.55

    0

    0

    0

    0

    210

    4

    Header information is the same as Table1. The Model C is similar to Model B except that its Moho is flat (Dip is 0°).

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