 Full paper
 Open Access
 Published:
Smallscale scattering heterogeneities beneath the northern Tien Shan from the teleseismic P wavefield
Earth, Planets and Space volume 72, Article number: 13 (2020)
Abstract
In order to investigate the smallscale scattering heterogeneities underneath the northern Tien Shan, we analyze the P wavefield from teleseismic events. By using the teleseismic fluctuation method, we separate the total wavefield into coherent and fluctuating parts in the frequency band of 0.1–8.0 Hz. Subsequently, we investigate the scattering characteristics by analyzing the frequencydependent intensities of the coherent and fluctuating wavefield between 0.3 and 2.5 Hz. We further constrain the velocity perturbations and correlation lengths by modeling the Pwave coda envelope with the Monte Carlo simulation. Strong scattering heterogeneities are revealed beneath the northern Tien Shan. The preferred scattering model can be described as a ~ 55 to 130kmthick randomly heterogeneous layer with velocity perturbations of 6–9% and correlation lengths on the order of 0.4 km. We attribute these smallscale scatterers to isolated melt pockets from the upwelling hot mantle materials.
Introduction
Most seismic studies of Earth’s velocity structure depend on the observations of travel times and waveforms of direct seismic waves (Shearer 2015). The analysis of these direct waves can in general resolve largescale heterogeneous structures in the Earth. For example, tomographic and waveform modeling studies have revealed seismic heterogeneities on the scale of hundreds or tens of kilometers (e.g., Tkalčić et al. 2015; French and Romanowicz 2015; Lai et al. 2019; Ma et al. 2019). However, the spatial resolution of such analysis is usually limited in resolving smallerscale heterogeneities, such as scattering media, due to the dominant wavelengths used. To solve this problem, coda waves are usually analyzed for characterizing much finer structures in a statistical sense based on the random medium approach (e.g., Aki 1969; Wu and Aki 1985). Using such an approach, the average statistical properties of the random heterogeneities can be obtained.
Seismic coda is generally defined as a tail of randomly fluctuating waves arriving after deterministic phases over an extended time interval in a seismogram (Sato et al. 2012). The coda waves are attributed to the superimposition of waves scattered off smallscale structural heterogeneities in various directions inside the Earth (Aki and Chouet 1975). Analysis of coda waves can thus lead to detailed views of seismic structure and provide valuable information on the dynamics and evolution of the Earth (e.g., Kubanza et al. 2006). To explore the stochastic properties of these smallscale heterogeneities in the crust and upper mantle, for several decades, direct and coda waves propagating in the random media have been intensively studied based on both theoretical and numerical methods (e.g., Aki 1973; Scherbaum and Sato 1991; Gusev and Abubakirov 1999; Kubanza et al. 2007; Takahashi et al. 2009; Carcolé and Sato 2010; Yoshimoto et al. 2015; Eulenfeld and Wegler 2017; Emoto and Sato 2018).
For example, the radiative transfer theory (RTT), also known as energy transport theory, has often been used for studying seismogram envelopes and scattering of wave intensity (e.g., Zeng et al. 1991; Wegler et al. 2006; Sato and Emoto 2018) as well as intrinsic and scattering attenuation (e.g., Wu 1985; Gaebler et al. 2015; Wang and Shearer 2017). In addition, the Markov approximation, as a stochastic treatment of the parabolic wave equation in random media (Sato 1989), is also used for analyzing peak delay and envelope broadening (e.g., Saito et al. 2002; Takahashi et al. 2009; Takahashi 2012). Furthermore, spatial variations of lithospheric heterogeneity have been globally established to correlate with tectonic settings based on Markov approximation (e.g., Kubanza et al. 2006, 2007). Besides the theoretical methods, numerical simulations of scattered waves propagating in random medium using finite difference methods have been conducted to determine the statistical parameters of random heterogeneities (e.g., Frankel and Clayton 1986; Yoshimoto et al. 2015; Emoto et al. 2017; Takemura et al. 2017) and effects on ground motions (e.g., Hartzell et al. 2010; Imperatori and Mai 2013; Savran and Olsen 2019). These studies have demonstrated various random models within the Earth’s lithosphere and revealed significantly variable regional randomnesses from the shallow crust to uppermost mantle (Kubanza et al. 2007).
In this study, we analyze the teleseismic P wavefield including the coherent direct Pwave arrivals and following coda waves (Ritter et al. 1998). Coherent signals in the direct P waves are generated in the source region and propagate along the raypath between the source and receivers (Bannister et al. 1990). These signals are recorded showing similar waveforms at closely distributed seismic stations and can be used for localizing deterministic structural anomalies (Rothert and Ritter 2000). By contrast, the following incoherent coda waves, regarded as fluctuating wavefield, are generally generated by nearreceiver scattering heterogeneities with sharp velocity and/or density contrasts in the lithosphere (Korn 1993). These incoherent coda waves can carry valuable information on finescale structures and provide a powerful tool for exploring average statistical properties of scattering regions beneath the stations (Ritter and Rothert 2000). In particular, modeling the temporal decay of coda wave amplitudes can further constrain the scattering parameters, such as the scattering strength and correlation length. The schematic illustration for the discipline is shown in Fig. 1.
Our study area is located in the northern part of Tien Shan. The Tien Shan region is known to be one of the most active intracontinental orogenic belts in the world caused by continent–continent convergence (Omuralieva et al. 2009). This orogenic belt consists of several east–west trending mountain ranges as well as intermountain basins (Lei and Zhao 2007; Li et al. 2016), displaying complex geologic and tectonic settings (Burtman 2015). Currently, the Tien Shan is experiencing an ongoing north–south crustal shortening due to the farfield India–Eurasia plate convergence. The crustal shortening rate is about 20 mm/year, which is nearly one half of the IndoEurasian convergence rate (Abdrakhmatov et al. 1996). Besides, the directions of crustal shortening are approximately in parallel with the north–south compressive stress axes (Ni 1978; Nelson et al. 1987). Therefore, the Tien Shan provides an ideal place for studying the mechanism of intracontinental mountain building and collision processes. During the last decade, numerous geophysical studies have been carried out for a better understanding of the mechanisms of regional geologic processes in this enigmatic region.
The velocity structure beneath this region is complicated by the presence of two underthrusting lithospheres imaged as highvelocity anomalies (Tarim Basin and Kazakh Shield) in tomographic models (e.g., Lei and Zhao 2007; Zabelina et al. 2013; Lü et al. 2019). Furthermore, tomographic studies have revealed prominent low seismic velocities in the upper mantle or even middle crust (e.g., Roecker et al. 1993; Li et al. 2009; Zabelina et al. 2013; Gilligan et al. 2014; Sychev et al. 2018) beneath the central Tien Shan. The lowvelocity anomalies possibly indicate a weak upper mantle (Gilligan et al. 2014) attributed to asthenospheric upwelling caused by lithospheric delamination (Lü et al. 2019). In addition, the presence of slow anomalies in the crust likely provides evidence for magmatic intrusion into the crust from the upper mantle. Therefore, the upwelling of mantle material may play a significant role in understanding the deep dynamic process and mechanism of mountain building (Li et al. 2016). However, by only analyzing coherent signals in the seismograms, these studies focus on tomographically resolved anomalies or sharp seismic discontinuities (e.g., Oreshin et al. 2002; Vinnik et al. 2004). Although some largescale features of the crust and mantle have been revealed, the stochastic properties of finerscale heterogeneities in the lithosphere of the northern Tien Shan are seldom investigated. Moreover, the relation between tomographically largescale structures and random scattering heterogeneities underneath this region is still poorly understood. Characterization of these random finescale structures in the lithosphere would shed light on dynamic processes in the tectonically complicated Tien Shan region.
In this paper, we aim to investigate the averaged scattering characteristics of the lithosphere in the northern Tien Shan region using teleseismic P wavefield recorded by densely distributed stations. The teleseismic fluctuating wavefield method developed by Ritter et al. (1998) is adopted to deduce statistical parameters of the random mediatype structures underneath the region. Then we model the envelope decay of the Pwave coda based on radiative transfer theory using a Monte Carlo simulation to further confine the scattering parameters. Our results reveal strong scattering with small correlation lengths in the whole crust or lithosphere beneath the study area.
Data set
We select the vertical component waveforms at stations from two networks (KN: Kyrgyz Seismic Telemetry Network; KR: Kyrgyz Digital Network) in the northern Tien Shan (NTS) region. Specifically, 6 stations from the network KR and 11 from the network KN are used together. These stations are uniformly distributed in the study region (Fig. 2a), equipped with threecomponent broadband sensors (Roecker 2001) with the sampling rate of 40 Hz for KN network and 50 Hz for KR network, respectively. Due to the different sensor types in these two networks, all the waveforms are further deconvolved with instrument responses and resampled to 40 samples per second. Then we choose events based on the following criteria: (1) the focal depth should be larger than 110 km to exclude depth phases (e.g., pP, sP) earlier than 25 s after the direct Pwave based on Ak135 model (Kennett et al. 1995); (2) the epicentral distance is between 50° and 80° to ensure a nearly vertical incoming wave front; (3) simple and clear firstarrival P waves are required to avoid complex source processes. After filtering the data with a frequency band of 0.1–8.0 Hz, the waveforms with signaltonoise ratio (SNR) less than 3 are further abandoned. The SNR is estimated by calculating the ratio of rootmeansquare (RMS) amplitudes of teleseismic Pwave and noise 10 s before the P wave. This is to guarantee that the SNR is high enough to characterize the coda decay (Wang and Shearer 2017). Moreover, to obtain the average coherent wavefield, at least 8 recordings should be available for stable stacking results. The distribution for selected events with magnitude between 5.0 and 7.1 from 1994 to 2016 is displayed in Fig. 2b. The parameter information for all used events is listed in Additional file 1: Table S1.
Method
We use both teleseismic fluctuating wavefield method and Monte Carlo simulation approach to extract scattering parameters (the correlation length a and RMS velocity contrast σ) of the random heterogeneity structure underneath the study area. It should be noted that in this study, we hypothetically ignore the scattering effects around the seismic source, since these effects may be weak compared to strong scattering in the lithosphere beneath the stations.
Teleseismic fluctuation wavefield method
To explore the scattering properties of a random medium, we use an approach called teleseismic fluctuation wavefield method (TFWM) (Ritter et al. 1998). This method assumes that the total wavefield (U_{t}) consists of the coherent wavefield (U_{c}) and fluctuating (incoherent) wavefield (U_{f}) after propagating through a random medium (Shapiro and Kneib 1993). We define ε as a measure of the wavefield fluctuations:
where ⟨⟩ denotes a spatial averaging. I_{f} and I_{c} represent the fluctuating and coherent intensities (squared amplitude spectrum), respectively. By assuming a weakfluctuating random medium with a Gaussian or exponential autocorrelation function (Sato 2019) as well as neglecting both backscattering and anelasticity effects, a relationship between ⟨ε^{2}⟩ and scattering parameters based on the Born approximation is derived (Ritter et al. 1998):
where L is the thickness of a scattering layer, ƒ is the frequency and v is the average P velocity in a background model. σ and a are the RMS velocity perturbation and isotropic correlation length, respectively. This equation is only valid under the assumptions akσ^{2} ≪ 1 as well as ka ≥ 1 (k is the wavenumber) (Shapiro and Kneib 1993).
Then we take the natural logarithm of both sides in Eq. (2):
The structural parameter γ can be determined from a linear regression of lefthanded side of Eq. (3) against ƒ^{2} by using the leastsquares method. By applying (3) to all the events and stacking the frequencydependent ln(⟨ε^{2}⟩+1), we can reduce the effects from source time functions and obtain the averaged ⟨γ⟩ value. Then we can determine the parameter aσ^{2} according to L/v^{2} taken from previous studies.
Monte Carlo simulation
To solve the strong tradeoffs in the scattering parameters, we model teleseismic P coda envelopes by using a Monte Carlo seismic phonon algorithm (Shearer and Earle 2004). This method is a powerful tool to simulate scattering processes and has been widely used in both regional and global studies (e.g., Margerin and Nolet 2003; Peng et al. 2008; Mancinelli and Shearer 2013; Wang and Shearer 2017). The details of this approach have been fully described in the previous paper (Shearer and Earle 2008). Here we only discuss some basic points.
This approach is based on the radiative transfer theory (Chandrasekhar 1960), which can describe the spatial–temporal distribution of energy of seismic wave in a scattering medium. In the simulation, the source radiates a large number of energy particles through the seismic velocity model based on ray theory. Whether a particle is scattered or not when hitting a scatterer is determined by the raypath length to a scatterer and scattering probabilities determined by random media models (Shearer and Earle 2004). As in previous studies, the random medium is generally characterized by power spectral density function (PSDF) type, the correlation length a, rootmeansquare (RMS) fractional velocity fluctuation σ and decay order in large wavenumbers (Sato et al. 2012). During the propagation through the model, the energy of particles is reduced due to intrinsic attenuation. In final, the particles reaching the Earth surface are summed up as energy flux in time–distance bins.
For this study, we assume the scattering layer is described as a random medium characterized by an exponential autocorrelation function and the density versus velocity fluctuation scaling factor is 0.8 according to Birch’s law (Birch 1961). Besides, the Q value is initially set to be 800 for the upper mantle. Since we only focus on random heterogeneity structures beneath the stations, we confine all the energy particles to propagate only downward from the source. In this way, we can in general avoid scattered energy from scattering in the lithosphere directly above the source.
Data analysis
We display an example of velocity seismograms from Event 2010.02.15.21.51 in Fig. 3. The total time window is chosen from 10 s before the direct Pwave arrival to about 25 s after the Pwave onset. The upper 12 traces (No. 1–12) show the original teleseismic P wavefield recordings representing the complete wavefield. We further normalize the waveforms to the maximum direct P waves. This normalization process could thus reduce the site amplification effects beneath each individual station (Additional file 1: Fig. S1). Coda waves are clearly visible following the impulsive P wave. In addition, the coda amplitudes are much higher than the noise amplitudes before the Pwave onset. The coherent mean wavefield recorded at the array is shown in trace No. 13, resulting from the stack of the 12 individual waveforms (trace No. 1–12). This stacking procedure can enhance the coherent phases and suppress the scattered phases and noises significantly. Subsequently, the fluctuating wavefield represented by residual seismograms is obtained by subtracting the coherent wavefield (stacked waveform) from individual original recordings (complete wavefield). The subtraction procedure can thus remove signals that are generated in the source region and leave scattered signals behind. Besides, both stacking and subtracting processes can reduce the effects of source time function on the wavefield. The corresponding residual waveforms are shown in traces No. 14–25 with the same amplitude scale and in the order as traces No. 1–12. Compared with original recordings, the residual waveforms mostly contain amplitude fluctuations of scattered phases that are incoherent.
To test whether the later coherent teleseismic phases (e.g., PcP) would emerge in the fluctuating coda wavefield, we further apply the 3rd root stacking method (Muirhead and Datt 1976) to the original waveforms for each event in the vespagram analysis (Davies et al. 1971; Rost and Thomas 2002). An example for Event 2010.02.15.21.51 is shown in Fig. 4. The vespagram is calculated from 2.5 to 8.0 s/deg with a step of 0.1 s/deg. The maximum stacked energy for the P arrival is generated with a slowness value of 5.8 s/deg, whereas the theoretical one is 6.11 s/deg in the AK135 model (Kennett et al. 1995) for this event. The difference between the observed and theoretical Pwave slowness values could possibly be caused by heterogeneous structures beneath the stations. Except for the clearly visible Pwave energy, there are no other strong coherent signals in this vespagram. In addition, the PcP phase with a theoretical value of 4.23 s/deg in the AK135 model is not visible due to its weak amplitude. Therefore, the vespagram analysis demonstrates that the residual seismograms (fluctuating wavefield) in Fig. 3 (traces No. 14–25) mostly consist of incoherent, scattered waves, with the coherent phases being removed. We apply the same procedure to all the selected events and exclude events showing coherent nondirect P phases in the time window of interest. In total, we select 188 events for further analysis. Then the separation of coherent and fluctuating waveforms in the data is used for further extracting property parameters of random media beneath the receivers.
Results
Results from TFWM
We calculate the intensity of the coherent (I_{c}) and fluctuating (I_{f}) wavefield to obtain the ratio value ⟨ε^{2}⟩ in the frequency domain. I_{c} is obtained by calculating the squared amplitude spectrum of the stacked waveform, whereas I_{f} is determined by stacking the amplitude spectrum of all residual waveforms. The plot is displayed in Fig. 5 for the event in Fig. 3. For frequencies lower than ~ 1.0 Hz, the intensity I_{c} is clearly larger than the intensity I_{f} (Fig. 5a). This means that the main energy of the incoming wavefield U_{c} is concentrated in this frequency range. However, for frequencies higher than about 1.5 Hz, the fluctuating wavefield dominates over the coherent wavefield. The logarithmic quotient ⟨ε^{2}⟩ against frequency is shown in Fig. 5b. It can be observed that, from 0.3 to 2.5 Hz, the value ln(ε^{2}) increases continuously, implying the scattering intensity increases. However, for frequencies larger than 2.5 Hz, the value of ln(ε^{2}) remains almost constant, due to the intensity I_{c} reaching the level of the background noise (Ritter et al. 1998). This can be observed from the filtered seismograms in the bottom right corner of Fig. 5b. In the frequency band of 3.0–8.0 Hz, the coherent seismic signals are strongly contaminated by the background noise.
The similar feature of the frequencydependent ln(ε^{2}) for all the events is presented in Fig. 6. The stacked curve represents the average properties of random structure beneath the stations in the NTS. We find that the value of ln(ε^{2}) is negative (I_{f} < I_{c}) below ~1.2 Hz, implying that the lowfrequency content of teleseismic wavefield is mainly affected by relatively weak scattering (Ritter et al. 1998). In comparison, the ln(ε^{2}) value is positive between 1.2 and 3.0 Hz, indicating a gradually strong fluctuation regime in this frequency band. The relationship between the scattering strength and frequency possibly indicates the presence of multiscale scattering heterogeneities. In addition, the frequencydependent scattering strength is important for us to further understand the characteristic of seismic attenuation caused by scattering (Shapiro and Kneib 1993). This is, however, beyond the scope of this study.
We choose the frequency range of 0.3–2.5 Hz to determine the parameter γ using a quadratic leastsquares fitting for Eq. (3). Figure 7 shows the fit of ln(ε^{2} + 1) for the single event in Fig. 3 and fit of the stacked ln(ε^{2} + 1) for all the events, respectively. The range of γ values for all events is between 0.16 and 0.67 Hz^{−2}, with an average of γ = 0.37 ± 0.12 Hz^{−2}. In comparison, the averaged value ⟨γ⟩ derived from the stacked curves of ln(ε^{2} + 1) against ƒ^{2} by the leastsquares fit is 0.36 Hz^{−2} (Fig. 7b). The consistence of these two results and the small variation of γ indicate that the obtained parameter is very stable in the analysis.
The extreme and average values of γ are further used to estimate the scattering characteristics σ^{2}a according to the presumed quantity L/v^{2} taken from previous studies (e.g., Roecker et al. 1993; Vinnik et al. 2004; Kumar et al. 2005). For this study region, we test four different scattering layers: L = 15 km, L = 55 km, L = 75 km and L = 130 km representing the upper crust, whole crust, lower lithosphere and whole lithosphere, respectively. The thicknesses and average velocities are listed in Table 1. We constrain the parameter σ to be less than 9%, considering that only small velocity perturbations are dominant in the lithosphere (Levander et al. 1994; Sobolev et al. 1997).
We display the curves of quantity σ^{2}a against L/v^{2} in Fig. 8. The extreme values of γ = 0.16 and 0.67 Hz^{−2} are shown as two boundary curves to constrain the uncertainties of scattering parameters σ^{2}a for fixed L/v^{2} values. For example, if the fluctuating waves following the direct Pwave are generated only in the whole crust (L/v^{2} = 1.3303), then the quantity σ^{2}a ranges from 0.00152 to 0.00638. Supposing the velocity variation in the crust beneath the NTS is 5%, the isotropic correlation length is then between 0.6 and 2.5 km. We list a range of correlation lengths according to different RMS velocity perturbations for three γ values in Table 2. In this study, the wavenumber k is between 0.3 and 2.6 km^{−1}, given the seismic wavelength in our data ranges approximately from 2.4 to 24 km (corresponding to the frequency band 0.3–2.5 Hz). Since all the σ^{2}a values are less than 0.021 km, the condition akσ^{2} ≪ 1 is thus satisfied and ka ≥ 1 is valid if a is approximately larger than 0.8 km with the dominant frequency of about 1.5 Hz.
Results from envelope modeling
To further resolve the tradeoffs for parameters a and σ, we model the temporal decay of the Pwave coda using the Monte Carlo simulation. We adopt the envelopestacking method (e.g., Shearer and Earle 2008) to stack the data, which ignores the phase information and only considers the amplitude in the seismograms. Prior to stacking, the seismograms are further filtered at 0.3–2.5 Hz with a zerophase thirdorder Butterworth filter. Envelopes of the seismograms are computed and aligned on the Pwave arrival and binned at 1.0° intervals in epicentral distance. The stacking process can further average out the focal mechanism effects by using many earthquakes. Thus we assume an isotropic point source at the 300 km depth for simplicity in our synthetic model. The frequency for synthetic model is set to 1.5 Hz, which is approximately the dominant frequency of the bandfiltered data. We then model the stacked data according to the correlation lengths and RMS velocity perturbations in Table 2.
The comparisons between the stacked data and synthetics for four scattering layers are shown in Fig. 9. It can be seen in Table 2 that small velocity perturbations (1%) would result in largesize scattering heterogeneities that are huge compared with the scattering layer and unrealistic (Ritter et al. 1998). Therefore, we only calculate the synthetics for models with σ = 3%, 5%, 7%, 9% and the corresponding a values. If the scattering is restricted only in the upper crust (L = 15 km), we find that synthetics from all upper crustal models cannot fit the stacked data. The amplitudes of scattered waves at short lapse times are all larger than those of the stacked data. The reason is probably that the mean freepath length (defined as inverse of total scattering coefficient in the inhomogeneous medium) is relatively large compared to the thin scattering layer. In such a case, the incident waves would interact with only a few scatterers, resulting in shortduration, but strong scattered wavefield. In comparison, for scattering existing in the whole crust (L = 55 km), the model with σ = 9% and a = 0.4 km can provide a reasonable fit to the stacked observations. A similar model (σ = 9% and a = 0.5 km) is found to match the stacked data, assuming the scattering is confined in the lower lithosphere (L = 75 km). In addition, if the scattering occurs in the whole lithosphere (L = 130 km), models with σ = 7% and a = 0.4 km can roughly fit the data stacks. In contrast, lithospheric scattering models with σ = 9% would underestimate the stacked data. Although the condition ka ≥ 1 is not strictly satisfied if a is on the order of 0.4 km, we attribute this inconsistence to the Born approximation in the TFWM, whereas the Monte Carlo approach can accommodate multiple scattering naturally.
We note that scattering with different velocity contrasts and correlation lengths in two or more layers beneath the receivers can also explain the stacked wavefield fluctuations. Such models, however, cannot be determined uniquely by the abovementioned TFWM. Moreover, it is impractical to perform a detailed grid search to perfectly model the data because there are such many free parameters to be constrained. Therefore, in this study, our main goal is to find model parameters obtained from TFWM that can produce a reasonable fit to the stacked observations.
Discussion
Factors affecting the simulations
Initially, we set the synthetic frequency value to be 1.5 Hz for the simulation. We notice that this frequency parameter can affect the P–P scattering coefficient in a very complicated way (see 4.64a in Sato et al. 2012), which changes the P coda envelope in our case. To test the effect of this factor on the synthetics, we run simulations for same scattering models using three different values of frequency and show the results in Fig. 10. The amplitudes of coda that is a few seconds later than the direct P waves increase with the frequency when the correlation length is on the order of ~ 0.4 km. Because the P–P scattering coefficient is fourthpower dependent on frequency, higher frequency values can result in larger amplitude of coda at short lapse times for teleseismic forward scattering. Future studies should involve studying the frequencydependent relation for decay of coda wave.
Besides the frequency parameter, both the Q value and velocity–density variation ratio in the lithosphere are initially fixed in the simulation, we also need test how these two parameters would affect our preferred scattering models. Firstly, we simulate the Pwave coda envelope for different Q values in the upper mantle (Q = 800 and 100). Results in Fig. 11a show that the damping by attenuation plays an insignificant role on the coda envelope. This is possibly due to the coda decay being dominated by the leaking of scattered energy into the lithosphere (Korn 1993). At the same time, this test confirms the assumption that anelasticity is negligible in the TFWM is valid. Secondly, we further test the effect of velocity–density variation scaling ratio on our synthetics. We recompute the synthetics for the scattering models with no density variations (the ratio value is 0) and find that the synthetics are not affected significantly (Fig. 11b). Because this ratio plays a major role in backscattering (Mancinelli and Shearer 2013), while the Pwave coda in our case are mostly generated due to nearforward scattering.
Comparisons with previous scattering studies
The observations of teleseismic P coda in our data provide direct evidence for smallscale scattering heterogeneities in the northern Tien Shan region. We further compare the scattering properties of random heterogeneities beneath our study area with results in other regions over the globe using Pwave data. By analyzing the teleseismic P coda, Aki (1973) estimated the lithospheric heterogeneity to be ~ 4% with a = 10 km at about 0.5 Hz in Montana. Using NORSAR array data, Flatté and Wu (1988) determined the statistical distribution of heterogeneities with RMS velocity variations of 1–4%. Similarly, random media with comparable RMS velocity variations are also detected in the southern California (Powell and Meltzer 1984) and southwestern Japan (Kobayashi et al. 2015; Emoto et al. 2017).
Based on the same TFWM, similar studies have revealed scattering heterogeneities with 1–7% Pwave velocity perturbations and correlation lengths ranging from 0.6 to 16 km in the whole crust or lithosphere of French Massif Central (Ritter et al. 1998), northern and central Europe (Hock et al. 2004), southwest Germany (Rothert and Ritter 2000), middle (Shen and Ritter 2010), northeast (Shen et al. 2010) and east China (Fan et al. 2017). On a global basis, previous studies have further revealed significant regional variations in random heterogeneity of the lithosphere and the relation between the derived scattering parameters and the different geological structures (Kubanza et al. 2006). By assuming a = 5 km for all frequency bands, Kubanza et al. (2007) estimated σ to be 2–4% for random heterogeneities within the lithosphere in the stable continents while 5–10% in the tectonically active regions (e.g., island arcs, collision zones or subduction zones). These scattering heterogeneities in the lithosphere are proposed to originate from subducted oceanic crust or magmatic intrusions due to the related asthenospheric upwelling (Nishimura 2002; Rothert and Ritter 2000).
It should be noted that the value of correlation length a in our study is approximately the lowermost limit of previous results (also see Shearer 2015 for a review). Our simulations further show that models with larger values of a (e.g., 1.5 km) tend to overpredict amplitudes of P coda waves at small lapse times at all distances (Fig. 12). It thus suggests that the length scales of these random heterogeneities in the lithosphere are quite small (Wu and Aki 1985). Besides, the value of a in our study is generally comparable with isotropic (1.0 km) (e.g., Kobayashi et al. 2015; Yoshimoto et al. 2015) and vertical correlation length (0.5 km) (Tittgemeyer et al. 1996; Ryberg et al. 1995, 2000) inferred from modeling of Pwave scattering.
Smallscale scattering heterogeneities
Our preferred model for explaining the observed Pwave coda is a random medium characterized by an exponential autocorrelation function with a layer thickness of ~ 55 km < L < 130 km, RMS velocity perturbations of 6–9% and correlation lengths on the order of 0.4 km. The large values of RMS velocity perturbation σ indicate that there are very strong scattering heterogeneities in the whole crust or lithosphere beneath the northern Tien Shan, suggesting that this is a tectonically active region.
The strong scattering inhomogeneities beneath the northern Tien Shan are approximately located in prominent lowvelocity zones in the middlelower crust and upper mantle revealed by seismic tomography studies (e.g., Omuralieva et al. 2009; Sychev et al. 2018; Lü et al. 2019). Some of lowvelocity anomalies can extend down to more than 150 km in the upper mantle (Roecker et al. 1993; Lei and Zhao 2007). The large Pwave velocity decrease in these anomalies could be likely caused by increased temperature, suggesting the existence of partial melting (Lei and Zhao 2007). A plausible explanation is that a smallscale convection or an intrusion of ascending hot mantle materials (e.g., Makeyava et al. 1992; Wolfe and Vernon 1998) are possibly trigged by the underthrusting of the Tarim and Kazakh lithosphere. Some segments of the thickened lithospheres can break off and sink into the deep mantle due to gravitational instability (Roecker et al. 1993; Lei and Zhao 2007). This would likely cause an upwelling mantle flow supplying a large amount of melts (Omuralieva et al. 2009). These melts would be formed in isolated pockets and show low resistivity in the upper mantle in the magnetotelluric study (Bielinski et al. 2003). The hot upwelling could be further confirmed by a thin mantle transition zone beneath the northern Tien Shan (Tian et al. 2010; Yu et al. 2017). A portion of these upwelling materials may further penetrate into the lithospheric mantle and lower crust to cause metasomatism as well as partial melting (Fig. 13). We speculate that such upwelling materials (melt pockets) are the origin of the strong smallscale velocity heterogeneities beneath the northern Tien Shan. Similarly, strong scattering heterogeneities (7–9%) within lowvelocity zones are also proposed to be related with random distribution of fluids/melts supplied by the dehydration of subducting oceanic crust underneath Japan (Takahashi et al. 2009; Carcolé and Sato 2010; Takemura and Yoshimoto 2014). When teleseismic P waves propagate through the lithosphere beneath the NTS, these melt pockets functioning as smallscale scatterers can scatter the incident waves, generating the fluctuating Pwave coda in the observations. However, due to the smallscale lengths, tomography studies can only image clusters of melt pockets as lowvelocity anomalies.
In the present study, we assume the scattering only exists above the lithospheric depth. However, we cannot exclude the possibility that the smallscale scattering heterogeneities in the mantle deeper than the lithosphere can also contribute to the Pwave coda. If this is the case, the scattering strength in the lithosphere would be weaker than the present results. Because the values of scattering thickness L cannot be obtained without knowledge from other studies, we can possibly optimize our results by combining results based on the energyflux model where L can be roughly estimated (e.g., Korn 1997; Hock et al. 2004). Thus more seismic data containing threecomponent waveforms are needed to compare results from these two approaches. Although coda waves can be strongly excited by scattering due to surface topography (e.g., Imperatori and Mai 2015; Takemura et al. 2015; Hartzell et al. 2017), the relative contribution of topographic scattering in the highfrequency wavefield is only approximately 12% (Takemura et al. 2015) in local areas. However, scattering due to surface topography cannot be completely ruled out on generating the teleseismic Pwave coda, a more realistic numerical hybrid method (Monteiller et al. 2013) is needed to model these effects in the future research.
Conclusion
The teleseismic P wavefield provides a useful tool for characterizing the scattering properties beneath the stations. By using the Pwave coda from teleseismic events, we explore smallscale scattering heterogeneities underneath the northern Tien Shan. We obtain the statistical parameters of the random heterogeneities by analyzing the coherent and fluctuating P wavefield. To resolve the tradeoffs in the scattering parameters, we further constrain the correlation lengths and velocity perturbations using the Monte Carlo simulation method. A crustal and/or lithospheric scattering model with velocity perturbations of 6–9% and isotropic correlation lengths on the order of 0.4 km is derived from the Pwave coda wavefield. The strong scattering is related with lowvelocity anomalies in the lithosphere and likely to be hot upwelling asthenospheric materials in the form of melt pockets.
Availability of data and materials
Teleseismic data supporting the results of the present paper are available through the Data Management Center (https://ds.iris.edu/ds/nodes/dmc/).
Abbreviations
 KN:

Kyrgyz Seismic Telemetry Network
 KR:

Kyrgyz Digital Network
 NTS:

northern Tien Shan
 PSDF:

power spectral density function
 RMS:

root mean square
 RTT:

radiative transfer theory
 SNR:

signaltonoise ratio
 TFWM:

teleseismic fluctuation wavefield method
References
Abdrakhmatov KY, Aldazhanov SA, Hager BH, Hamburger MW, Herring TA, Kalabaev KB, Makarov VI, Molnar P, Panasyuk SV, Prilepin MT, Reilinger RE, Sadybakasov IS, Souter BJ, Trapeznikov YA, Tsurkov VY, Zubovich AV (1996) Relatively recent construction of the Tien Shan inferred from GPS measurements of presentday crustal deformation rates. Nature 384:450–453
Aki K (1969) Analysis of the seismic coda of local earthquakes as scattered waves. J Geophys Res 74:615–631
Aki K (1973) Scattering of waves under the Montana Lasa. J Geophys Res 78:1334–1346
Aki K, Chouet B (1975) Origin of coda waves: source, attenuation, and scattering effects. J Geophys Res 80:3322–3342
Bannister SC, Husebye ES, Ruud BO (1990) Teleseismic P coda analysed by threecomponent and array techniques: deterministic location of topographic PtoRg scattering near the NORESS array. Bull Seismol Soc Am 80:1969–1986
Beyreuther M, Barsch R, Krischer L, Megies T, Behr Y, Wassermann J (2010) ObsPy: a python toolbox for seismology. Seismol Res Lett 81:530–533
Bielinski RA, Park SK, Rybin A, Batalev V, Jun S, Sears C (2003) Lithospheric heterogeneity in the Kyrgyz Tien Shan imaged by magnetotelluric studies. Geophys Res Lett 30:1806
Birch F (1961) Composition of the earth’s mantle. Geophys J R Astron Soc 4:295–311
Burtman VS (2015) Tectonics and geodynamics of the Tian Shan in the Middle and Late Paleozoic. Geotectonics 49:302–319
Carcolé E, Sato H (2010) Spatial distribution of scattering loss and intrinsic absorption of shortperiod S waves in the lithosphere of Japan on the basis of the Multiple Lapse Time Window Analysis of Hinet data. Geophys J Int 180:268–290
Chandrasekhar S (1960) Radiative Transfer. Dover, New York
Davies D, Kelly EJ, Filson JR (1971) Vespa process for analysis of seismic signals. Nat Phys Sci 232:8–13
Emoto K, Sato H (2018) Statistical characteristics of scattered waves in threedimensional random media: comparison of the finite difference simulation and statistical methods. Geophys J Int 215:585–599
Emoto K, Saito T, Shiomi K (2017) Statistical parameters of random heterogeneity estimated by analysing coda waves based on finite difference method. Geophys J Int 211:1575–1584
Eulenfeld T, Wegler U (2017) Crustal intrinsic and scattering attenuation of highfrequency shear waves in the contiguous United States. J Geophys Res Solid Earth 122:4676–4690
Fan XP, He YC, Wang JF, Yang Y (2017) Crust seismic scattering strength below the middlesouth segment of TanchengLujiang fault zone. Chin J Geophys 60:244–253
Flatté SM, Wu RS (1988) Smallscale structure in the lithosphere and asthenosphere deduced from arrival time and amplitude fluctuations at NORSAR. J Geophys Res 93:6601–6614
Frankel A, Clayton RW (1986) Finite difference simulations of seismic scattering: implications for the propagation of shortperiod seismic waves in the crust and models of crustal heterogeneity. J Geophys Res 91:6465–6489
French SW, Romanowicz B (2015) Broad plumes rooted at the base of the Earth’s mantle beneath major hotspots. Nature 525:95–99
Gaebler PJ, Eulenfeld T, Wegler U (2015) Seismic scattering and absorption parameters in the WBohemia/Vogtland region from elastic and acoustic radiative transfer theory. Geophys J Int 203:1471–1481
Gilligan A, Roecker SW, Priestley KF, Nunn C (2014) Shear velocity model for the Kyrgyz Tien Shan from joint inversion of receiver function and surface wave data. Geophys J Int 199:480–498
Goldstein P, Snoke A (2005) “SAC Availability for the IRIS Community”. Incorporated Institutions for Seismology Data Management Center Electronic Newsletter
Gusev AA, Abubakirov IR (1999) Vertical profile of effective turbidity reconstructed from broadening of incoherent bodywave pulsesII. Application to Kamchatka data. Geophys J Int 136:309–323
Hartzell S, Harmsen S, Frankel A (2010) Effects of 3D random correlated velocity perturbations on predicted ground motions. Bull Seismol Soc Am 100:1415–1426
Hartzell S, RamírezGuzmán L, Meremonte M, Leeds A (2017) Ground motion in the presence of complex topography II: earthquake sources and 3D simulations. Bull Seismol Soc Am 107:344–358
Hock S, Korn M, Ritter JRR, Rothert E (2004) Mapping random lithospheric heterogeneities in northern and central Europe. Geophys J Int 157:251–264
Hunter JD (2007) Matplotlib: a 2D graphics environment. Comput Sci Eng 9:90–95
Imperatori W, Mai PM (2013) Broadband nearfield ground motion simulations in 3dimensional scattering media. Geophys J Int 192:725–744
Imperatori W, Mai PM (2015) The role of topography and lateral velocity heterogeneities on nearsource scattering and groundmotion variability. Geophys J Int 202:2163–2181
Kennett BLN, Engdahl ER, Buland R (1995) Constraints on seismic velocities in the Earth from travel times. Geophys J Int 122:108–124
Kobayashi M, Takemura S, Yoshimoto K (2015) Frequency and distance changes in the apparent Pwave radiation pattern: effects of seismic wave scattering in the crust inferred from dense seismic observations and numerical simulations. Geophys J Int 202:1895–1907
Korn M (1993) Determination of sitedependent scattering Q from Pwave coda analysis with an energyflux model. Geophys J Int 113:54–72
Korn M (1997) Modelling the teleseismic P coda envelope: depth dependent scattering and deterministic structure. Phys Earth Planet Int 104:23–36
Kubanza M, Nishimura T, Sato H (2006) Spatial variation of lithospheric heterogeneity on the globe as revealed from transverse amplitudes of shortperiod teleseismic Pwaves. Earth Planets Space 58:45–48. https://doi.org/10.1186/BF03352618
Kubanza M, Nishimura T, Sato H (2007) Evaluation of strength of heterogeneity in the lithosphere from peak amplitude analyses of teleseismic shortperiod vector P waves. Geophys J Int 171:390–398
Kumar P, Yuan X, Kind R, Kosarev G (2005) The lithosphere–asthenosphere boundary in the Tien ShanKarakoram region from S receiver functions: evidence for continental subduction. Geophys Res Lett 32:L07305
Lai Y, Chen L, Wang T, Zhan Z (2019) Mantle transition zone structure beneath Northeast Asia from 2D triplicated waveform modeling: implication for a segmented stagnant slab. J Geophys Res Solid Earth 124:1871–1888
Lei J, Zhao D (2007) Teleseismic P wave tomography and the upper mantle structure of the central Tien Shan orogenic belt. Phys Earth Planet Inter 162:165–185
Levander A, Hobbs RW, Smith SK, England RW, Snyder DB, Holliger K (1994) The crust as a heterogeneous ‘optical’ medium, or ‘crocodiles in the mist’. Tectonophysics 232:281–297
Li Y, Shi L, Gao J (2016) Lithospheric structure across the central Tien Shan constrained by gravity anomalies and joint inversions of receiver function and Rayleigh wave dispersion. J Asian Earth Sci 124:191–203
Li Z, Roecker S, Li Z, Wei B, Wang H, Schelochkov G, Bragin V (2009) Tomographic image of the crust and upper mantle beneath the western Tien Shan from the MANAS broadband deployment: Possible evidence for lithospheric delamination. Tectonophysics 477:49–57
Lü Z, Gao H, Lei J, Yang X, Rathnayaka S, Li C (2019) Crustal and upper mantle structure of the Tien Shan orogenic belt from fullwave ambient noise tomography. J Geophys Res Solid Earth 124:3987–4000
Ma X, Sun X, Thomas C (2019) Localized ultralow velocity zones at the eastern boundary of Pacific LLSVP. Earth Planet Sci Lett 507:40–49
Makeyava I, Vinnik L, Roecker S (1992) Shearwave splitting and smallscale convection in the continental upper mantle. Nature 358:144–147
Mancinelli NJ, Shearer PM (2013) Reconciling discrepancies among estimates of smallscale mantle heterogeneity from PKP precursors. Geophys J Int 195:1721–1729
Margerin L, Nolet G (2003) Multiple scattering of highfrequency seismic waves in the deep earth: modeling and numerical examples. J Geophys Res 108(B5):2234
Monteiller V, Chevrot S, Komatitsch D, Fuji N (2013) A hybrid method to compute shortperiod synthetic seismograms of teleseismic body waves in a 3D regional model. Geophys J Int 192:230–247
Muirhead KJ, Datt R (1976) The Nth root process applied to seismic array data. Geophys J R Astron Soc 47:197–210
Nelson MR, McCaffrey R, Molnar P (1987) Source parameters for 11 earthquakes in the Tien Shan, central Asia, determined by P and SH waveform inversion. J Geophys Res 92:12629–12648
Ni J (1978) Contemporary tectonics in the Tien Shan region. Earth Planet Sci Lett 41:347–354
Nishimura T (2002) Spatial distribution of lateral heterogeneity in the upper mantle around the western Pacific region as inferred from analysis of transverse components of teleseismic Pcoda. Geophys Res Lett 29:521–524
Omuralieva A, Nakajima J, Hasegawa A (2009) Threedimensional seismic velocity structure of the crust beneath the central Tien Shan, Kyrgyzstan: implications for large and smallscale mountain building. Tectonophysics 465:30–44
Oreshin S, Vinnik L, Peregoudov D, Roecker S (2002) Lithosphere and asthenosphere of the Tien Shan imaged by S receiver functions. Geophys Res Lett 29:1191
Peng Z, Koper KD, Vidale JE, Leyton F, Shearer P (2008) Innercore finescale structure from scattered waves recorded by LASA. J Geophys Res 113:B09312
Powell CA, Meltzer AS (1984) Scattering of Pwaves beneath SCARLET in southern California. Geophys Res Lett 11:481–484
Ritter J, Rothert E (2000) Variations of the lithospheric seismic scattering strength below the Massif Central, France and the Frankonian Jura, SE Germany. Tectonophysics 328:297–305
Ritter JRR, Shapiro SA, Schechinger B (1998) Scattering parameters of the lithosphere below the Massif Central, France, from teleseismic wavefield records. Geophys J Int 134:187–198
Roecker S (2001) Constraints on the crust and upper mantle of the Kyrgyz Tien Shan from the preliminary analysis of GHENGIS broadband data. Russ Geol Geophys 42:1554–1565
Roecker SW, Sabitova TM, Vinnik LP, Burmakov YA, Golvanov MI, Mamatkanova R, Munirova L (1993) Threedimensional elastic wave velocity structure of the western and central Tien Shan. J Geophys Res 98:15779–15795
Rost S, Thomas C (2002) Array seismology: methods and applications. Rev Geophys 40:1–27
Rothert E, Ritter JRR (2000) Smallscale heterogeneities below the Graefenberg array, Germany, from seismic wavefield fluctuations of Hindu Kush events. Geophys J Int 140:175–184
Ryberg T, Fuchs K, Egorkin V, Solodilov L (1995) Observation of highfrequency teleseismic Pn waves on the longrange Quartz profile across northern Eurasia. J Geophys Res 100:18151–18163
Ryberg T, Tittgemeyer M, Wenzel F (2000) Finite difference modeling of Pwave scattering in the upper mantle. Geophys J Int 141:787–800
Saito T, Sato H, Ohtake M (2002) Envelope broadening of spherically outgoing waves in threedimensional random media having powerlaw spectra. J Geophys Res 107:1
Sato H (1989) Broadening of seismogram envelopes in the randomly inhomogeneous lithosphere based on the parabolic approximation: southeastern Honshu, Japan. J Geophys Res 94:17735–17747
Sato H (2019) Power spectra of random heterogeneities in the solid earth. Solid Earth 10:275–292
Sato H, Emoto K (2018) Synthesis of a scalar wavelet intensity propagating through von Kármántype random media: radiative transfer theory using the Born and phasescreen approximations. Geophys J Int 215:909–923
Sato H, Fehler MC, Maeda T (2012) Seismic Wave Propagation and Scattering in the Heterogeneous Earth. Springer, New York
Savran WH, Olsen KB (2019) Ground motion simulation and validation of the 2008 Chino Hills earthquake in scattering media. Geophys J Int 219:1836–1850
Scherbaum F, Sato H (1991) Inversion of full seismogram envelopes based on the parabolic approximation: estimation of randomness and attenuation in southeast Honshu, Japan. J Geophys Res 96:2223–2232
Shapiro SA, Kneib G (1993) Seismic attenuation by scattering: theory and numerical results. Geophys J Int 114:373–391
Shearer PM (2015) Deep earth structure: seismic scattering in the deep earth. In: Schubert G (ed) Treatise on geophysics, 2nd edn. Elsevier BV, Amsterdam, pp 759–787
Shearer PM, Earle PS (2004) The global shortperiod wavefield modelled with a Monte Carlo seismic phonon method. Geophys J Int 158:1103–1117
Shearer PM, Earle PS (2008) Observing and modeling elastic scattering in the deep earth. Adv Geophys 50:167–193
Shen XZ, Ritter JRR (2010) Smallscale heterogeneities below the Lanzhou CTBTO seismic array, from seismic wave field fluctuations. J Seismol 14:481–493
Shen XZ, Zhang SZ, Zheng Z, Hao CY (2010) Study on the smallscale heterogeneities below the Hailaer CTBTO seismic array. Chin J Geophys 53:1158–1166 (in Chinese with English abstract)
Sobolev SV, Zeyen H, Granet M, Achauer U, Bauer C, Werling F, Altherr R, Fuchs K (1997) Upper mantle temperatures and lithosphereasthenosphere system beneath the French Massif Central constrained by seismic, gravity, petrologic and thermal observations. Tectonophysics 275:143–164
Sychev IV, Koulakov I, Sycheva NA, Koptev A, Medved I, El Khrepy S, AlArifi N (2018) Collisional processes in the crust of the northern Tien Shan inferred from velocity and attenuation tomography studies. J Geophys Res Solid Earth 123:1752–1769
Takahashi T (2012) Threedimensional attenuation structure of intrinsic absorption and wideangle scattering of S waves in northeastern Japan. Geophys J Int 189:1667–1680
Takahashi T, Sato H, Nishimura T, Obara K (2009) Tomographic inversion of the peak delay times to reveal random velocity fluctuations in the lithosphere: method and application to northeastern Japan. Geophys J Int 178:1437–1455
Takemura S, Yoshimoto K (2014) Strong seismic wave scattering in the lowvelocity anomaly associated with subduction of oceanic plate. Geophys J Int 197:1016–1032
Takemura S, Furumura T, Maeda T (2015) Scattering of highfrequency seismic waves caused by irregular surface topography and smallscale velocity inhomogeneity. Geophys J Int 201:459–474
Takemura S, Kobayashi M, Yoshimoto K (2017) Highfrequency seismic wave propagation within the heterogeneous crust: effects of seismic scattering and intrinsic attenuation on ground motion modelling. Geophys J Int 210:1806–1822
Tian X, Zhao D, Zhang H, Tian Y, Zhang ZJ (2010) Mantle transition zone topography and structure beneath the central Tien Shan orogenic belt. J Geophys Res 115:B10308
Tittgemeyer MF, Wenzel F, Fuchs K, Ryberg T (1996) Wave propagation in a multiplescattering upper mantle: observations and modeling. Geophys J Int 127:492–502
Tkalčić H, Young MK, Muir JB, Davies R, Mattesini M (2015) Strong, multiscale heterogeneity in earth’s lowermost mantle. Sci Rep 5:18416
Vinnik LP, Reigber C, Aleshin IM, Kosarev GL, Kaban MK, Oreshin SI, Roecker SW (2004) Receiver function tomography of the central Tien Shan. Earth Planet Sci Lett 225:131–146
Wang W, Shearer PM (2017) Using direct and coda wave envelopes to resolve the scattering and intrinsic attenuation structure of Southern California. J Geophys Res Solid Earth 122:7236–7251
Wegler U, Korn M, Przybilla J (2006) Modeling full seismogram envelopes using radiative transfer theory with Born scattering coefficients. Pure Appl Geophys 163:503–531
Wessel P, Smith WHF, Scharroo R, Luis J, Wobbe F (2013) Generic mapping tools: improved version released. EOS Trans Am Geophys Union 94:409–410
Wolfe C, Vernon F (1998) Shearwave splitting at central Tien Shan: evidence for rapid variation of anisotropic patterns. Geophys Res Lett 25:1217–1220
Wu RS (1985) Multiple scattering and energy transfer of seismic waves separation of scattering effect from intrinsic attenuation I. Theoretical modelling. Geophys J Int 82:57–80
Wu R, Aki K (1985) Elastic wave scattering by a random medium and the smallscale inhomogeneities in the lithosphere. J Geophys Res 90:10261–10273
Yoshimoto K, Takemura S, Kobayashi M (2015) Application of scattering theory to Pwave amplitude fluctuations in the crust. Earth Planets Space 67:199. https://doi.org/10.1186/s4062301503660
Yu Y, Zhao D, Lei J (2017) Mantle transition zone discontinuities beneath the Tien Shan. Geophys J Int 211:80–92
Zabelina IV, Koulakov IYu, Buslov MM (2013) Deep mechanisms in the Kyrgyz Tien Shan orogen (from results of seismic tomography). Russ Geol Geophys 54:695–706
Zeng Y, Su F, Aki K (1991) Scattering wave energy propagation in a random isotropic scattering medium: 1. Theory. J Geophys Res 96:607–619
Acknowledgements
We would like to thank the editor Junichi Nakajima and two anonymous reviewers for their constructive comments to improve this manuscript. The present study is funded by the NSFC project (No. 41803034). We downloaded data from IRIS data repositories (NSF grant EAR1261681). SAC (Goldstein and Snoke 2005) and ObsPy (Beyreuther et al. 2010) are used to analyze and process the seismograms. The figures are made using GMT5 (Wessel et al. 2013) and Matplotlib (Hunter 2007).
Funding
This study is supported by the NSFC project (No. 41803034) from National Natural Science Foundation of China.
Author information
Affiliations
Contributions
XM and ZH carried out the research. XM analyzed the seismic data and performed the simulation. XM and ZH wrote the manuscript. Both authors read and approved the final manuscript.
Corresponding author
Ethics declarations
Ethics approval and consent to participate
Not applicable.
Consent for publication
Not applicable.
Competing interests
The authors declare that they have no competing interests.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Ma, X., Huang, Z. Smallscale scattering heterogeneities beneath the northern Tien Shan from the teleseismic P wavefield. Earth Planets Space 72, 13 (2020). https://doi.org/10.1186/s4062302011361
Received:
Accepted:
Published:
Keywords
 Pwave coda
 Smallscale scattering heterogeneities
 Random media
 Monte Carlo simulation
 Melt pockets
 Upwelling mantle materials