The deployment of a dense seismic array of portable broadband stations has presented a number of imaging opportunities using scattered teleseismic waves. Interferometric seismic imaging (ISI) of surface-related multiple reflections extracted from cross-correlations of teleseismic waves among pairs of receiver stations was investigated for possible applications and compared to receiver function(RF) method. Synthetic seismograms simulated by the elastic pseudospectral method for a simple 2-D crustal model demonstrate the potential imaging capabilities of ISI for the Moho structure with high spatial resolution. ISI has also been applied to teleseismic data from dense-array experiments conducted at the Northern Fossa Magna Basin in central Japan. The results indicate that the Moho phase, with positive polarity at a depth of 38–40 km in the ISI profile, is consistent with the lower crustal structure estimated by RF imaging.
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 For horizontally layered media, Claerbout  formulated a relation between the reflection response and the autocorrelation of the transmission response. In recent years, the correlation-type reciprocity theorem for one-way wave fields has been used to derive relations between the reflection and transmission responses of an arbitrary 3-D inhomogeneous medium with distributed sources below irregular layers [Wapenaar et al., 2004]. This concept is equivalent to the extraction of pseudo-shot records related to surface-related multiples at all receiver stations. The Green's function between two stations for any inhomogeneous medium can be retrieved from the causal part of the cross-correlation of seismograms recorded at these two stations on the free surface. Schuster et al.  extended the derivations of the Green's function to include an imaging step after the cross-correlations and termed the method “interferometric seismic imaging (ISI)”. They showed the application of ISI method to various source-receiver geometries, including teleseismic receiver function (RF) imaging.
 Teleseismic receiver functions are broadly used for the imaging of Moho and mantle discontinuities. The fundamental analysis of RF imaging focused on the estimation of one-dimensional velocity structures for solitary stations [e.g., Langston, 1979]. With improved accessibility to a larger number of three-component broadband sensors, using direct converted P-to-S(Ps) phases in teleseismic data, common-conversion-point (CCP) stacking and Kirchhoff depth/time migration, which are routinely applied in reflection seismology, have become popular methods for detailed imaging of the continental lithosphere. Over the past few years, it has been recognized that RF migration for surface-related multiples, combined with migration for the direct Ps phase, reduces the artifacts due to uneven data coverage and reverberation effects in sedimentary basins [e.g., Wilson and Aster, 2005].
 In teleseismic records, first-order surface-related multiples emanate from direct P waves or converted Ps waves that reflect off the free surface and propagate downward to reflect from the crustal layer interfaces. In this paper, the potential imaging capabilities of the ISI approach to teleseismic data was investigated by first applying it to synthetic seismograms for a 2-D crustal model and then applying it to teleseismic records from dense-array experiments conducted at the Northern Fossa Magna Basin, central Japan.
2. Imaging of Teleseismic Wave
 Extraction of pseudo-shot records from teleseismic data observed at a dense seismic array can be realized by cross-correlation of the seismic traces recorded at each station. Figure 1 shows the schematic explanation of seismic interferometry for teleseismic coda waves, where a direct-wave term is explicitly given for trace A and a multiple-reflection term is explicitly given for trace B. Cross-correlation of the two teleseismic traces at surface stations A and B yield seismic trace with kinematics that are equivalent to that of the primary reflection generated by a pseudo source at station A and recorded by station B. It can be seen from Figure 1 that the cross-correlation of trace A with trace B will annihilate the common-phase term of the directly transmitted wave TcA. The pseudo-shot records obtained by cross-correlating all other traces inherently realizes symmetric shot-receiver sampling [Vermeer, 1991], and prevents irregularities arising from offset distributions in common-mid-point ensembles. Therefore, standard-processing sequences including velocity analysis and prestack time/depth migration, which are extensively used in exploration seismology, can be applied to pseudo-shot records of teleseismic coda waves. For interferometric imaging of teleseismic waves incorporating plane waves and horizontal interfaces, the pseudo-shot records are classified into the following two categories; symmetric P-P or S-S reflections (Type-A) and asymmetric P-S or S-P reflections (Type-B). P-P, S-S, P-S and S-P reflections indicate the extracted first-order backscattering modes after cross-correlation. For Type-A, the input data is assumed to be surface-related P-wave multiples (PpPp or PsPp) or S-wave multiples (PpSs or PsSs), which are sorted into symmetric common-mid-point (CMP) geometries after cross-correlation. On the other hand, for Type-B, the input data is assumed to be surface-related P-to-S converted multiples (PpPs or PsPs) or S-to-P converted multiples (PpSp or PsSp), which are sorted into asymmetric CCP geometries after cross-correlation. Here, for example, the surface-related multiple PpPs is P-to-S backscattered phase of incoming refracted P-to-P(Pp) wave at a discontinuity. Other multiple phases are defined in the same manner as PpPs.
 The fundamental processing steps for RF analysis of teleseismic waves are spectral deconvolution for the removal of source time function and near-source structural effects, moveout correction, CCP binning and stacking. On the other hand, the processing procedure for ISI includes geometry application, gain recovery, predictive deconvolution, normal moveout correction, CMP/CCP stacking and signal enhancement based on Karhunen-Loeve (K-L) or Frequency-Space (F-X) filtering, which is relatively simple and the same as that used in exploration seismology. Although the CMP/CCP binning and stacking methods are easily applied and transform the teleseismic data into offset and time domains, it is not necessarily appropriate for scattered energy and surface-related multiples. Seismic migration can produce structural images that are properly corrected for wave-propagation effects due to lateral heterogeneity, and focus of the scattered energy.
 For RF analysis, prestack depth migration operator that back-propagates the surface response to subsurface imaging point is defined for each plane-wave incidence with constraints on the constant time difference between the scattered Ps wave from the subsurface imaging point and the direct P wave from the same wavefront that passes through the imaging point. Recent efforts to apply seismic migration in RF analysis have included both poststack [Ryberg and Weber, 2000; Chen et al., 2005] and prestack algorithms [Sheehan et al., 2000; Poppeliers and Pavlis, 2003; Morozov and Dueker, 2003; Wilson et al., 2003]. On the other hand, for ISI, the prestack depth migration operator is defined with constraints on the constant traveltime from the pseudo source to the receiver via subsurface imaging points. The traveltime is calculated based on the finite-difference eikonal solver or ray tracing for the interval velocity model.
3. Synthetic Examples
 In order to demonstrate the potential imaging capabilities of ISI, we calculated synthetic seismograms for a 2-D crustal model with an assumed Moho step using the elastic pseudospectral method. The model structure, with P-wave and S-wave velocity, and density is shown in Figure 2a, and is defined over a 250 km × 500 km grid which is discretized at 1.0 km intervals. The receiver stations were evenly distributed on the surface over a horizontal range of 480 km and the station interval was 1.0 km. Fifteen earthquakes were simulated, and were characterized by plane P-waves with ray parameters from 0.048 to 0.074 s/km, illuminating this region from the lower left (epicentral distances from 23 to 80 degrees). The source signature was a 0.4–0.6–1.0–1.2 Hz Ormsby wavelet.
 Pseudo-shot records of symmetric P-P reflections are generated by cross-correlating one seismic trace with other traces in the vertical component. In the same manner as P-P wave, pseudo-shot records of symmetric S-S reflections are generated by cross-correlating one seismic trace with other traces in the radial component. On the other hand, pseudo-shot records of asymmetric P-S and S-P reflections are generated by cross-correlating vertical components with radial components. The number of pseudo-shot records is 480 for each of the P-P, S-S, P-S and S-P reflections. The direct Pp phase in the radial component was muted before cross-correlation. Geometrical spreading compensation, band-pass filtering, and zero-phase deconvolution, which are routinely used in reflection seismology, are applied to the pseudo-shot records before prestack depth migration. Figures 2b and 2c show depth migrated sections for synthetic P-P wave and S-S wave pseudo-shot records, respectively. Intermediate gathers before the final profiling of P-P wave are displayed in Figure S1. Figure 2d shows the stacked profile of separately depth migrated P-S and S-P modes. The true reflectors in ISI profiles are degraded by interference from spurious events created by second-order multiples and the leakage of P-wave into radial component and that of S-wave into vertical component. Theoretically, three-component measurements including various types of backscattered waves should be decomposed into one-way P- and S-waves before cross-correlation. However, it is expected that teleseismic data from different epicentral distances and the azimuth will suppress migration artifacts and spurious events, which are especially notable in the S-S wave section. Another approach, used to reduce the spurious events, is the stacking of all contributions of surface-related P-P, S-S, P-S and S-P multiples. Figure 2e shows a stacked profile of separately depth migrated P-P, S-S, P-S and S-P images with spectral balancing before summation. This multimode method substantially improves the resolution of the ISI profile with less spurious events and imaging artifacts.
 To compare the prestack migrated profile from ISI with that from the RF analysis, we applied prestack depth migration for receiver functions after spectral deconvolution. Figure 2f shows the depth migrated sections obtained from the standard Ps receiver functions containing the contribution of 15 earthquakes. Figure 2g shows the multimode RF profile of Ps+PpPs-PsPs-PpSs images estimated from prestack Kirchhoff depth migration. The numerical modeling results show that the reflector positions of the Moho-offset structure can be accurately reconstructed by the prestack depth migrated sections via ISI in comparison with the result from multimode RF imaging. The migration velocity profile for ISI and RF imaging was the true 2D velocity model used to generate the synthetic data.
4. Applications to Field Data
 In order to demonstrate the potential imaging capabilities of ISI for field data, we used the teleseismic data observed across the Itoigawa-Shizuoka Tectonic Line (ISTL), which bounds the western part of the northern Fossa Magna basin in central Japan. The northern Fossa Magna is a sedimentary basin that formed as a back-arc rift during the final stage of the opening of the Sea of Japan and has undergone convergence since the late Neogene. Seismic reflection and wide-angle reflection profiling were carried out across the ISTL active fault system. Along the reflection survey line, a dense seismic array with 60 short-period sensors was deployed for teleseismic and local-earthquake observation [Kurashimo and Hirata, 2004]. Figure 3a depicts the regional and local maps showing the location of the seismic array stations across the northern part of ISTL. The results of reflection and refraction/wide-angle reflection profiling undertaken across the northern part of the ISTL are summarized by Sato et al. [2004a]. From September to November, 2002, portable recorders with 1.0 Hz three-component seismometers were deployed along a 60.0 km line resulting in 60 locations with 0.9–1.2 km receiver intervals. For the RF analysis, 59 earthquakes were used, which ranged in epicentral distance from 25 to 80 degrees and 5.7 to 7.0 in magnitude. On the other hand, for the ISI, 10 relatively large earthquakes with magnitudes of 6.2 to 7.0 were used that included first-order surface-related multiple reflections in the time window of the coda waves. The cross-correlation window length for ISI was 160 s.
 For ISI, first-order free-surface P-wave multiples in the vertical component, were converted to pseudo-P-wave shot records after cross-correlating neighboring traces. Standard pre-processing sequences, including gain compensation, shot-consistent predictive deconvolution, and frequency-space prediction filtering for signal enhancement, were applied to the pseudo-P-wave shot records. The average operator for predictive deconvolution was designed for each earthquake event based on the minimum-phase assumption for the earthquake source-time function. The final profiles for the ISI of the pseudo-P wave were then obtained from depth migration or common-midpoint stacking followed by depth conversion. Figures 3b and 3d show the common-midpoint stacked profile and depth migrated profile for pseudo-P waves, respectively.
 We have estimated receiver functions from spectral deconvolution. All receiver functions are then moveout corrected to the horizontal slowness p = 0, and sorted into different conversion-point bins, with respect to each depth, to achieve the optimum focusing effect. CCP zero-offset profiles are obtained by stacking the receiver functions after depth-variant CCP sorting. In addition to the CCP zero-offset profiles, depth migrated profiles of receiver functions are generated. For each station ray tracing was applied to obtain direct Ps converted arrivals from all possible scattering points within the model space. The RF amplitudes are then scaled by an obliquity factor, geometrical spreading factor, and S-wave point scattering patterns, and are then summed onto an output migration grid based on the Kirchhoff integral. Figures 3c and 3e show the CCP stacked profile and depth migrated profile, respectively.
 For the crustal velocity model used in ISI and Ps RF imaging along the survey line, we referred to the P-wave velocity and Vp/Vs distributions estimated by the traveltime inversion of local earthquakes [Kurashimo and Hirata, 2004] and the detailed P-wave velocity derived from the refraction and wide-angle reflection profiling [Sato et al., 2004b].
 The phase with positive polarity at the depth of 37–40 km in both the ISI and Ps RF images can be interpreted as that of the Moho. This result is consistent with that obtained from the global RF analysis around the central Honshu island, as reported by Yoshimoto et al. . The coherent reflections of a laminated lower crust detected from a wide-angle reflection profile can be recognized as terminating at approximately 12–13 s (two-way traveltime) [Sato et al., 2004b], which supports the result that the depth of the Moho estimated by ISI analysis is approximately 40 km. For the depth conversion of the wide-angle reflection profile, we assumed the same crustal velocity model used in ISI and RF imaging. The seismic profiles from both ISI and RF show that the Moho topography has a lateral variation and discontinuity in the survey area between the ISTL and the western part of the Central Uplift Zone. From a multidisciplinary active and passive geophysical survey, Sato et al. [2004a] reported that low Vp, low Vp/Vs and low resistivity zones were observed beneath the folded zone of the ISTL active fault system. The apparent difference in the two depth migration images shown in Figure 3 is that the Moho boundary in the ISI profile is slightly more distorted than that in the Ps RF profile beneath the ISTL and the western part of the Central Uplift Zone. The distortion of the reflectors associated with the Moho boundary in the ISI profile suggests that surface-related multiples are progressively more attenuated than Ps conversions in the Ps RF analysis, due to the triplicated length of raypath in the crust through the folded zone of the ISTL active fault system. On the other hand, the Ps RF profile at stations deployed across the Komoro basin is more distorted than ISI profile. The image of Ps RF profile is degraded by the artifacts and spurious time shift due to the reverberation in the sedimentary basin.
 The remarkable difference between the ISI and Ps RF profiles is the resolution of the Moho boundary. As we showed with the synthetic examples, the ISI profile tends to have higher temporal and spatial resolution compared with that of a standard Ps RF profile. In regard to lower-crustal reflections, the east-dipping events at the depth of 19–30 km beneath the Central Uplift Zone, which are identified as the upper boundary of laminated lower crust detected from wide-angle reflection profile [Sato et al., 2004b], can be recognized in ISI profile (Figures 3b and 3d), while these reflectors are obscured in the Ps RF profile (Figures 3c and 3e). These results suggest that the ISI method has an advantage over the Ps RF approach in investigating relatively smaller-scale heterogeneity in the crust rather than overall lithospheric structure.
 Synthetic experiments and application to field data represent the feasibility and applicability study of teleseismic body waves recorded at a dense seismic array for ISI. Besides RF analysis, ISI is a promising tool for imaging detailed geometries of the crust and upper-mantle structures. The main disadvantage of ISI is that spurious reflectors, which can lead to migration artifacts, are created by partial focusing of second-order multiples and the leakage of P- and S-energy between components due to incomplete wavefield decomposition prior to cross-correlations. By using teleseismic data from different epicentral distances and the azimuths, migration artifacts and spurious events can be suppressed. Another approach for the reduction of spurious events is the stacking of all the contributions of surface-related P-P, S-S, P-S and S-P multiples. The synthetic experiments and application to field data indicates that the ISI profile shows higher temporal and spatial resolution than that of a standard Ps RF profile. However, larger magnitude earthquakes are required in seismic interferometry to assure the generation of surface-related multiples.
 We are grateful to the members of the research project on “Slip and Flow Processes in and below the Seismogenic Region” for helpful discussions and comments. The seismic experiment was performed as part of this research project, which was supported by the Ministry of Education, Culture, Sports, Science and Technology, Japan.