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The shot-profile migration approach of wave-equation migration generates subsurface images using the interferometric principle of crosscorrelating two passive wavefields. These wavefields are typically a source wavefield containing energy from an excited source and a receiver wavefield comprised of scattered-source wavefield energy by the discontinuous earth structure. Shot-profile migration can be recast as a novel way of imaging the earth's lithosphere using teleseismic wavefield data, where the source wavefield is the directly arriving wavefront and the receiver wavefield is the following wavefield coda. We demonstrate that the shot-profile technique can be tailored to suit teleseismic acquisition geometry and wavefields. Assuming an acoustic framework and 2.5D experimental geometry, we develop procedures that enable kinematic and structural imaging (migration) using both transmission and free-surface reflected passive wavefields. Experiments with synthetic data demonstrate the method's applicability and illustrate the negative imaging consequence of using inaccurate migration velocity profiles. We apply shot-profile migration to a suite of teleseismic events acquired during the IRIS-PASSCAL CASC-1993 experiment in central Oregon. The imaging results are interpreted to show the Juan de Fuca plate subducting beneath the North American plate. We attribute the observed dissimilarities between these results and other Juan de Fuca subduction- zone images to the combination of different imaging goals and the use of more accurate migration velocity profiles.

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... Among various seismic exploration methods using the bodywave of natural earthquakes [1,2], seismic interferometry (SI) has been recently employed to retrieve the reflection response. Although the receiver function method [1] has been broadly used to image the Moho and mantle discontinuities, there is a study claiming that retrieving and migrating the reflection response using SI is superior to the receiver function method [3]. ...

... Superscript d or r indicates that we only consider a direct wave for x A and reflected wave for x B . Note that the amplitudes of these wavefields are assumed to be normalized in (2). Substituting these waves into (1) and applying stationary phase approximation (e.g., [5,16]) yields the following equation: ...

Seismic interferometry (SI) has been recently employed to retrieve the reflection response from natural earthquakes. We perform experimental study to apply SI to Ocean Bottom Seismogram (OBS) records in the Nankai Trough, southwest Japan in order to reveal the relatively shallow geological boundaries including surface of oceanic crust. Although the local earthquakes with short raypath we use to retrieve reflection response are expected to contain the higher-frequency components to detect fine-scale structures by SI, they cannot be assumed as plane waves and are inhomogeneously distributed. Since the condition of inhomogeneous source distribution violates the assumption of SI, the conventional processing yields to the deteriorated subsurface images. Here we adopt the raypath calculation for stationary phase evaluation of SI in order to overcome this problem. To find stationary phase, we estimate the raypaths of two reflections: (1) sea-surface P-wave reflection and (2) sea-surface multiple P-wave reflection. From the estimated raypath, we choose the crosscorrelation traces which are expected to produce objective reflections considering the stationary phase points. We use the numerical-modeling data and field data with 6 localized earthquakes and show that choosing the crosscorrelation traces by stationary phase evaluation improves the quality of the reflections of the oceanic crust surface.

... The idea can be generalized to generate a virtual shot record at any desired location from traces recorded at other locations as long as all receivers are surrounded by the two sources (Bakulin and Calvert 2006). The SI concept has found many applications in exploration seismology including noise suppression (Berkhout and Verschuur 2006), redatuming (Schuster and Zhou 2006), and imaging (Shragge et al. 2006). Wapenaar et al. (2010a, b) cite more references on the theory and applications of SI in exploration seismology. ...

This book examines the effects of incoherent noise and how it leads to the misinterpretation of seismic data. It also reviews common noise reduction approaches and their drawbacks, focusing on developments that have occurred in the past decade.
The main features of this book include:
• Hands-on implementation in MATLAB and/or C
• In-depth discussions of both theoretical and practical aspects of the subject
• Supplementary, real-world seismic data
• Detailed descriptions of structure-enhancing filters.
Connecting the theory and practical implementation of noise reduction, the book helps readers fill the gap from equations to code, and from classical filters to the preservation and enhancement of a robust structure. Lastly, it highlights cutting-edge research in the area.
As such, it is of interest to researchers in the fields of petroleum engineering, exploration seismology, and geophysics, as well as to practitioners working in the petroleum industry.

... The idea can be generalized to generate a virtual shot record at any desired location from traces recorded at other locations as long as all receivers are surrounded by the two sources (Bakulin and Calvert 2006). The SI concept has found many applications in exploration seismology including noise suppression (Berkhout and Verschuur 2006), redatuming (Schuster and Zhou 2006), and imaging (Shragge et al. 2006). Wapenaar et al. (2010a, b) cite more references on the theory and applications of SI in exploration seismology. ...

Understand the various types of noise that appear in seismic images and volumes.

... The idea can be generalized to generate a virtual shot record at any desired location from traces recorded at other locations as long as all receivers are surrounded by the two sources (Bakulin and Calvert 2006). The SI concept has found many applications in exploration seismology including noise suppression (Berkhout and Verschuur 2006), redatuming (Schuster and Zhou 2006), and imaging (Shragge et al. 2006). Wapenaar et al. (2010a, b) cite more references on the theory and applications of SI in exploration seismology. ...

In this chapter, we consider the case when performing EPS on noisy section with impulse noise. Vector median filter has been applied to dip vector smoothing and prestack source separation, etc. However, in these applications, the local structure is not fully explored.

The main objective of the seismic exploration method is to map the structure of subsurface formations to infer the existence of possible petroleum traps.

In this chapter, we go one-step further from last chapter, i.e., from structure preservation to structure enhancement. The flow-like structures are commonly observed in seismic images. These structures usually are related to subsurface structures, such as Channel, curved stratum. So, enhancing these structures and making it more prominent may help the interpreter to pick important information. To enhance the local structure while suppressing noise, the noise suppressing filter must be structure-aware. Local orientation and its Coherence are Fundamental to the Formation of structures, so it should be analyzed and incorporated into the filter. Furthermore, Geometry of the image surface can also be utilized. To promote the effect of structure enhancement, the structure-aware filters are usually iterated several times.

... 1. Bootstrap resampling of the waveforms would provide a measure of the statistical significance of any observed reflections and could be used to replace our requirement of at least 200 seismograms to display the result. 2. In principle, migration approaches, such as those described by Pavlis (2011), Shang et al. (2012, Shragge et al. (2006), and for receiver functions and/or free-surface multiples, could be applied to better image dipping structures. However, migration methods work best with uniform data coverage, so the very uneven distribution of earthquake sources may present challenges. ...

Topside reverberations off mantle discontinuities are commonly observed at long periods, but their interpretation is complicated because they include both near‐source and near‐receiver reflections. We have developed a method to isolate the stationside reflectors in large data sets with many sources and receivers. Analysis of USArray transverse‐component data from 3,200 earthquakes, using direct S as a reference phase, shows clear reflections off the 410‐ and 660‐km discontinuities, which can be used to map the depth and brightness of these features. Because our results are sensitive to the impedance contrast (velocity and density), they provide a useful complement to receiver‐function studies, which are primarily sensitive to the S velocity jump alone. In addition, reflectors in our images are more spread out in time than in receiver functions, providing good depth resolution. Our images show strong discontinuities near 410 and 660 km across the entire USArray footprint, with intriguing reflectors at shallower depths in many regions. Overall, the discontinuities in the east appear simpler and more monotonous with a uniform transition zone thickness of 250 km compared to the western United States. In the west, we observe more complex discontinuity topography and small‐scale changes below the Great Basin and the Rocky Mountains, and a decrease in transition‐zone thickness along the western coast. We also observe a dipping reflector in the west that aligns with the top of the high‐velocity Farallon slab anomaly seen in some tomography models, but which also may be an artifact caused by near‐surface scattering of incoming S waves.

... Teleseismic waves provide tremendous amounts of information for the detection of crustal and upper mantle structures (Rondenay, 2009). Over the past forty years, many techniques have been developed to analyze teleseismic wave datasets, including receiver function analysis (Langston, 1977;Kind et al., 2012), teleseismic wave travel-time tomography based on ray theory (Zhang et al., 2011), teleseismic migration (Shragge et al., 2006), and teleseismic scattering tomography (Roecker et al., 2010;Tong et al., 2014a). To achieve the high-resolution imaging of lithospheric structures, the adjoint-state method has become the state-of-the-art technique for teleseismic wave imaging (Tong et al., 2014a;Monteiller et al., 2015). ...

The development of an efficient algorithm for teleseismic wave field
modeling is valuable for calculating the gradients of the misfit function
(termed misfit gradients) or Fréchet derivatives when the teleseismic
waveform is used for adjoint tomography. Here, we introduce an
element-by-element parallel spectral-element method (EBE-SEM) for the
efficient modeling of teleseismic wave field propagation in a reduced geology
model. Under the plane-wave assumption, the frequency–wavenumber (FK)
technique is implemented to compute the boundary wave field used to construct
the boundary condition of the teleseismic wave incidence. To reduce the
memory required for the storage of the boundary wave field for the incidence
boundary condition, a strategy is introduced to efficiently store the
boundary wave field on the model boundary. The perfectly matched layers
absorbing boundary condition (PML ABC) is formulated using the EBE-SEM to
absorb the scattered wave field from the model interior. The misfit gradient
can easily be constructed in each time step during the calculation of the
adjoint wave field. Three synthetic examples demonstrate the validity of the
EBE-SEM for use in teleseismic wave field modeling and the misfit gradient
calculation.

... The main difference is the scale. Also, Shragge et al. (2006), Fan et al. (2006, Kumar and Bostock (2006) and Abe et al. (2007) applied seismic interferometry on regional-scale seismology using scattered teleseismic arrivals. Seismic interferometry has not yet been applied in globalscale body-wave seismology. ...

... Equations 13 and 14 are used by various authors to turn ambient seismic noise into virtual exploration seismic reflection data Draganov et al., 2006Draganov et al., , 2007Draganov et al., , 2009Hohl and Mateeva, 2006;Torii et al., 2007. Interestingly, the teleseismic community has recognized in- dependently that the coda of transmission responses from distant sources contains reflection information which can be used to image the earth's crust Bostock et al., 2001;Rondenay et al., 2001;Shragge et al., 2001Shragge et al., , 2006Mercier et al., 2006. The link between teleseismic coda imaging and seismic interferometry is exploited by Kumar and Bostock 2006, Nowack et al. 2006, Chaput and Bostock 2007, and Tonegawa et al. 2009. ...

... Recently, other migration techniques have been borrowed from industry and applied to teleseismic receiver functions, such as oneway wave-equation migration (Chen et al. 2005), which is a 2-D scheme that still relies on 1-D horizontal layer assumption for the moveout correction; teleseismic shot profile migration (Shragge et al. 2006), which is also a 2-D wavefield extrapolation scheme. Another example is reverse time migration (Shang et al. 2013), which highly depends on computation capability and image scale. ...

We present a novel 3-D pre-stack Kirchhoff depth migration (PKDM) method for teleseismic receiver functions. The proposed algorithm considers the effects of diffraction, scattering and traveltime alteration caused by 3-D volumetric heterogeneities. It is therefore particularly useful for imaging complex 3-D structures such as dipping discontinuities, which is hard to accomplish with traditional methods. The scheme is based on the acoustic wave migration principle, where at each time step of the receiver function, the energy is migrated back to the ensemble of potential conversion points in the image, given a smooth 3-D reference model. Traveltimes for P and S waves are computed with an efficient eikonal solver, the fast marching method.We also consider elastic scattering patterns, where the amplitude of converted S waves depends on the angle between the incident P wave and the scattered S wave. Synthetic experiments demonstrate the validity of the method for a variety of dipping angle discontinuities. Comparison with the widely used common conversion point (CCP) stacking method reveals that our migration shows considerable improvement. For example, the effect of multiple reflections that usually produce apparent discontinuities is avoided. The proposed approach is practical, computationally efficient, and is therefore a potentially powerful alternative to standard CCP methods for imaging large-scale continental structure under dense networks. © The Authors 2016. Published by Oxford University Press on behalf of The Royal Astronomical Society.

... Various methods including receiver function (RF) analysis through single station stacking [e.g., Langston, 1977;Yan and Clayton, 2007], common conversion point (CCP) stacking [e.g., Revenaugh, 1995;Sheehan et al., 2000;Chen et al., 2005], inverse scattering approaches based on asymptotic methods such as generalized Radon transform [e.g., Bostock et al., 2001;Cao et al., 2010;Shang et al., 2014], teleseismic migration [e.g., Shragge et al., 2006;Shang et al., 2012] and teleseismic scattering tomography [e.g., Frederiksen and Revenaugh, 2004;Pageot et al., 2013;Burdick et al., 2014;Tong et al., 2014] have been developed for specific imaging purposes. ...

We present a three-dimensional (3D) hybrid method that interfaces the spectral-element method (SEM) with the frequency-wavenumber (FK) technique to model the propagation of teleseismic plane-waves beneath seismic arrays. The accuracy of the resulting 3D SEM-FK hybrid method is benchmarked against semi-analytical FK solutions for 1D models. The accuracy of 2.5D modelling based on 2D SEM-FK hybrid method is also investigated through comparisons to this 3D hybrid method. Synthetic examples for structural models of the Alaska subduction zone and the central Tibet crust show that this method is capable of accurately capturing interactions between incident plane waves and local heterogeneities. This hybrid method presents an essential tool for the receiver-function and scattering-imaging community to verify and further improve their techniques. These numerical examples also show the promising future of the 3D SEM-FK hybrid method in high-resolution regional seismic imaging based on waveform inversionsof converted/scattered waves recorded by seismic array.

... To provide an image of the discontinuities at depth, these so-called receiver functions used to be subjected to simple stacking at common conversion points (CCP stacks), but lately more sophisticated imaging methods like the generalized Radon transform (Bostock et al., 2001) have been put to use. Several recent studies focused with substantial success on wave-equation migration of converted phases and multiples (Shragge et al., 2006;Chen et al., 2009;Shang et al., 2012). ...

Converted and multiply reflected phases from teleseismic events are
routinely used to create structural images of the crust-mantle boundary
(Moho) and the elasticity contrasts within the crust and upper mantle.
The accuracy of these images is to a large extent determined by the
background velocity model used to propagate these phases to depth. In
order to improve estimates of 3-D velocity variations and, hence,
improve imaging, we develop a method of reverse-time migration-based
reflection tomography for use with wavefields from teleseismic
earthquakes recorded at broad-band seismograph arrays. Reflection
tomography makes use of data redundancy-that is, the ability to generate
numerous structural images of the subsurface with different parts of the
wavefield. In exploration seismology (where it is known as migration
velocity analysis) reflection tomography typically involves the
generation of an extended image (e.g. offset- or angle-gathers), and the
fitness of the background model is evaluated through the application of
image-domain annihilators. In regional-scale passive source seismology,
however, annihilation-based methods are inadequate because the sparse
and irregular distribution of teleseismic sources is not likely to
produce illumination over a sufficient range of angles. To overcome this
problem we turn towards a source-indexed moveout scheme. Instead of
extended image annihilation, we determine the success of the tomographic
velocity model by cross correlating images produced with multiply
scattered waves from different teleseismic sources. The optimal velocity
model is the one that minimizes correlation power between windowed
images away from zero depth shift. We base our inversion scheme on the
seismic adjoint method and a conjugate gradient solver. For each image
pair, the update direction is determined by correlations between
downgoing wavefields with upgoing adjoint wavefields for both images.
The sensitivity kernels used in this method is similar to those found in
other forms of adjoint tomography, but their shapes are controlled by
the spatial distribution of the error function. We present the method
and a proof-of-concept with 2-D synthetic data.

... As an imaging condition, one can use the zero lag of the autocorrelation of the time trace at each image point after each extrapolation step and sum the result over all extrapolation times ). Alternatively, the crosscorrelation between different propagation modes (e.g., P-waves and S-waves) can be used as an imaging condition (Shragge et al., 2006;. ...

We analyzed ambient seismic noise from a broadband passive seismic survey acquired in an urban area in Germany. Despite a high level of anthropogenic noise, we observe lateral variations in the quasi-stationary spectra that are of natural origin and indicative of the subsurface in the survey area. The best diagnostic is the ellipticity spectrum which is the spectral ratio of the vertical over the horizontal components. Deviations of the observed spectra from a pure Rayleigh-wave ellipticity allow an approximate separation of surface-wave from body-wave components in the analyzed frequency range, distinguishing shallow (upper tens of meters) from deeper (upper three kilometers) subsurface effects. We observe an increase of vertically polarized body waves between 1 and 4 Hz that is correlated to a subsurface structure that contains an oil reservoir at about 2-km depth. We located the source of the observed body wave microtremor in depth by applying an elastic wavefield back projection and imaging technique. The method includes normalization by the impulse response of the velocity model, effects of the receiver geometry, and lateral variation of incoherent noise. The source region of the low-frequency body wave microtremor is centered above the location of the oil reservoir. Two possible explanations for the deep microtremor are elastic body-wave scattering due to the impedance contrast of the structural trap, and viscoelastic scattering due to poroelastic effects in the partially saturated reservoir.

... In shallow underwater acoustics, direct and reflected wave fronts have been retrieved from ambient noise (Roux et al. 2004;Sabra et al. 2005a). In some applications, passive seismic interferometry has been used to image the Earth's subsurface structure based on noise recordings (Scherbaum 1987a,b;Daneshvar et al. 1995;Sheng et al. 2001Sheng et al. , 2003Shragge et al. 2006;Draganov et al. 2006Draganov et al. , 2007Draganov et al. , 2009. ...

Passive seismic interferometry is a new promising methodology for
seismic exploration. Interferometry allows information about the
subsurface structure to be extracted from ambient seismic noise. In this
study, we apply the cross-correlation technique to approximately 25 hr
of recordings of ambient seismic noise at the Ketzin experimental
CO2 storage site, Germany. Common source gathers were
generated from the ambient noise for all available receivers along two
seismic lines by cross-correlation of noise records. This methodology
isolates the interstation Green's functions that can be directly
compared to active source gathers. We show that the retrieved response
includes surface waves, refracted waves and reflected waves. We use the
dispersive behaviour of the retrieved surface waves to infer geological
properties in the shallow subsurface and perform passive seismic imaging
of the subsurface structure by processing the retrieved reflected waves.

... This vector-wavefield processing yields P-and S-wave data sections appropriate for use in shot-profile migration (Shragge et al., 2005). We migrated the data sections for both P − P and P − S scattering modes. ...

We extend the 2-D theory of angle-domain common-image gathers (ADCIGs) to forward- scattered wavefields, and present a method for extracting re flectivity as a function of either the reflected or converted-wave receiver-side scattering a ngle. We use the shot-profile con- figuration of wave-equation migration along with planar sou rce and receiver wavefields to generate an analytic hyper-plane surface in the intermediate offset-domain common- image gather space. Geometrical relations and partial derivatives of the hyper-plane func- tion generate six constraint equations for the the unknown six parameters, allowing us to solve for the source- and receiver-side reflection angles and geologic dip angle. Re- sults of numerical experiments indicate that information on wavefield focusing is present in forward-scattered ADCIGs, which suggests that this algorithm may be useful tool for improving wave-equation based tomography of transmission wavefields.

... where subscripts d and u refer to extraction of the HP's from the down-going and up-coming wave fields. Shragge et al. (2006) introduced imaging forward scattered mode conversions in teleseismic data by simply changing the causality of the source propagation, which effectively changes P d above to P u . The forward scattering (one-way) P to S imaging condition can also be interpreted as the location of an oriented source, which leads to the concept of imaging an actual "explosion" instead of the "exploding reflector." ...

Since the Earth is elastic, it is worth the computational burden to process multicomponent data for elastic phenomena with fully coupled time-domain wave-equation propagators. At every time sample in the back-propagated model domain, the complete wave field is decomposed exactly into compressional and shear wave components by simple spatial derivatives. Then, physically significant images are extracted from extrapolated hyper-cubes by applying appropriate imaging conditions. To locate subsurface sources (or diffractors) with the time-reverse modeling algorithm, the imaging condition required is the correlation of P and S energy since only at the source location are the two events collocated. The impulse response of the algorithm is anti-symmetric in physical space and can be enhanced through post-processing with a spatial derivative or integral.

... Note that several researchers have used single-scattered waves isolated from a teleseismic event for imaging subsurface structures (e.g. Bostock et al. 2001; Rondenay et al. 2001; Shragge et al. 2001 Shragge et al. , 2006). Our technique clearly differs from their analyses because we use random signals generated by a teleseismic event, as shown in In order to compute the CCF, we used teleseismic S coda with a time length of 500 s (Fig. 5a) and a frequency band of 0.07–0.5 Hz. ...

The reconstruction of surface waves from the cross-correlation of random wavefields has recently been extensively inspected by theoretical and experimental approaches. However, the reconstruction of body waves has not been extensively studied. In this study, we present a method for extracting body waves, that is, direct P and S waves, and reflected waves from the Philippine Sea slab. We use the cross-correlation of the wavefield generated by the teleseismic S waves observed by Hi-net tiltmeters with a passband of 0.07-0.5 Hz. To enhance the contribution of the S coda, we reduced the source-time function and the deterministic phases sS, ScS and SS, and the surface wave in S coda. The records of the processed S coda observed at every station-pair are cross-correlated for each teleseismic event. The cross-correlation functions (CCFs) of different earthquakes are stacked to retrieve wavefields propagating between the station-pairs. As a result, direct P, S and the reflected waves could be extracted when the stacked CCFs are aligned as a function of distance of separation between two stations. The gradients of the traveltime curves for the direct P and S waves are approximately 5-7 and 3 km s-1, respectively. These velocities correspond to the seismic velocities of the crust or the P-wave velocity of the uppermost mantle. In order to enhance the reflected waves, we searched for the reflection points by assuming that the later phases in the CCFs are SS reflections and map the amplitudes onto the depth sections. As a result, the negative phases dipping to the north can be traced right below the region of hypocentre distribution. These negative phases probably correspond to the oceanic Moho within the Philippine Sea slab. We also show that the oceanic Moho can also be traced by assuming PP reflections. These results indicate that the CCFs plausibly contain information regarding both P and S waves propagating between the two receivers, and are capable of detecting reflected phases in addition to the direct waves.

... Artman and Shragge (2003) show the applicability of direct migration for transmission wave- fields. Artman et al. (2004) provide the mathematical justification for zero-phase source func- tions. Shragge et al. (2005) show results for the special case of imaging with teleseisms. Direct migration of transmission wavefields requires an imaging algorithm composed of wavefield extrapolation and a correlation based imaging condition. Shot-profile (Claerbout, 1971) wave-equation depth migration, described in Appendix A, fulfills these requirements. Shot-pr ...

Passive seismic imaging is the process of synthesizing the wealth of subsurface informa-tion available from reflection seismic experiments by recording ambient sound with an array of geophones distributed at the surface. Cross-correlating the traces of such a pas-sive experiment can synthesize data that is immediately useful for analysis by the various techniques that have been developed for the manipulation of reflection seismic data. With a correlation-based imaging condition, wave-equation shot-profile depth migration can use raw transmission wavefields as input to produce a subsurface image. For passively acquired data, migration is even more important than for active data because the source wavefields are likely weak and complex which leads to a low signal-to-noise ratio. Fourier analysis of correlating long field records shows that aliasing of the wavefields from distinct shots is unavoidable. While this reduces the order of computations for correlation by the length of the original trace, the aliasing produces an output volume that may not be substantially more useful than the raw data due to the introduction of cross talk between multiple sources. Direct migration of raw field data can still produce an accurate image even when the transmission wavefields from individual sources are not separated. I illustrate the method with images from a shallow passive investigation targeting a buried hollow pipe and the water table reflection. The images show a strong anomaly at the 1 m depth of the pipe and faint events that could be the water table around 3 m. The images are not so clear as to be irrefutable. A number of deficiencies in the survey design and execution are identified for future efforts.

... Equations 13 and 14 are used by various authors to turn ambient seismic noise into virtual exploration seismic reflection data ͑Draganov et al., 2006͑Draganov et al., , 2007͑Draganov et al., , 2009Hohl and Mateeva, 2006;Torii et al., 2007͒. Interestingly, the teleseismic community has recognized independently that the coda of transmission responses from distant sources contains reflection information which can be used to image the earth's crust Rondenay et al., 2001;Shragge et al., 2001Shragge et al., , 2006Mercier et al., 2006͒. The link between teleseismic coda imaging and seismic interferometry is exploited by Kumar and Bostock ͑2006͒, Nowack et al. ͑2006͒, Chaput and Bostock ͑2007͒, and Tonegawa et al. ͑2009͒. ...

Seismic interferometry involves the crosscorrelation of responses at different receivers to obtain the Green's function between these receivers. For the simple situation of an impulsive plane wave propagating along the x-axis, the crosscorrelation of the responses at two receivers along the x-axis gives the Green's function of the direct wave between these receivers. When the source function of the plane wave is a transient (as in exploration seismology) or a noise signal (as in passive seismology), then the crosscorrelation gives the Green's function, convolved with the autocorrelation of the source function. Direct-wave interferometry also holds for 2D and 3D situations, assuming the receivers are surrounded by a uniform distribution of sources. In this case, the main contributions to the retrieved direct wave between the receivers come from sources in Fresnel zones around stationary points. The main application of direct-wave interferometry is the retrieval of seismic surface-wave responses from amb

The increasing demand for the high-resolution imaging of deep lithosphere structures requires the utilization of a teleseismic dataset for waveform inversion. The construction of an efficient algorithm for the teleseismic wavefield modeling is valuable for the calculation of misfit kernels or Fréchet derivatives when the teleseismic waveform is used for adjoint tomography. Here, we introduce an element-by-element parallel spectral-element method (EBE-SEM) for the efficient modeling of teleseismic wavefield propagation in a localized geology model. Under the assumption of the plane wave, the frequency-wavenumber (FK) technique is implemented to compute the boundary wavefield used for constructing the boundary condition of the teleseismic wave incidence. To reduce the memory required for the storage of the boundary wavefield for the incidence boundary condition, an economical strategy is introduced to store the boundary wavefield on the model boundary. The perfectly matched layers absorbing boundary condition (PML ABC) is formulated by the EBE-SEM to absorb the scattered wavefield from the model interior. The misfit kernel (derivatives of the waveform misfit with respect to model parameters) can be easily constructed without extra computational effort for the calculation of the element stiffness matrix per time step during the calculation of the adjoint wavefield. Three synthetic examples demonstrate the validity of EBE-SEM for use in teleseismic wavefield modeling and the misfit kernel calculation.

Since the Earth is elastic, it is worth the computational burden to process multicomponent data for elastic phenomena with fully coupled time-domain wave-equation propagators. At every time sample in the back-propagated model domain, the complete wave field is decomposed exactly into compressional and shear wave components by simple spatial derivatives. Then, physically significant images are extracted from extrapolated hyper-cubes by applying appropriate imaging conditions. To locate subsurface sources (or diffractors) with the time-reverse modeling algorithm, the imaging condition required is the correlation of P and S energy since only at the source location are the two events collocated. The impulse response of the algorithm is anti-symmetric in physical space and can be enhanced through post-processing with a spatial derivative or integral.

Seismic interferometry is an exciting new field in geophysics utilizing multiple scattering events to provide unprecedented views of the Earth's subsurface. This is the first book to describe the theory and practice of seismic interferometry with an emphasis on applications in exploration seismology. Exercises are provided at the end of each chapter, and the text is supplemented by online MATLAB codes that illustrate important ideas and allow readers to generate synthetic traces and invert these to determine the Earth's reflectivity structure. Later chapters reinforce these principles by deriving the rigorous mathematics of seismic interferometry. Incorporating examples that apply interferometric imaging to synthetic and field data, from applied geophysics and earthquake seismology, this book is a valuable reference for academic researchers and oil industry professionals. It can also be used to teach a one-semester course for advanced students in geophysics and petroleum engineering.

Interferometric migration of free-surface multiples in vertical-seismic-profile (VSP) data has two significant advantages over standard VSP imaging: (1) a significantly larger imaging area compared to migrating VSP primaries and (2) less sensitivity to velocity-estimation and static errors than other methods for migration of multiples. In this paper, we present a 3D wave-equation interferometric migration method that efficiently images VSP free-surface multiples. Synthetic and field data results confirm that a reflectivity image volume, comparable in size to a 3D surface seismic survey around the well, can be computed economically. The reflectivity image volume has less fold density and lower signal-to-noise ratio than that obtained by a conventional 3D surface seismic survey because of the relatively weak energy of multiples and the limited number of geophones in the well. However, the efficiency of this method for migrating VSP multiples suggests that it might sometimes be a useful tool for 4D seismic monitoring where reflectivity images can be computed quickly for each time-lapse survey.

We discuss Rodney Calvert's work on the Virtual Source method in the context of seismic interferometry. Moreover, we present a systematic analysis of seismic interferometry by cross‐correlation versus multi‐dimensional deconvolution and we discuss applications of both approaches.

ABSTRACT We present the chain of time-reverse modeling, image space wavefield decomposition and several imaging conditions as a migration-like algorithm called time-reverse imaging. The algorithm locates subsurface sources in passive seismic data and diffractors in active data. We use elastic propagators to capitalize on the full waveforms available in multicomponent data, although an acoustic example is presented as well. For the elastic case, we perform wavefield decomposition in the image domain with spatial derivatives to calculate P and S potentials. To locate sources, the time axis is collapsed by extracting the zero-lag of auto and cross-correlations to return images in physical space. The impulse response of the algorithm is very dependent on acquisition geometry and needs to be evaluated with point sources before processing field data. Band-limited data processed with these techniques image the radiation pattern of the source rather than just the location. We present several imaging conditions but we imagine others could be designed to investigate specific hypotheses concerning the nature of the source mechanism. We illustrate the flexible technique with synthetic 2D passive data examples and surface acquisition geometry specifically designed to investigate tremor type signals that are not easily identified or interpreted in the time domain.

Progress in the imaging of the mantle and core is partially limited by the sparse distribution of natural sources; the earthquake hypocenters are mainly along the active lithospheric plate boundaries. This problem can be approached with seismic interferometry. In recent years, there has been considerable progress in the development of seismic interferometric techniques. The term seismic interferometry refers to the principle of generating new seismic responses by cross-correlating seismic observations at different receiver locations. The application of interferometric techniques on a global scale could create sources at locations where no earthquakes occur. In this way, yet unknown responses would become available for the application of travel-time tomography and surface-wave dispersion studies. The retrieval of a dense-enough sampling of source gathers would largely benefit the application of reflection imaging.

Analysis of a deployment of broadband sensors along a 500-km-long line crossing the Yellowstone hotspot track (YHT) has provided 423 in-plane receiver functions with which to image lateral variations in mantle discontinuity structure. Imaging is accomplished by performing the converted wave equivalent of a common midpoint stack, which significantly improves resolution of mantle discontinuity structure with respect to single-station stacks. Timing corrections are calculated from locally derived tomographic P and S wave velocity images and applied to the Pds (where dis the depth of the conversion) ray set in order to isolate true discontinuity topography. Using the one-dimensional TNA velocity model and a V P/V S ratio of 1.82 to map our Pds times to depth, the average depths of the 410- and 660-km discontinuities are 423 and 664 km, respectively, giving an average transition zone thickness of 241 km. Our most robust observation is provided by comparing the stack of all NW back-azimuth arrivals versus all SE back-azimuth arrivals. This shows that the transition zone thickness varies between 261 and 232 km, between the NW and SE portions of our line. More spatially resolved images show that this transition zone thickness variation results from the occurrence of 20-30 km of topography over 200-300 lateral scale lengths on the 410- and 660-km discontinuities. The topography on the 410- and 660-km discontinuities is not correlated either positively or negatively beneath the 600-km-long transect, albeit correlation could be present for wavelengths larger than the length of our transect. If this discontinuity topography is controlled exclusively by thermal effects, then uncorrelated 250° lateral temperature variations are required at the 410- and 660-km discontinuities. However, other sources of discontinuity topography such as the effects of garnet-pyroxene phase transformations, chemical layering, or variations in mantle hydration may contribute. The most obvious correlation between the discontinuity structure and the track of the Yellowstone hotspot is the downward dip of the 410-km discontinuity from 415 km beneath the NW margin of the YHT to 435 km beneath the easternmost extent of Basin and Range faulting. Assuming this topography is thermally controlled, the warmest mantle resides not beneath the Yellowstone hotspot track, but 150 km to the SE along the easternmost edge of the active Basin and Range faulting.

Analysis of seismograms from teleseismic rays traversing the Coso
geothermal area near Ridgecrest, California, suggests the geothermal
system lies over a single shallow magma reservoir (˜5 km below the
surface) that also plays a crucial role in the local change in
deformation style from areas to the north and west. The character of the
magma reservoir and the absence of a lower crustal magma reservoir is
inferred from three crustal P-to-S conversions observed using receiver
function analysis: (1) A high-amplitude, shallow, negative arrival, Ps-P
time of 0.7-0.9 s (3-5 km below sea level (bsl)), (2) a moderate
amplitude, positive conversion, Ps-P time of 2.1-2.5 s (14-17 km bsl),
and (3) the Moho conversion, Ps-P time of 4.0-4.2 s (30-32 km bsl).
Observations of Moho converted arrivals indicate that the interface is
mostly flat and uncomplicated throughout the study area, while the
midcrustal conversion is laterally variable in amplitude and depth. The
absence of the large negative amplitude conversion on waveforms recorded
at stations outside the geothermal area strongly suggests that the
feature lies only underneath the modern geothermal area. In addition,
rays sampling the shallow converter also contain later arrivals with
retrograde moveout consistent with an origin as reverberations above the
conversion. Receiver functions calculated from synthetic data using a
single isotropic layer over a half-space indicates that the shear
velocity decreases by 30% across the interface (VS1 = 2.6
km/s; VS2 = 1.8 km/s; layer one thickness 4.9 km), further
supporting the presence of shallow magma.

We experiment with backprojection migration processing of teleseismic receiver functions from the Snake River Plain (SRP) broadband seismic experiment. Previous analyses of data from this experiment have used a common midpoint (CMP) stacking approach, a method widely applied for analysis of P-SV converted phases (receiver functions) to obtain high-resolution imaging of upper mantle discontinuities. The CMP technique assumes that all P-SV conversions are produced by flat-lying structures and may not properly image dipping, curved, or laterally discontinuous interfaces. In this paper we adopt a backprojection migration scheme to solve for an array of point scatterers that best produces the large suite of observed receiver functions. We first perform synthetic experiments that illustrate the potential improvement of migration processing over CMP stacks. Application of the migration processing to the SRP data set shows most of the major features as in the original CMP work, but with a weaker 410-km discontinuity and a more intermittent discontinuity at 250 km apparent depth. Random resampling tests are also performed to assess the robustness of subtle features in our discontinuity images. These tests show that a 20-km elevation of the 660-km discontinuity directly beneath the Snake River Plain is robust, but that the variations in 410-km discontinuity topography that we observe are not stable upon resampling. ``Bright spots'' near 250 km apparent depth are robust upon resampling, but interpretation of these features is complicated by possible sidelobe artifacts from topside Moho reverberations.

Analysis of a deployment of broadband sensors along a 500-km-long line crossing the Yellowstone hotspot track (YHT) has provided 423 in-plane receiver functions with which to image lateral variations in mantle discontinuity structure. Imaging is accomplished by performing the converted wave equivalent of a common midpoint stack, which significantly improves resolution of mantle discontinuity structure with respect to single-station stacks. Timing corrections are calculated from locally derived tomographic P and S wave velocity images and applied to the Pds (where d is the depth of the conversion) ray set in order to isolate true discontinuity topography. Using the one-dimensional TNA velocity model and a Vp/Vs ratio of 1.82 to map our Pds times to depth, the average depths of the 410- and 660-km discontinuities are 423 and 664 km, respectively, giving an average transition zone thickness of 241 km. Our most robust observation is provided by comparing the stack of all NW back-azimuth arrivals versus all SE back-azimuth arrivals. This shows that the transition zone thickness varies between 261 and 232 km, between the NW and SE portions of our line. More spatially resolved images show that this transition zone thickness variation results from the occurrence of 20-30 km of topography over 200-300 lateral scale lengths on the 410- and 660-km discontinuities. The topography on the 410- and 660-km discontinuities is not correlated either positively or negatively beneath the 600-km-long transect, albeit correlation could be present for wavelengths larger than the length of our transect. If this discontinuity topography is controlled exclusively by thermal effects, then uncorrelated 250° lateral temperature variations are required at the 410- and 660-km discontinuities. However, other sources of discontinuity topography such as the effects of garnet-pyroxene phase transformations, chemical layering, or variations in mantle hydration may contribute. The most obvious correlation between the discontinuity structure and the track of the Yellowstone hotspot is the downward dip of the 410-km discontinuity from 415 km beneath the NW margin of the YHT to 435 km beneath the easternmost extent of Basin and Range faulting. Assuming this topography is thermally controlled, the warmest mantle resides not beneath the Yellowstone hotspot track, but 150 km to the SE along the easternmost edge of the active Basin and Range faulting.

Passive seismic imaging is the process of synthesizing the wealth of subsurface informa-tion available from reflection seismic experiments by recording ambient sound with an array of geophones distributed at the surface. Cross-correlating the traces of such a pas-sive experiment can synthesize data that is immediately useful for analysis by the various techniques that have been developed for the manipulation of reflection seismic data. With a correlation-based imaging condition, wave-equation shot-profile depth migration can use raw transmission wavefields as input to produce a subsurface image. For passively acquired data, migration is even more important than for active data because the source wavefields are likely weak and complex which leads to a low signal-to-noise ratio. Fourier analysis of correlating long field records shows that aliasing of the wavefields from distinct shots is unavoidable. While this reduces the order of computations for correlation by the length of the original trace, the aliasing produces an output volume that may not be substantially more useful than the raw data due to the introduction of cross talk between multiple sources. Direct migration of raw field data can still produce an accurate image even when the transmission wavefields from individual sources are not separated. I illustrate the method with images from a shallow passive investigation targeting a buried hollow pipe and the water table reflection. The images show a strong anomaly at the 1 m depth of the pipe and faint events that could be the water table around 3 m. The images are not so clear as to be irrefutable. A number of deficiencies in the survey design and execution are identified for future efforts.

The split‐step Fourier method is developed and applied to migrating stacked seismic data in two and three dimensions. This migration method, which is implemented in both the frequency‐wavenumber and frequency‐space domains, takes into account laterally varying velocity by defining a reference slowness (reciprocal of velocity) as the mean slowness in the migration interval and a perturbation term that is spatially varying. The mean slowness defines a reference vertical wavenumber which is used in the frequency‐wavenumber domain to downward continue the data across a depth interval as in constant‐velocity phase‐shift migration. The perturbation term is used to define a “source” contribution that is taken into account by the application of a second phase shift in the frequency‐space domain. Since the method does not include the effects of second and higher order spatial derivatives of the slowness field, the method theoretically is accurate only when there are no rapid lateral slowness variations combined with steep angles of propagation. However, synthetic and real examples indicate that good results are obtained for realistic geologic structures.

Structure under Corvallis, Oregon, was examined using long-period Ps and Sp conversions and P reverberations from teleseismic events as recorded at the WWSSN station COR. A distinct low-velocity zone in the uppermost mantle is inferred by modeling these phases in the time domain using a data set composed of six deep and intermediate-depth earthquakes. The lower boundary occurs at 45-km depth and has S and P velocity contrasts of 1.3 and 1.4 km/sec, respectively. The material comprising the low-velocity zone has a Poisson ratio of at least 0.33 and is constrained by the average P and S travel times determined from the converted phases. The top of the earth model conforms to previously published refraction results.

We have seen that the complete seismic field induced in a radially heterogeneous sphere can be expressed as an infinite sum of standing waves, namely the normal modes. However, we know from seismogram analysis that most of the recorded earth motion can be explained in terms of propagating waves. There must exist a link, therefore, between these two seemingly different aspects of wave motion.

Schemes for seismic mapping of reflectors in the presence of an arbitrary velocity model, dipping and curved reflectors, diffractions, ghosts, surface elevation variations, and multiple reflections are reviewed and reduced to a single formula involving up and downgoing waves. The mapping formula may be implemented without undue complexity by means of difference approximations to the relativistic Schroedinger equation.

Crucial image resolution may be lost when spatially aliased data are imaged with Kirchhoff algorithms that employ standard antialiasing methods. To maximize resolution, I introduce a method that enables the proper imaging of some aliased components in the data, while avoiding aliasing artifacts. The proposed method is based on a detailed analysis of the different types of aliasing that affect Kirchhoff imaging. In particular, it is based on the observation that operator aliasing depends on the dip spectrum of the data. A priori knowledge on the characteristics of the dip spectrum of the data, in particular on its asymmetry, can thus be exploited to enable "imaging beyond aliasing." The method is not of general applicability, but it successfully improves the image resolution when a priori assumptions on the data dips are realistic. The imaging of salt-dome flanks in the Gulf of Mexico has been enhanced by the application of the proposed method.

In part 1 we developed the theoretical foundations of a prestack migration procedure to image forward scattered P to S (PdS) converted waves in the coda of teleseismic P waves. This paper addresses the issue of how to optimally stack data from multiple events migrated by this procedure. We apply matrix perturbation theory to develop an objective way to quantify noise in deconvolved PdS data. Application of the theory demonstrates that an optimal stack requires weighting the migrated data from each event by a signal-to-noise ratio criterion. We also find that the migrated PdS images have to be binned by back azimuth and balanced prior to the final stack. This is necessary to mitigate coherent noise that results from aliased microseism noise that is enhanced by our processing method. We processed 23 events recorded by the Lodore array in northwestern Colorado with our procedure. The results indicate the presence of a major, lithospheric scale discontinuity defined by a south dipping boundary within the crust that we interpret as the subsurface expression of the Cheyenne Belt. The suture is also marked by a transition in crustal thickness from 35 km on the Archean side to over 40 km on the Colorado Plateau side. We also observe a strong difference in the lithospheric mantle PdS conversion signature on opposite sides of the suture that suggests delamination and northward convergence of the Colorado lithosphere beneath the Wyoming province.

Long-period P waves from distant earthquakes have been analyzed from seismograms recorded at Albuquerque and Bermuda in the light of Haskel's theory of the spectral response of a layered crust. By using the ratio of the vertical spectrum to the horizontal component spectrum, we obtain a function which depends on structure beneath the station. Because of the poorly understood nature of the signal which follows the first P wave motion, the methods of power spectrum analysis are applied and a lag window selected to discriminate against long time correlations within the signal. Corrections for the differing responses of the three components are made by using the power spectral matrix of calibration signals. A range of crustal models has been found which agrees with the data. We are restricted primarily in choosing models for the lower half of the crust; variations of structure in the upper half do not noticeably affect the theoretical curves in the period range considered (0.02 to 0.20 cps). At Albuquerque the crust is about 40 km thick and the lower crust has velocities in the range 6.6 to 7.0 km/sec. The Mohorovicic (M) discontinuity under Bermuda is 12 km below sea level, and the structure appears to be a normal oceanic crust depressed elastically by the weight of the volcanics which compose the island.

Stacking, either by itself or as a part of depth migration, is usually used for noise suppression in teleseismic receiver function (RF) images. However, stacking is neither the only signal enhancement method available, nor is it the most efficient in the environment of receiver-side source-generated noise typical for RF imaging. We generalize prestack depth migration methodology by introducing numerous signal-enhancement schemes in place of final summation. The method operates in full 3D, incorporates most of the existing imaging techniques, and suggests a generalized framework of RF depth imaging. We present four applications of this technique using the data from the teleseismic Continental Dynamics-Rocky Mountains teleseismic experiment: (1) building common-image gathers to assess depth focusing of RF images, (2) imaging using median and (3) coherency filters for noise suppression, and (4) generalized 3D common conversion point stacking. The results suggest that with the limited volumes and quality of the existing RF datasets, adaptive filters could be superior to record summation used in conventional depth migration.

Prestack elastic migration by displacement potential extrapolation is a mixed, systematic, and function-blocked vector wavefield migration algorithm. A new wavefield extrapolation method for inhomogeneous media is introduced here according to the following sequence: displacements → potentials → extrapolation of the potentials → displacements, which is relatively accurate and not computer-time intensive. Traveltimes of both direct downgoing P- and S-waves, which are necessary in elastic migration, are calculated with a modified convolutional acoustic forward modeling program applicable to complex structures. A new image condition based on the time consistent principle is developed. It involves first obtaining an image condition section. Then two images (PP and SS) are obtained from the product of the extrapolated and decomposed P P- and S S-wave displacement amplitudes and the image condition section. All P P-, P S-, S P- and S S-waves are considered when the image condition section is calculated. The image condition section minimizes cross-talk between modes. Compared to previous treatments, the newly developed image condition formula is superior since it allows migration of multicomponent seismic data produced using a combined P and S source. Numerical test results are very encouraging and clearly demonstrate the robustness of the technique. Further work is continuing so as to overcome ray angle and polarity problems in the image condition.

We present the theoretical foundations for a prestack migration technique to image teleseismic P-to-S converted phases. The method builds on teleseismic P wave deconvolution, pseudostation stacking [Neal and Pavlis, 1999] and on the idea of using a plane wave decomposition for imaging as introduced by Treitel et al. [1982]. Deconvolution operators are constructed by pseudostation stacking of the array aligned to the incident P wave arrival times to produce a space-variable deconvolution operator. The resulting data are then muted to remove the deconvolved direct P wave pulse and pseudostation stacked over a grid of feasible slowness vectors. The pseudostation stack interpolates the wave field onto a regular grid along Earth's surface producing a series (one per slowness vector) of uniformly sampled three-dimensional data cubes (two space variables and time). The plane wave components can be propagated downward using a form of approximate ray tracing with a three-dimensional Earth model. This yields a series of distorted cubes topologically equivalent to the original uniformly sampled data cubes. These data volumes are summed as a weighted stack with the weights derived from an integration formula for inverse scattering based on the generalized Radon transform. This allows an image of the subsurface to be constructed on an event by event basis beneath the array. We apply this technique to data from the Lodore array that was deployed in northwestern Colorado. The results suggest the presence of a major lithospheric-scale discontinuity defined by a south dipping boundary.

The effect of the free surface can be removed from three-component seismic recordings to recover the incident upgoing wavefield, if the slowness and azimuth of the current wavefront are known as a function of time. For a single three-component station it is usually possible to estimate an azimuth for an event from the first arriving P-waves, but slowness estimates are less reliable when more than one wavetype is presented in the seismic wavetrain. However, the free surface correction operators are generally slowly varying functions of slowness and so some error in slowness can be tolerated.
Effective approximations for the removal of the free surface effects can be made for hard rock sites to cover slowness bands for the main regional phases Pn, Pg, Sn and Lg. By applying these operators in turn over group velocity windows appropriate to the particular phases, the relative amplitude of the P, SV and SH contributions to the wavefield can be estimated. Because the free surface amplification effects have been removed, the amplitudes can be compared directly and provide useful constraints on the radiation characteristics of the source. This procedure is therefore helpful for developing discrimination measures for different classes of sources.

This is the third paper in a three-part series that examines formal inversion of the teleseismic P wave coda for discontinuous, two-dimensional (2-D) variations in elastic properties beneath dense arrays of three-component, broadband seismometers. In this paper, the method is applied to data from the Incorporated Research Institutions for Seismology-Program for Array Seismic Studies of the Continental Lithosphere (IRIS-PASSCAL) Cascadia 1993 experiment undertaken across central Oregon. Two major features are imaged in the resulting model. The continental Moho becomes evident $150 km from the coast beneath the Western Cascades and extends through the eastern end of the profile at 35 –40 km depth. In the western portion of the model, oceanic crust of the subducting Juan de Fuca plate dips shallowly (12°) at the coast and more steeply (27°) below the Willamette Valley and is evident to depths of >100 km beneath the High Cascades. The abrupt increase in plate dip at $40 km depth coincides with an apparent thickening of the oceanic crust followed by a diminution in its signature. Building on previous work, we argue that these results are consistent with the consequences of prograde metamorphic reactions occurring within the oceanic crust. Progressive dehydration at lower-grade facies conditions culminates in the transformation to eclogite, producing a pronounced increase in the seismic velocity, density and dip of the subducting plate, and structural complexity in the overlying wedge.

This is the first paper in a three-part series that examines formal inversion of the teleseismic P wave coda for discontinuous variations in elastic properties beneath dense, three-component, seismic arrays. In this paper, we develop the theoretical framework for a migration method that draws upon the tenets of inverse scattering theory and is amenable to practical implementation. The forward problem is formulated for two-dimensional (2-D) heterogeneity in observance of formal sampling requirements and currently accessible instrumentation. A ray theoretic Green's function, corresponding to a line source with axial component of forcing, is employed within the 2-D Born approximation to accommodate planar, incident wave fields at arbitrary back azimuths. Both the forward scattered response generated by the upgoing incident wave field and the backscattered response created by its reflection at the free surface are included within the formulation. In accordance with the high-frequency and single-scattering approximations employed in the forward problem the inverse problem is cast as a generalized Radon transform. The resulting back projection operator is well suited to the teleseismic context in several respects. It is tolerant of irregularities in array geometry and source distribution and allows a full complement of global seismicity to be utilized through its accommodation of oblique incidence. By permitting both independent and simultaneous treatment of different scattering modes (reflections, transmissions, conversions) the inversion formula facilitates a direct appraisal of individual mode contributions to the recovery of structure. In particular, it becomes evident that incorporation of backscattered modes leads to (1) a better localization of structure than possible using forward scattered energy and (2) the imposition of complementary constraints on elastic properties.

In this paper, we investigate the formal inversion of synthetic teleseismic P coda waves for subsurface elastic properties using a ray theoretic approach which assumes single scattering [Bostock et al., this issue]. We consider a model comprising an idealized lithospheric suture zone whose geometrical configuration is drawn from previous deep crustal seismic studies. Two-dimensional, pseudospectral synthetic seismograms representing plane waves propagating through this model are preprocessed to extract an estimate of the scattered wave field generated by short-wavelength structure. These data are employed in a series of numerical simulations which examine the dependence of multiparameter inversion results on a range of input parameters. In particular, we demonstrate (1) the contrasting sensitivity which forward and backscattered waves display to structural recovery, (2) the diminution of the problem null-space accompanied by increased source coverage, (3) improvements in model reconstruction achieved through simultaneous treatment of multiple scattering modes, and (4) the robustness of the method for data sets with noise levels and receiver geometries that approach those of field experiments.

The Karhunen-Loéve transform, which optimally extracts coherent information from multichannel input data in a least-squares sense, is used for two specific problems in seismic data processing.The first is the enhancement of stacked seismic sections by a reconstruction procedure which increases the signal-to-noise ratio by removing from the data that information which is incoherent trace-to-trace. The technique is demonstrated on synthetic data examples and works well on real data. The Karhunen-Loéve transform is useful for data compression for the transmission and storage of stacked seismic data.The second problem is the suppression of multiples in CMP or CDP gathers. After moveout correction with the velocity associated with the multiples, the gather is reconstructed using the Karhunen-Loéve procedure, and the information associated with the multiples omitted. Examples of this technique for synthetic and real data are presented.

The retrieval of near-receiver mantle structure from scattered waves associated with teleseismic P and S and recorded on three-component, linear seismic arrays is considered in the context of inverse scattering theory. A Ray + Born formulation is proposed which admits linearization of the forward problem and economy in the computation of the elastic wave Green’s function. The high-frequency approximation further simplifies the problem by enabling (1) the use of an earth-flattened, 1-D reference model, (2) a reduction in computations to 2-D through the assumption of 2.5-D experimental geometry, and (3) band-diagonalization of the Hessian matrix in the inverse formulation. The final expressions are in a form reminiscent of the classical diffraction stack of seismic migration. Implementation of this procedure demands an accurate estimate of the scattered wave contribution to the impulse response, and thus requires the removal of both the reference wavefield and the source time signature from the raw record sections. An approximate separation of direct and scattered waves is achieved through application of the inverse free-surface transfer operator to individual station records and a Karhunen–Loeve transform to the resulting record sections. This procedure takes the full displacement field to a wave vector space wherein the first principal component of the incident wave-type section is identified with the direct wave and is used as an estimate of the source time function. The scattered displacement field is reconstituted from the remaining principal components using the forward free-surface transfer operator, and may be reduced to a scattering impulse response upon deconvolution of the source estimate. An example employing pseudo-spectral synthetic seismograms demonstrates an application of the methodology.

We computed a reflectivity image for the Earth beneath the Jemez volcanic field, New Mexico, using a novel adaptation of petroleum exploration seismic imaging. This image was obtained by applying the Kirchhoff wave field imaging method to digitally recorded teleseismic data. The volume imaged has a lateral extent of 30 km, extends to 45 km depth, and lies beneath the Valles caldera, to the west of Los Alamos, New Mexico. The derived picture of the Earth is a three-dimensional (3-D) map of the locations of impedance changes within the crust and upper mantle below the Jemez volcanic field, with a spatial resolution on the order of a kilometer. Significant features seen in the image include the base of the caldera fill; several reflectors in the crust we interpret to be associated with intrusions coming from the mantle and/or other crystallized chambers such as a low-velocity zone seen in the tomographic image; two strong reflectors coincident with the crust-mantle interface, and a zone of layered reflect

We have developed a semi-automated method of determining accurate relative phase arrival times and uncertainty estimates for teleseisms recorded on regional networks. Our analysis begins by obtaining preliminary arrival times with a single-trace phase-picking algorithm. For each possible pair of traces we then perform a search for the maximum of their cross-correlation function in order to obtain relative delay times. Depending on event magnitude, the best results are obtained by using correlation windows containing 2 to 4 sec of the initial energy pulse of the phase. The cross-correlation derived delay times are then used to generate an overdetermined system of linear equations whose solution is an optimized set of relative arrival times. We solve for these times using least squares. Cycle skipping is eliminated through the automatic re-evaluation of cross-correlation functions which yield high equation residuals. Quantitative estimates of timing uncertainty are obtained from the variance of equation

Volatiles that are transported by subducting lithospheric plates to depths greater than 100 km are thought to induce partial melting in the overlying mantle wedge, resulting in arc magmatism and the addition of significant quantities of material to the overlying lithosphere. Asthenospheric flow and upwelling within the wedge produce increased lithospheric temperatures in this back-arc region, but the forearc mantle (in the corner of the wedge) is thought to be significantly cooler. Here we explore the structure of the mantle wedge in the southern Cascadia subduction zone using scattered teleseismic waves recorded on a dense portable array of broadband seismometers. We find very low shear-wave velocities in the cold forearc mantle indicated by the exceptional occurrence of an 'inverted' continental Moho, which reverts to normal polarity seaward of the Cascade arc. This observation provides compelling evidence for a highly hydrated and serpentinized forearc region, consistent with thermal and petrological models of the forearc mantle wedge. This serpentinized material is thought to have low strength and may therefore control the down-dip rupture limit of great thrust earthquakes, as well as the nature of large-scale flow in the mantle wedge.

Deconvolving orbital surface waves for the source duration of large earthquakes and modeling the recevier functions for the earth structure beneath a broadband seismometer array in the Cascadia subduction zone

- X Li

Li, X.-Q., 1996, Deconvolving orbital surface waves for the source duration of large earthquakes and
modeling the recevier functions for the earth structure beneath a broadband seismometer array in
the cascadia subduction zone:.

Geophysical estimation by example: Environmental soundings image enhancement

- J Claerbout

Claerbout, J., 1999, Geophysical estimation by example: Environmental soundings image enhancement: Stanford Exploration Project, http://sepwww.stanford.edu/sep/prof/.

A high-resolution image of the Cascadia subduction zone from teleseismic converted phases recorded by a broadband seismic array: EOS

- J Nabelek
- X.-Q Li
- S Azevedo
- J Baunmiller
- A Fabritius
- B Leitner
- A Tréhu
- G Zandt

Nabelek, J., Li, X.-Q., Azevedo, S., Baunmiller, J., Fabritius, A., Leitner, B., Tréhu, A., and Zandt,
G., 1993, A high-resolution image of the Cascadia subduction zone from teleseismic converted
phases recorded by a broadband seismic array: EOS, Transactions of the American Geophysical
Union 74 (43, Fall meeting supplement).