We introduce an auto-encoder called SymAE that learns to redatum time-lapse data recorded in passive-seismic subsurface-monitoring experiments. SymAE analyzes the baseline and monitor records and creates new monitor records that behave as if the virtual baseline sources were active in the monitoring medium. No explicit modeling is required for this redatuming as SymAE can automatically extract both the baseline sources and the monitoring medium from large amounts of passive-seismic data. As a result, differences between the virtual and actual baseline-source records primarily contain only about the subsurface time-lapse changes with minimal pollution from the variability in passive-source characteristics such as e.g., location, signature, radiation pattern, direction-of-arrival in case of incoming planewaves etc. This is an essential first step towards realistic passive timelapse analysis as it overcomes the requirement of stationary passive sources, which currently limits conventional interferometric processing. SymAE is trained to represent passive seismic data using two separate latent codes produced by its encoder. The first latent code represents the similarity or coherency among multiple instances of passive data; therefore it is associated with the path-specific effects. The second latent code represents the remaining dissimilarities; therefore it can be associated with information that varies among the passive sources. Finally, the above-mentioned virtual records can be created by mixing latent codes of seismic records — a demo is given in the figure attached.
We introduce SymAE, an auto-encoder architecture that learns to separate multichannel passive-seismic datasets into qualitatively interpretable components: one component corresponds to path-specific effects associated with subsurface properties while the other component corresponds to the spectral signature of the passive sources. This information is represented by two latent codes produced by our encoder. The novelty that enables SymAE to achieve this separation lies with the physical symmetries that are directly embedded into the architectural design of the encoder. These symmetries impose that 1. the output of the source-specific encoder is indifferent to the ordering of the receivers; and 2. the output of the path-specific encoder is indifferent to the source signatures. Our numerical experiments demonstrate that this is sufficient for achieving the intended separation. The ability to qualitatively distinguish between source- and path-induced effects plays a critical role for time-lapse monitoring of visco-acoustic subsurface models where data is generated from induced passive seismic sources e.g., during CO2 injection or hydraulic fracturing. Here the problem suffers from inherent ambiguities in whether the time-lapse changes in the data should be attributed to subsurface changes such as P-wave velocity, mass density, and seismic quality factor (i.e., path effects) or because of difficulties in physically-reproducing the source wavelet (i.e. source effects). SymAE resolves these ambiguities by construction and enables reliable subsurface monitoring in these settings. We provide numerical results to show that we can accurately detect changes arising from both effects.
Systems and methods for performing focused blind deconvolution of signals received by a plurality of sensors are disclosed. In some embodiments, this may include determining a cross-correlation of first and second signals, obtaining a cross-correlation of a first response function and a second response function based on the cross-correlation of the first and second signals and subject to a first constraint that the first and second response functions are maximally white, and obtaining the first and second response functions based on the cross-correlation of the first and second response functions and subject to a second constraint that the first and second response functions are maximally front-loaded.
We present a robust factorization of the teleseismic waveforms resulting from an earthquake source into signals that originate from the source and signals that characterize the path effects. The extracted source signals represent the earthquake spectrum and its variation with azimuth. Unlike most prior work on source extraction, our method is data-driven, and it does not depend on any path-related assumptions e.g., the empirical Green’s function. Instead, our formulation involves focused blind deconvolution (FBD), which associates the source characteristics with the similarity among a multitude of recorded signals. We also introduce a new spectral attribute, to be called redshift, which is based on the Fraunhofer approximation. Redshift describes source-spectrum variation, where a decrease in frequency occurs at the receiver in the opposite direction of unilateral rupture propagation. Using the redshift, we identified unilateral ruptures during two recent strike-slip earthquakes. The FBD analysis of an earthquake, which originated in the eastern California shear zone, is consistent with observations from local seismological or geodetic instrumentation.
We introduce a novel multichannel blind deconvolution (BD) method that extracts sparse and front-loaded impulse responses from the channel outputs, i.e., their convolutions with a single arbitrary source. Unlike most prior work on BD, a crucial feature of this formulation is that it does not encode support restrictions on the unknowns, except for fixing their duration lengths. The indeterminacy inherent to BD, which is difficult to resolve with a traditional l1 penalty on the impulse responses, is resolved in our method because it seeks a first approximation where the impulse responses are: “maximally white” over frequency-encoded as the energy focusing near zero lag of the impulse-response temporal autocorrelations; and “maximally front-loaded”-encoded as the energy focusing near zero time of the impulse responses. Hence, we call the method focused BD (FBD). It partitions BD into two separate optimization problems and uses the focusing constraints in succession. The respective constraints in both these problems are removed as the iterations progress. A multichannel BD problem whose physics calls for sparse and front-loaded impulse responses arises in seismic inversion, where the impulse responses are the Green’s function evaluations at different receiver locations, and the operation of a drill bit inputs the noisy and correlated source signature into the subsurface. We demonstrate the benefits of FBD using seismic-while-drilling numerical experiments, where the noisy data recorded at the receivers are hard to interpret, but FBD can provide the processing essential to separate the drill-bit (source) signature from the interpretable Green’s function.
One of the formation properties that most can impact drilling risk is pore-fluid pressure. While the literature abounds with analyses, computation and laboratory experiments, and case studies purportedly providing the remote estimation of pressure, none has yet lead to a technology that is confidently adopted in general drilling situations, or even in well-defined specific situations. It is a consequence of physics that direct measurement of pressure can be performed only by sensors in contact with the medium; whereas indirect, remote estimation may be enabled by the effect of pressure on mechanical or electromagnetic fields propagating through the bulk to recording receivers. Technology has not been confidently adopted mainly due to large uncertainties of how measurable formation properties relate measurable fields to pressure. To advance this situation, in our research program we propose to combine: a new, hypothetical downhole tool using acoustic sources with geophones and electric receivers along the drill string; a new LWD system, firing drill-string sources designed to concentrate acoustic energy in a spatially compact locus many 10s of meters ahead of the bit; and a new real-time inversion problem comprising estimation of zonation i.e., formation layer interfaces, jointly from concurrent drilling-operation parameters and seismoelectric gradient-response signals, plus estimation of uniform acoustic and electric properties within depth intervals. The aim of this program, ultimately to be conjoined with petrophysical and geomechanical modeling based on zonation and interval properties, is to estimate pore pressure many 10s of meters ahead of the drill bit. This abstract presents a preliminary outline of the tool and system, a formal sensitivity analysis of the inversion computation procedure with respect to the properties being estimated, and numerical simulations of just the seismoelectric aspect of its overall operation, in a field populated by properties from actual well logs.
We detail a novel multichannel blind deconvolution (BD) algorithm that extracts the cross-correlated or interferometric Green’s functions from the records due to a single noisy source. In this framework, we perform a least-squares fit of the crosscorrelated records, rather than the raw records, which greatly reduces the indeterminacy inherent to traditional BD methods. To resolve the remaining degrees of freedom, we seek a first approximation where the Green’s functions are maximally white, and relax this requirement as the iterations progress. This requirement is encoded as the focusing near zero lag of the energy of the auto-correlated Green’s functions, hence we call the method focused blind deconvolution (FBD). We demonstrate the benefits of FBD using synthetic seismic-while-drilling experiments to look around and ahead of a bore-hole. Here, the noise due to the operation of the drill bit is not directly usable for reflection imaging, but FBD can provide the processing needed to extract the noise signature without unrealistically assuming the drill noise to be uncorrelated. The interferometric Green’s functions obtained from FBD can either be directly imaged or further processed to output the usual subsurface Green’s functions. Note that FBD is designed for an acquisition where the noise is recorded for a longer time period than the propagation time of the seismic waves e.g., as could be done during normal drilling operations. Traditional seismic imaging may now be augmented by added information around and ahead of the drill bit, potentially allowing less frequent traditional surveys.
Focused blind deconvolution (FBD) is the state-of-the-art blind deconvolution algorithm that can simultaneously estimate the subsurface Green’s function and the earthquake source signature from the records at multiple receiver stations. The inherent indeterminacy in multichannel blind deconvolution, which is difficult to resolve with the traditional sparsity assumptions on the Green’s functions, is resolved in FBD because it seeks a solution where the Green’s functions are maximally “white” and “front-loaded”. These assumptions, which are suitable in the seismic context, are numerically encoded as energy focusing constraints. FBD allows reliable blind deconvolution of the earthquake records without any of the following prerequisites: knowledge on the focal mechanism of the earthquake; synthetic wave modeling to construct the deconvolution operator; identification or windowing of the body-wave phases; and accurate determination of the source duration. Obtaining knowledge about the earthquake source is only possible by analyzing the far-field records as most of the events occur in places with sparse local seismological or geodetic instrumentation. In FBD, the source signature is isolated from the records by undoing the propagation effects in order to learn the fault mechanism. In addition to this, the estimated Green’s function can be independently studied to understand the subsurface mechanical properties. For example, the FBD-estimated Green’s functions due to multiple events, with arbitrary source signatures, occurring at the same location can be interpreted to map the time-lapse changes in these properties. FBD is a multichannel processing algorithm, i.e., it heavily relies on fact that the waves are recorded at multiple far-field receiver stations. Also, FBD requires that the records are sufficiently low-pass filtered such that the fault length of the earthquake is much smaller than the wavelength corresponding to the maximum frequency. In this abstract, we deconvolve the events occurred in the Tohuku region to test whether the FBD outputs are conforming with the existing literature.
In the case of multi-parameter full-waveform inversion, the computation of the additional Hessian terms that contain derivatives with respect to more than one type of parameter is necessary. If a simple gradient-based minimization is used, different choices of parameterization can be interpreted as different preconditioners that change the condition number of the Hessian. If the non-linear inverse problem is well-posed, then the inversion should converge to a band-limited version of the true solution irrespective of the parameterization choice, provided we start sufficiently close to the global minimum. However, the choice of parameterization will affect the rate of convergence to the exact solution and the best choice of parameterization is the one with the fastest rate. In this paper, we search for the best choice for acoustic multi-parameter full-waveform inversion, where 1. anomalies with a size less than a quarter of the dominant wavelength have to be estimated without the risk of converging to a local minimum; 2. the scattered wavefield is recorded at all the scattering angles; 3. a steepest-descent minimization scheme is used. Our examples suggest that the best choice of parameterization depends on the contrast of the subsurface scatterer that the inversion tries to estimate. Based on the results, we observe that there is no best parameterization choice for full-waveform inversion. We also observe that a parameterization using the acoustic impedance and mass density has the worst convergence rate. Finally, we also show that the parameterization analysis during a hierarchical inversion, where the data have limited scattering angles, only helps to select a subspace for mono-parameter inversion. For multi-parameter hierarchical inversion, the search for the best parameterization in terms of the convergence speed might be obfuscated by non-uniqueness problems.
We consider the question of deblending for seismic shot records generated from simultaneous random sources at different locations, i.e., how to decompose them into isolated records involving one source at a time. As an example, seismic-while-drilling experiments use active drill-string sources and receivers to look around and ahead of the borehole, but these receivers also record noise from the operation of the drill bit. A conventional method for deblending is independent component analysis (ICA), which assumes a “cocktail-party” mixing model where each receiver records a linear combination of source signals assumed to be statistically independent, and where only one source can have a Gaussian distribution. In this note, we extend the applicability of ICA to seismic shot records with markedly more complex mixing models with unknown wave kinematics, provided the following assumptions are met. 1. The active source is fully controllable, which means that it can be used to input a wide range of non-Gaussian random signals into the subsurface. 2. The waves are a linear function of the source, have a finite speed of propagation, and follow finite-length paths. The last assumption implies a scale separation, in frequency, between the mixing matrix elements (Green’s functions) and the random input signals. In this regime, we show that the key to the success of ICA is careful windowing to frequency bands over which the Green’s functions are approximately constant.
In the near surface with unconsolidated soils, shear-wave properties can often be characterised better and with a higher resolution than compressional-wave properties. To enable imaging ahead of a tunnel-boring machine, we developed a seismic prediction system with a few shear-wave vibrators and horizontal receivers. The boring process is interrupted at regular intervals to carry out active surveys. The vibrators are then pushed against the rock or soil in front of the cutting wheel of the machine. The design of the vibrators is based on linear synchronous motor technology that can generate very low frequencies, starting at 5 Hz. These vibrators generate a force in a direction perpendicular to the tunnel axis. Horizontal receivers measure the particle velocity, mainly due to the horizontally polarised shear waves. Because imaging with conventional migration methods suffers from artefacts, caused by the incomplete aperture and inaccuracies in the assumed velocity model, we use two-dimensional horizontally polarised shear full-waveform inversion to resolve the subsurface shear properties. The classic cycle-skipping problem, which can make the application of full-waveform inversion cumbersome, is avoided by the capacity of the vibrators to generate low frequencies. In this paper, we demonstrate the capabilities of the proposed seismic system through a number of synthetic and field experiments.
Least-squares inversion of seismic arrivals can provide remarkably detailed models of the Earth’s subsurface. However, cycle skipping associated with these oscillatory arrivals is the main cause for local minima in the least-squares objective function. Therefore, it is often difficult for descent methods to converge to the solution without an accurate initial large-scale velocity estimate. The low frequencies in the arrivals, needed to update the large-scale components in the velocity model, are usually unreliable or absent. To overcome this difficulty, we propose a multi-objective inversion scheme that uses the conventional least-squares functional along with an auxiliary data-domain objective. As the auxiliary objective effectively replaces the seismic arrivals by bumps, we call it the bump functional. The bump functional minimization can be made far less sensitive to cycle skipping and can deal with multiple arrivals in the data. However, it can only be used as an auxiliary objective since it usually does not provide a unique model after minimization even when the regularized-least-squares functional has a unique global minimum and hence a unique solution. The role of the bump functional during the multi-objective inversion is to guide the optimization towards the global minimum by pulling the trapped solution out of the local minima associated with the least-squares functional whenever necessary. The computational complexity of the bump functional is equivalent to that of the least-squares functional. In this paper, we describe various characteristics of the bump functional using simple and illustrative numerical examples. We also demonstrate the effectiveness of the proposed multi-objective inversion scheme by considering more realistic examples. These include synthetic and field data from a cross-well experiment, surface-seismic synthetic data with reflections and synthetic data with refracted arrivals at long offsets.
In the near-surface with unconsolidated soils, shear properties can be well imaged, sometimes better than P-wave properties. To facilitate ground prediction ahead of a tunnel boring machine (TBM), active ‘surveys’ with shear-wave vibrators are carried out during boring. In such surveys, only a few shear-wave vibrators can be placed in front of the machine’s cutter head. The vibrators inject a force in the direction perpendicular to the drilling path. We use a vibrator that is capable of exciting low frequencies. Therefore, a full waveform inversion (FWI) approach can be used, which would make the imaging more automatic. Imaging with conventional migration methods suffers from artifacts caused by incomplete aperture and inadequate velocity analysis. In this abstract, we examine the potential of 2-D SH FWI to reconstruct anomalies. In contrast to FWI for hydrocarbon exploration, we have access to reliable low frequencies in the data and are working in the near-field regime. The very limited maximum offset causes diving waves to be absent. This lack of aperture makes it difficult to reconstruct the shear-wave velocity away from the source-receiver array even in the presence of low frequencies. Our study shows that FWI with SH waves should offer a valuable look-ahead capability.
To overcome the local minima problem in FWI, we propose to use an auxiliary data-domain objective function during inversion. It reduces the data to a simpler form by squaring, followed by blurring to ensure that events that are too far apart can still interact during the inversion. As it effectively replaces seismic arrivals by bumps, we call it the bump functional. This objective function is less sensitive to cycle skipping. Its role is to guide the inversion towards the global minimum by pulling the trapped solution out of the local minima associated with the least-squares functional whenever necessary. Waveform inversion cannot be performed with only the auxiliary objective function because it is insensitive to the polarity of the arrivals and the source signature. Therefore, we alternate between minimization with this and the classic least-squares functional. We confirm the validity of the approach using a simple numerical example with reflection data.
With single-parameter full waveform inversion, estimating the inverse of the Hessian matrix will accelerate the convergence, but is computationally expensive. Therefore, an approximate Hessian, which is easier to compute, is often used. Similarly, in the case of multi-parameter full waveform inversion, the computation of the Hessian terms that contain derivatives with respect to more than one type of parameter, called cross-parameter Hessian terms, is not usually feasible. If the non-linear inverse problem is well-posed, then the result should be independent of the parametrization choice provided we start close to the global minimum. However, the choice of parametrization will affect the rate of convergence to the exact solution and the ‘best’ choice of parametrization is the one with the fastest rate. If the inverse problem is ill-posed the choice of parametrization introduces a bias towards a particular solution among the non-unique ones that explain the data. This obfuscates the search for the ‘best’ parametrization. We investigated parametrization choices for a 2-D SH experiment where only the reflected wavefield is recorded. Our numerical examples suggest that certain type of scatterers are better inverted by one parametrization choice than another due to the parametrization bias. Therefore, there is nothing like a ‘best’ parametrization in these single-component SH examples.
Least-squares inversion of seismic reflection waveforms can reconstruct remarkably detailed models of the Earth’s subsurface. However, the cycle-skipping associated with the highfrequency waveforms are responsible for spurious local minima in its objective function. Therefore, it is often difficult for descent methods to converge to the true model without starting from an accurate large-scale velocity estimate. To partially overcome this difficulty, we propose to use multiple objective functions for inversion. An additional constraint based on cross-correlation is added to the conventional least-squares (LS) inversion. Observations suggest this will result in a model with an accurate background velocity and reflectivity that corresponds to the global minimum of the least-squares objective function. Optimization of a cross-correlation based function (CC) in the data domain appears to pull the trapped solution out of the local minima associated with the least-squares objective function, and vice versa. Some 2-D numerical tests confirm the validity of the approach in the absence of low temporal data frequencies, starting from a constant initial velocity model.
The theory of supervirtual interferometry is modified so that free-surface related multiple refractions can be used to enhance the signal-to-noise ratio (SNR) of primary refraction events by a factor proportional to sqrt(Ns), where Ns is the number of post-critical sources for a specified refraction multiple. We also show that refraction multiples can be transformed into primary refraction events recorded at virtual hydrophones located between the actual hydrophones. Thus, data recorded by a coarse sampling of ocean bottom seismic (OBS) stations can be transformed, in principle, into a virtual survey with P times more OBS stations, where P is the order of the visible free-surface related multiple refractions. The key assumption is that the refraction arrivals are those of head waves, not pure diving waves. The effectiveness of this method is validated with both synthetic OBS data and an OBS data set recorded offshore from Taiwan. Results show the successful reconstruction of far-offset traces out to a source receiver offset of 120 km. The primary supervirtual traces increase the number of pickable first arrivals from approximately 1600 to more than 3100 for a subset of the OBS data set where the source is only on one side of the recording stations. In addition, the head waves associated with the first order free surface refraction multiples allow for the creation of six new common receiver gathers recorded at virtual OBS station located about half way between the actual OBS stations. This doubles the number of OBS stations compared to the original survey and increases the total number of pickable traces from approximately 1600 to more than 6200. In summary, our results with the OBS data demonstrate that refraction interferometry can sometimes more than quadruple the number of usable traces, increase the source receiver offsets, fill in the receiver line with a denser distribution of OBS stations, and provide more reliable picking of first arrivals. A potential liability of this method is that long-offset refraction arrivals extracted by interferometry might not necessarily be head waves from deeper refraction interfaces. The extracted arrivals might be from a shallower interface, and so only supply redundant information about that portion of the subsurface. Nevertheless, our tomography example shows the value of these arrivals in reducing artefacts and increasing resolution in the tomogram.
The theory of supervirtual interferometry is modified so that free-surface related multiple refractions can be used to enhance the signal-to-noise ratio (SNR) of primary refraction events by a factor proportional to Ns, where Ns is the number of post-critical sources for a specified refraction multiple. We also show that refraction multiples can be transformed into primary refraction events recorded at virtual hydrophones located between the actual hydrophones. Thus, data recorded by a coarse sampling of ocean bottom seismic (OBS) stations can be transformed, in principle, into a virtual survey with P times more OBS stations, where P is the order of the visible free-surface related multiple refractions. The key assumption is that the refraction arrivals are those of head waves, not pure diving waves. The effectiveness of this method is validated with both synthetic OBS data and an OBS data set recorded offshore from Taiwan. Results show the successful reconstruction of far-offset traces out to a source receiver offset of 120 km. The primary supervirtual traces increase the number of pickable first arrivals from approximately 1600 to more than 3100 for a subset of the OBS data set where the source is only on one side of the recording stations. In addition, the head waves associated with the first-order free-surface refraction multiples allow for the creation of six new common receiver gathers recorded at virtual OBS station located about half way between the actual OBS stations. This doubles the number of OBS stations compared to the original survey and increases the total number of pickable traces from approximately 1600 to more than 6200. In summary, our results with the OBS data demonstrate that refraction interferometry can sometimes more than quadruple the number of usable traces, increase the source receiver offsets, fill in the receiver line with a denser distribution of OBS stations, and provide more reliable picking of first arrivals. A potential liability of this method is that long-offset refraction arrivals extracted by interferometry might not necessarily be head waves from deeper refraction interfaces. The extracted arrivals might be from a shallower interface, and so only supply redundant information about that portion of the subsurface. Nevertheless, our tomography example shows the value of these arrivals in reducing artefacts and increasing resolution in the tomogram.
Inverting for the subsurface velocity distribution by refraction traveltime tomography is a well‐accepted imaging method by both the exploration and earthquake seismology communities. A significant drawback, however, is that the recorded traces become noisier with increasing offset from the source position, and so accurate picking of traveltimes in far‐offset traces is often prevented. To enhance the signal‐to‐noise ratio (SNR) of the far‐offset traces, we present the theory of supervirtual refraction interferometry where the SNR of far‐offset head‐wave arrivals can be theoretically increased by a factor proportional to ￼; here, N is the number of receiver or source positions associated with the recording and generation of the head‐wave arrival. There are two steps to this methodology: correlation and summation of the data to generate traces with virtual head‐wave arrivals, followed by the convolution of the data with the virtual traces to create traces with supervirtual head‐wave arrivals. This method is valid for any medium that generates head‐wave arrivals recorded by the geophones. Results with both synthetic traces and field data demonstrate the feasibility of this method. There are at least four significant benefits of supervirtual interferometry: (1) an enhanced SNR of far‐offset traces so the first‐arrival traveltimes of the noisy far‐offset traces can be more reliably picked to extend the useful aperture of the data, (2) the SNR of head waves in a trace that arrive later than the first arrival can be enhanced for accurate traveltime picking and subsequent inversion by later‐arrival traveltime tomography, (3) common receiver‐pair gathers can be analysed to detect the presence of diving waves in the first arrivals, which can be used to assess the nature of the refracting boundary, and (4) the source statics term is eliminated in the correlation operations so that the timing of the virtual traces is independent of the source excitation time. This suggests the possibility of applying this method to earthquake data recorded by receivers that are inline with the refraction paths and source locations.
Water is an important natural resource, which is available both on surface as well as in recharge zone of weathered layer and in various other suitable water reservoir formations/structures below the surface. As the availability of surface water is erratic and irregular one needs to study and map the underground water reservoirs. Dhanbad district of Jharkhand state is in general part of hard rock terrain, which is mainly covered by Chottanagpur Granite Gneissic Complex and has no perennial river sources for water supply. Therefore, in view of the upcoming industrialization in the region there is need to exploit groundwater resource, which is limited and confined to fractured and weathered zones. Even though the region receives copious rain, the terrain and soil condition allows little storage of water. Hence, the region faces shortage of water in dry seasons. Therefore, it is necessary to explore and study the ground water resources effectively using suitable techniques. Various workers have successfully applied Remote Sensing technique in exploration, evaluation and management of ground water resources in an area as a whole and the results have been published. In this paper also mapping and management strategies for ground water resources have been studied, by analyzing IRS LISS II multi band remote sensing data along with geological as well as geophysical resistivity sounding data carried out at places in GIS environment. Finally, based on the integrated thematic maps, weighted analysis in Arc GIS ground water resource prospect map of the area has been prepared and discussed. The study has brought out that the high groundwater potential zones are confined along lineaments and in pediment areas. Also alluvial fills, valley fills form potential zones. The other geomorphic units like buried pediplain, peniplains and denundational hills form zones of moderate to good groundwater prospects. Dissected pediments, inselberg complex, undulating upland and buried pediment with intermontane valley are zones of poor prospects. Very poor regions occupy a small part of total study area and are mainly confined to undulating upland and residual hills.
A supervirtual interferometry (SVI) method is presented that enhances the signal-to-noise ratio of core mantle boundary (CMB) diffractions by O(sqrt(N)), where N is the number of inline receivers that record the CMB diffractions from more than one event. Here, the events are chosen to be inline with the receivers along the same great circle. Results with synthetic data and teleseismic records recorded by USArray stations demonstrate that formerly unusable records with low signal-to-noise ratio (SNR) can be transformed into ones with high SNR where the CMB diffractions are clearly visible. Another benefit is that SVI allows for the virtual recording of an earthquake at stations not deployed during the time of the earthquake. This means that transient arrays such as USArray can extend the aperture of one recorded earthquake from the West coast to the East coast, even though the teleseism might have only been recorded during the West Coast deployment. In summary, SVI applied to teleseismic data can significantly enlarge the catalog and increase the aperture of usable records for analyzing CMB diffractions. The potential drawback of this method is that it generally provides the correct kinematics of CMB diffractions, but does not necessarily preserve correct amplitude information.
Inverting for the subsurface velocity distribution by refraction traveltime tomography is a well accepted imaging method by both the exploration and earthquake seismology communities. A significant drawback, however, is that the recorded traces become noisier with increasing offset from the source position, and so prevents accurate picking of traveltimes in far offset traces. To enhance the signal to noise ratio of the far offset traces, we present the theory of super virtual refraction interferometry where the signal to noise ratio (SNR) of far offset head wave arrivals can be theoretically increased by a factor proportional to N; here, N is the number of receiver and source positions associated with the recording and generation of the head wave arrival. There are two steps to this methodology: correlation and summation of the data to generate traces with virtual head wave arrivals, followed by the convolution of the data with the virtual traces to create traces with super virtual head wave arrivals. This method is valid for any medium that generates head wave arrivals. There are at least three significant benefits to this methodology: 1). enhanced SNR of far offset traces so the first arrival traveltimes of the noisy far offset traces can be more reliably picked to extend the useful aperture of data, 2). the SNR of head waves in a trace that arrive after the first arrival can be enhanced for accurate traveltime picking and subsequent inversion by traveltime tomography, and 3). common receiver pair gathers can be analyzed to detect the presence of diving waves in the first arrivals, which can be used to assess the nature of the refracting boundary.
We present successful results for applying refraction interferometry to ocean bottom seismic (OBS) data. The OBS data were recorded by six inline OBS stations with a 15 km station spacing and a source ship shooting every 150 meters; the maximum source offset from an OBS station is 181 km. Each virtual trace was created by correlating and stacking up to 150 trace pairs to create a super-virtual refraction arrival having a theoretical signal-to-noise ratio (SNR) enhancement of up to 12:1. Free-surface refraction multiples were also utilized to enhance the SNR of primary refractions and virtually double the number of OBS sites from six to twelve stations. Results show the successful reconstruction of far-offset traces out to a source-receiver offset of 120 km. The super-virtual traces increase the number of pickable first arrivals from approximately 1,600 to more than 3,100 for a subset of the OBS data where the source is only on one side of the recording stations. In addition, the head waves associated with the first-order free-surface multiples allow for the creation of six new common receiver gathers (CRGs) recorded at virtual OBS stations, located about 5 km from any of the actual OBS stations. These new traces double the number of OBS stations compared to the original survey and increases the number of pickable traces from 1600 to 6200. In summary, our results with this OBS data set demonstrate that refraction interferometry can more than triple the number of pickable first arrivals in long-offset traces. This suggests the possibility that the number of independent OBS stations can be increased by N-fold if the free-surface refraction multiples up to the Nth-order are of high SNR and if the recording time is appropriately lengthened.
Refraction surveys are a well-established method of imaging subsurface velocities, both in terms of the deep crustal structure at global scales and in the shallow near surface. These surveys generally involve deploying an array of receivers on the surface (or water bottom) and recording arrivals from a seismic source initiated at or near the surface. In an ideal case where an interface defines a boundary with a sharp increase in velocity, the head-wave refraction arrivals are described by raypaths which follow a diving-wave path down to the interface and refract along it, then follow a diving-wave path back to the surface (or water bottom) where the receivers are located. These arrivals, if they have a suffi ciently high signal-to-noise ratio (SNR), are picked in the shot gathers and inverted to give the traveltime tomograms in either exploration-scale or global-scale tomography. However there are two common limitations of conventional refraction tomography:
As result the maximum depth of investigation of refraction surveys is limited by the inability to identify later head-wave arrivals in the record. Refraction interferometry offers the possibility of overcoming these limitations as it aligns and stacks together refraction arrivals that propagate along the same portion of the refractor (Dong et al., 2006). Similar to the NMO correction that flattens reflections in a CMP gather, interferometric correlation of traces recorded at two fixed geophones aligns the refraction arrivals from the same refractor; this alignment is valid for a large number of different source positions. Th e result is that head-wave arrivals generated from diff erent sources can be stacked together to form virtual head-wave traces with an enhanced SNR (Bharadwaj and Schuster, 2010). This potentially offers a significant improvement over conventional processing of head-wave arrivals