The interaction of a solitary wave front with an interface formed by two strongly-nonlinear non-c... more The interaction of a solitary wave front with an interface formed by two strongly-nonlinear non-cohesive granular lattices displays rich behaviour, characterized by the breakdown of continuum equations of motion in the vicinity of the interface. By treating the solitary wave as a quasiparticle with an effective mass, we construct an intuitive (energy and linear momentum conserving) discrete model to predict the amplitudes of the transmitted solitary waves generated when an incident solitary wave front, parallel to the interface, moves from a denser to a lighter granular hexagonal lattice. Our findings are corroborated with simulations. We then successfully extend this model to oblique interfaces, where we find that the angle of refraction and reflection of a solitary wave follows, below a critical value, an analogue of Snell's law in which the solitary wave speed replaces the speed of sound, which is zero in the sonic vacuum.
We study seismic noise recorded in the northeast of the Netherlands by beamforming and by using e... more We study seismic noise recorded in the northeast of the Netherlands by beamforming and by using empirical Green's functions obtained by seismic interferometry. From beamforming we found differences in noise directions in different frequency bands. The main source region for primary microseisms (0.05-0.08 Hz) is in the west-northwest direction, while the secondary microseisms (0.1-0.14 Hz) have a west-southwest back azimuth. Furthermore, we observed a fast (∼4 km=s) arrival corresponding to the Rayleigh wave overtone. This arrival is also in the secondary microseism band (between 0.15 and 0.2 Hz), but has a west-northwest back azimuth. Both arrivals in the secondary microseism band gain in strength during winter, as does the average wave height in the North Atlantic. We measured phase velocity dispersion curves from both beamforming and noise cross-correlations, as well as group velocity from the latter. These are then jointly inverted for an average 1D S-wave model. The results show how the combination of different methods leads to a more complete characterization of the propagation modes and an improved knowledge of the subsurface, especially as the group velocity measurements increase the upper frequency limit of analysis, providing valuable information of the shallowest subsurface.
1] The successful surface waves retrieval in solid-Earth seismology using long-time correlations ... more 1] The successful surface waves retrieval in solid-Earth seismology using long-time correlations and subsequent tomographic images of the crust have sparked interest in extraction of subsurface information from noise in the exploration seismology. Subsurface information in exploration seismology is usually derived from body-wave reflections > 1 Hz, which is challenging for utilization of ambient noise. We use 11 h of noise recorded in the Sirte basin, Libya. First, we study the characteristics of the noise. We show that the bulk of the noise is composed of surface waves at frequencies below 6 Hz. Some noise panels contain nearly vertically traveling events. We further characterize these events using a beamforming algorithm. From the beamforming, we conclude that these events represent body-wave arrivals with a fairly rich azimuthal distribution. Having body-wave arrivals in the noise is a prerequisite for body-wave reflections retrieval. We crosscorrelate and sum the recorded ambient-noise panels to retrieve common-source gathers, following two approaches-using all the noise and using only noise panels containing body-wave arrivals likely to contribute to the reflections retrieval. Comparing the retrieved gathers with active seismic data, we show that the two-way traveltimes at short offsets of several retrieved events coincide with those of reflections in the active data and thus correspond to apexes of reflections. We then compare retrieved stacked sections of the subsurface from both approaches with the active-data stacked section and show that the reflectors are consistent along a line. The results from the second approach exhibit the reflectors better.
We study theoretically the interaction of elastic waves caused by non-linearities of rock elastic... more We study theoretically the interaction of elastic waves caused by non-linearities of rock elastic moduli, and assess the possibility to use this phenomenon in hydrocarbon exploration and in the analysis of rock samples. In our calculations we use the five-constant model by Gol'dberg. It is shown that the interaction of plane waves in isotropic solids is completely described by five coupling coefficients, which have the same order of magnitude. By considering scattering of compressional waves generated by controlled sources at the Earth surface from a non-linear layer at the subsurface, we conclude that non-linear signals from deep formations are unlikely to be measured with the current level of technology. Our analysis of field tests where non-linear signals were measured, suggests that these signals are generated either in the shallow subsurface or in the vicinity of sources. Non-linear wave interaction might be observable in lab tests with focused ultrasonic beams. In this case, the non-linear response is generated in the secondary parametric array formed by linear beams scattered from inclusions. Although the strength of this response is controlled by non-linearity of the surrounding medium rather than by non-linearity of inclusions, its measurement can help to obtain better images of rock samples.
Keywords: Body waves Interferometry Ambient noise Microseism Lithosphere Mots cle´s : Ondes de vo... more Keywords: Body waves Interferometry Ambient noise Microseism Lithosphere Mots cle´s : Ondes de volume Interfé romé trie Bruit ambiant Microsé isme Lithosphè re A B S T R A C T
Several geophysical methods exist to delineate the lower interface of a sedimentary basin. Most p... more Several geophysical methods exist to delineate the lower interface of a sedimentary basin. Most popularly employed are gravity and magnetic surveys and surface-wave inversion. While all three methods are successful overall in estimating an average basin depth, they fail to find a more detailed depth variation. As an alternative, we consider three passive seismic techniques, using especially body waves. We analyze 40 hours of data, recorded with 110 stations installed over the Abu Gharadig basin in Egypt. In an earlier study we found the frequency band of 0.09-1.0 Hz to be dominated by body waves. As a first method we apply body-wave seismic interferometry (SI). Using body-wave noise, we extract PP and SS reflections from the basin floor. We estimate the depth of the basin to be around 4.8 km. As a second technique we estimate the resonance spectra of the basin, using the horizontal-to-vertical (H/V) spectral ratio. Using surface-wave noise, we find an extremum that is probably related to the complete sedimentary package. Using this peak, we find a basin depth of 5.4 km. Using S-phase arrivals, we find two extrema in the H/V, which are probably related to the S-wave resonances of two distinct layers in the basin. As a third method we compute receiver functions (RFs). Based on the RFs, we can confirm the presence of a large interface in the upper crust, but we cannot well constrain its depth.
Seismic interferometry involves the crosscorrelation of responses at different receivers to obtai... more 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 seismology͒ or a noise signal ͑as in passive seismology͒, 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 ambient noise and the subsequent tomographic determination of the surfacewave velocity distribution of the subsurface. Seismic interferometry is not restricted to retrieving direct waves between receivers. In a classic paper, Claerbout shows that the autocorrelation of the transmission response of a layered medium gives the plane-wave reflection response of that medium. This is essentially 1D reflected-wave interferometry. Similarly, the crosscorrelation of the transmission responses, observed at two receivers, of an arbitrary inhomogeneous medium gives the 3D reflection response of that medium. One of the main applications of reflected-wave interferometry is retrieving the seismic reflection response from ambient noise and imaging of the reflectors in the subsurface. A common aspect of direct-and reflected-wave interferometry is that virtual sources are created at positions where there are only receivers without requiring knowledge of the subsurface medium parameters or of the positions of the actual sources.
One application of seismic interferometry is to retrieve the impulse response ͑Green's function͒ ... more One application of seismic interferometry is to retrieve the impulse response ͑Green's function͒ from crosscorrelation of ambient seismic noise. Various researchers show results for retrieving the surface-wave part of the Green's function. However, reflection retrieval has proven more challenging. We crosscorrelate ambient seismic noise, recorded along eight parallel lines in the Sirte basin east of Ajdabeya, Libya, to obtain shot gathers that contain reflections. We take advantage of geophone groups to suppress part of the undesired surface-wave noise and apply frequency-wavenumber filtering before crosscorrelation to suppress surface waves further.After comparing the retrieved results with data from an active seismic exploration survey along the same lines, we use the retrieved reflection data to obtain a migrated reflection image of the subsurface.
Surface-wave analysis is a key tool for seismologists, ranging from near-surface characterization... more Surface-wave analysis is a key tool for seismologists, ranging from near-surface characterization in geotechnical applications to global seismology. Even in exploration seismology, where surface waves are regarded as a kind of noise, the fact that they typically represent the bulk of the recorded energy makes an understanding of surface-wave propagation important. On the other hand, the heterogeneity of the near surface can make such analyses difficult since the heterogeneity is responsible for scattering and mode conversion.
In recent years, there has been an increase in the deployment of relatively dense arrays of seism... more In recent years, there has been an increase in the deployment of relatively dense arrays of seismic stations. The availability of spatially densely sampled global and regional seismic data has stimulated the adoption of industry-style imaging algorithms applied to converted-and scattered-wave energy from distant earthquakes, leading to relatively high-resolution images of the lower crust and upper mantle. We use seismic interferometry to extract reflection responses from the coda of transmitted energy from distant earthquakes. In theory, higher-resolution images can be obtained when migrating reflections obtained with seismic interferometry rather than with conversions, traditionally used in lithospheric imaging methods. Moreover, reflection data allow the straightforward application of algorithms previously developed in exploration seismology. In particular, the availability of reflection data allows us to extract from it a velocity model using standard multichannel data-processing methods. However, the success of our approach relies mainly on a favourable distribution of earthquakes. In this paper, we investigate how the quality of the reflection response obtained with interferometry is influenced by the distribution of earthquakes and the complexity of the transmitted wavefields. Our analysis shows that a reasonable reflection response could be extracted if (1) the array is approximately aligned with an active zone of earthquakes, (2) different phase responses are used to gather adequate angular illumination of the array and (3) the illumination directions are properly accounted for during processing. We illustrate our analysis using a synthetic data set with similar illumination and source-side reverberation characteristics as field data recorded during the 2000-2001 Laramie broad-band experiment. Finally, we apply our method to the Laramie data, retrieving reflection data. We extract a 2-D velocity model from the reflections and use this model to migrate the data. On the final reflectivity image, we observe a discontinuity in the reflections. We interpret this discontinuity as the Cheyenne Belt, a suture zone between Archean and Proterozoic terranes.
Empirical Green's functions (EGFs) between receivers can be obtained from seismic interferometry ... more Empirical Green's functions (EGFs) between receivers can be obtained from seismic interferometry through cross-correlation of pairs of ground motion records. Full reconstruction of the Green's function requires diffuse wavefields or a uniform distribution of (noise) sources. In practice, EGFs differ from actual Green's functions because wavefields are not diffuse and the source distribution not uniform. This difference, which may depend on medium heterogeneity, complicates (stochastic) medium characterization as well as imaging and tomographic velocity analysis with EGFs. We investigate how source distribution and scale lengths of medium heterogeneity influence surface wave Green's function reconstruction in the period band of primary microseisms (T = 10-20 s). With data from a broad-band seismograph array in SE Tibet we analyze the symmetry and travel-time properties of surface wave EGFs from correlation of data in different windows: ambient noise, direct surface waves, and surface wave coda. The EGFs from these different windows show similar dispersion characteristics, which demonstrates that the Green's function can be recovered from direct wavefields (e.g., ambient noise or earthquakes) or from wavefields scattered by heterogeneity on a regional scale. Directional bias and signal-to-noise ratio of EGFs can be understood better with (plane wave) beamforming of the energy contributing to EGF construction. Beamforming also demonstrates that seasonal variations in cross-correlation functions correlate with changes in ocean activity.
The recent introduction of novel redatuming techniques, based on the principles of time-reversed ... more The recent introduction of novel redatuming techniques, based on the principles of time-reversed acoustics and source-receiver reciprocity, has allowed seismic measurements collected on one datum to be extrapolated to another datum. Under favourable conditions, this process can approximately remove the complicated overburden structures without any velocity information. We introduce an elastic redatuming scheme for walkaway vertical seismic profiles (WVSPs) based on these principles, using P- and S-wave potentials, which are derived from the spatial derivatives of the measured wavefields. Additional field acquisition is utilized to directly measure these derivatives. We test our elastic redatuming scheme on data simulated with an elastic finite difference algorithm. The elastodynamic Green's functions between multicomponent receivers in a borehole are then extracted from data recorded using multicomponent (P- and S-wave) sources at the surface. The wavefields are redatumed as four parts: two related to the P-wave potential, and another two related to the S-wave potential. These parts are migrated separately and form four independent images of the salt dome flank, providing a more complete elastic description of the subsurface.
Seismic surface wave analysis has provided important insight in the Earth's crustal and upper man... more Seismic surface wave analysis has provided important insight in the Earth's crustal and upper mantle structure and has recently become a standard tool in geotechnical engineering. Most current surface wave inversion methods are aimed at recovering near-surface (shear) velocity profiles from dispersion curves, assuming a (smoothly varying) horizontally layered Earth. In some cases, however, one is interested in the location, strength or shape of local heterogeneities in the shallow subsurface. In this paper we focus on estimating the strength of near-surface heterogeneity from scattered surface waves. This is a non-linear inversion problem as the wavefield in the scatterer also depends on the contrast. For this reason the inversion is cast as an optimization problem in which we minimize the difference between the observed data and the modelled scattered field. The minimization problem is solved using a conjugate gradient algorithm. To accurately estimate the contrast we account for non-linear interactions such as multiple scattering within the scattering domain in the forward problem. To do so, we use a domain-type integral representation to express the near-surface scattered wavefield, which is solved using the method of moments. The entire inversion is carried out in the frequency domain. This way, we may take advantage of the fact that the decay of surface waves with depth depends on frequency. We study 3-D sensitivity kernels for the given inversion problem and observe that sensitivity of the wavefield with respect to heterogeneity in depth depends on frequency in the same way. We therefore, expect to be able to constrain heterogeneity in depth. A numerical example illustrates this and we conclude that it is in principle possible to reliably resolve heterogeneities and estimate their strengths. We compare the results from our algorithm to a similar but more efficient inversion scheme based on the Born approximation and show that, for the shallowest heterogeneities, this inversion can also recover the contrast well.
Summary We present results of applying seismic interferometry to image dipping sediments abutting... more Summary We present results of applying seismic interferometry to image dipping sediments abutting a salt dome. We create a set of synthetic traces representing a multi-level, walk away Vertical Seismic Profile (VSP) for a model composed of a simplified Gulf of Mexico vertical-velocity gradient and an embedded overhanging salt dome. The sediment reflectors in the model dip up towards the salt dome flank. To process these data, we create a set of redatummed traces using seismic interferometry. This is done without having to perform ...
We describe a new shortcut strategy for imaging the sediments and salt edge around a salt flank t... more We describe a new shortcut strategy for imaging the sediments and salt edge around a salt flank through an overburden salt canopy. We tested its performance and capabilities on 2D synthetic acoustic seismic data from a Gulf of Mexico style model. We first redatumed surface shots, using seismic interferometry, from a walkaway vertical seismic profile survey as if the source and receiver pairs had been located in the borehole at the positions of the receivers. This process creates effective downhole shot gathers by completely moving surface shots through the salt canopy, without any knowledge of overburden velocity structure. After redatuming, we can apply multiple passes of prestack migration from the reference datum of the bore-hole. In our example, first-pass migration, using only a simple vertical velocity gradient model, reveals the outline of the salt edge. A second pass of reverse-time, prestack depth migration using full two-way wave equation was performed with an updated velocity model that consisted of the velocity gradient and salt dome. The second-pass migration brings out dipping sediments abutting the salt flank because these reflectors were illuminated by energy that bounced off the salt flank, forming prismatic reflections. In this target-oriented strategy, the computationally fast redatuming process eliminates the need for the traditional complex process of velocity estimation, model building, and iterative depth migration to remove effects of the salt canopy and surrounding overburden. This might allow this strategy to be used in the field in near real time.
When traveling through a complex overburden, upcoming seismic body waves can be disturbed by scat... more When traveling through a complex overburden, upcoming seismic body waves can be disturbed by scattering from local heterogeneities. Currently, surfaceconsistent static and amplitude corrections correct for rapid variations in arrival times and amplitudes of a reflector, but these methods impose strong assumptions on the near-surface model. Observations on synthetic and laboratory experiments of near-surface scattering with densely sampled data suggest that removing noise from near-receiver scattering requires multichannel approaches rather than single-channel, near-surface corrections.
Upgoing body waves that travel through a heterogeneous near-surface region can excite scattered w... more Upgoing body waves that travel through a heterogeneous near-surface region can excite scattered waves. When the scattering takes place close to the receivers, secondary waves interfere with the upcoming reflections, diminishing the continuity of the wavefront. We estimate a near-surface scattering distribution from a subset of a data record and use this scattering distribution to predict the secondary waves of the entire data record with a wave-theoretical model for near-receiver scattering. We then subtract the predicted scattered waves from the record to obtain the wavefield that would have been measured in the absence of near-surface heterogeneities. We apply this method to part of a field data set acquired in an area with significant near-surface heterogeneity. The main result of our processing scheme is that we effectively remove near-surface scattered waves. This, in turn, increases trace-to-trace coherence of reflection events. Moreover, application of our method improves the results obtained from just an application of a dip filter because we remove parts of the scattered wave with apparent velocities that are typically accepted by the pass zone of the dip filter. Based on these results, we conclude that our method for suppressing near-receiver scattered waves works well on densely sampled land data collected in areas with strong near-surface heterogeneity.
When traveling through a complex overburden, upcoming seismic body waves can be disturbed by scat... more When traveling through a complex overburden, upcoming seismic body waves can be disturbed by scattering from local heterogeneities. Currently, surfaceconsistent static and amplitude corrections correct for rapid variations in arrival times and amplitudes of a reflector, but these methods impose strong assumptions on the near-surface model. Observations on synthetic and laboratory experiments of near-surface scattering with densely sampled data suggest that removing noise from near-receiver scattering requires multichannel approaches rather than single-channel, near-surface corrections.
Statics and near‐field scattering. [SEG Technical Program Expanded Abstracts 20, 2029 (2001)]. Xa... more Statics and near‐field scattering. [SEG Technical Program Expanded Abstracts 20, 2029 (2001)]. Xander H. Campman, C. Dwi Riyanti, Gérard C. Herman.
In this paper we present initial results of applying Time-Reversed Acoustics (TRA) technology to ... more In this paper we present initial results of applying Time-Reversed Acoustics (TRA) technology to saltdome flank, seismic imaging. We created a set of synthetic traces representing a multilevel, walkaway VSP for a model composed of a simplified Gulf of Mexico vertical-velocity gradient and an embedded salt dome. We first applied the concepts of TRA to the synthetic traces to create a set of redatummed traces without having to perform velocity analysis, moveout corrections, or complicated processing. Each redatummed trace approximates the output of a zero-offset, downhole source and receiver pair. To produce the final salt-dome flank image, we then applied conventional, poststack, depth migration to the zero-offset section. Our results show a very good image of the salt when compared to an image derived using data from a downhole, zero-offset source and receiver pairs. The simplicity of our TRA implementation provides a virtually automated method to estimate a zero-offset, seismic section as if it had been collected from the reference frame of the borehole containing the VSP survey.
The interaction of a solitary wave front with an interface formed by two strongly-nonlinear non-c... more The interaction of a solitary wave front with an interface formed by two strongly-nonlinear non-cohesive granular lattices displays rich behaviour, characterized by the breakdown of continuum equations of motion in the vicinity of the interface. By treating the solitary wave as a quasiparticle with an effective mass, we construct an intuitive (energy and linear momentum conserving) discrete model to predict the amplitudes of the transmitted solitary waves generated when an incident solitary wave front, parallel to the interface, moves from a denser to a lighter granular hexagonal lattice. Our findings are corroborated with simulations. We then successfully extend this model to oblique interfaces, where we find that the angle of refraction and reflection of a solitary wave follows, below a critical value, an analogue of Snell's law in which the solitary wave speed replaces the speed of sound, which is zero in the sonic vacuum.
We study seismic noise recorded in the northeast of the Netherlands by beamforming and by using e... more We study seismic noise recorded in the northeast of the Netherlands by beamforming and by using empirical Green's functions obtained by seismic interferometry. From beamforming we found differences in noise directions in different frequency bands. The main source region for primary microseisms (0.05-0.08 Hz) is in the west-northwest direction, while the secondary microseisms (0.1-0.14 Hz) have a west-southwest back azimuth. Furthermore, we observed a fast (∼4 km=s) arrival corresponding to the Rayleigh wave overtone. This arrival is also in the secondary microseism band (between 0.15 and 0.2 Hz), but has a west-northwest back azimuth. Both arrivals in the secondary microseism band gain in strength during winter, as does the average wave height in the North Atlantic. We measured phase velocity dispersion curves from both beamforming and noise cross-correlations, as well as group velocity from the latter. These are then jointly inverted for an average 1D S-wave model. The results show how the combination of different methods leads to a more complete characterization of the propagation modes and an improved knowledge of the subsurface, especially as the group velocity measurements increase the upper frequency limit of analysis, providing valuable information of the shallowest subsurface.
1] The successful surface waves retrieval in solid-Earth seismology using long-time correlations ... more 1] The successful surface waves retrieval in solid-Earth seismology using long-time correlations and subsequent tomographic images of the crust have sparked interest in extraction of subsurface information from noise in the exploration seismology. Subsurface information in exploration seismology is usually derived from body-wave reflections > 1 Hz, which is challenging for utilization of ambient noise. We use 11 h of noise recorded in the Sirte basin, Libya. First, we study the characteristics of the noise. We show that the bulk of the noise is composed of surface waves at frequencies below 6 Hz. Some noise panels contain nearly vertically traveling events. We further characterize these events using a beamforming algorithm. From the beamforming, we conclude that these events represent body-wave arrivals with a fairly rich azimuthal distribution. Having body-wave arrivals in the noise is a prerequisite for body-wave reflections retrieval. We crosscorrelate and sum the recorded ambient-noise panels to retrieve common-source gathers, following two approaches-using all the noise and using only noise panels containing body-wave arrivals likely to contribute to the reflections retrieval. Comparing the retrieved gathers with active seismic data, we show that the two-way traveltimes at short offsets of several retrieved events coincide with those of reflections in the active data and thus correspond to apexes of reflections. We then compare retrieved stacked sections of the subsurface from both approaches with the active-data stacked section and show that the reflectors are consistent along a line. The results from the second approach exhibit the reflectors better.
We study theoretically the interaction of elastic waves caused by non-linearities of rock elastic... more We study theoretically the interaction of elastic waves caused by non-linearities of rock elastic moduli, and assess the possibility to use this phenomenon in hydrocarbon exploration and in the analysis of rock samples. In our calculations we use the five-constant model by Gol'dberg. It is shown that the interaction of plane waves in isotropic solids is completely described by five coupling coefficients, which have the same order of magnitude. By considering scattering of compressional waves generated by controlled sources at the Earth surface from a non-linear layer at the subsurface, we conclude that non-linear signals from deep formations are unlikely to be measured with the current level of technology. Our analysis of field tests where non-linear signals were measured, suggests that these signals are generated either in the shallow subsurface or in the vicinity of sources. Non-linear wave interaction might be observable in lab tests with focused ultrasonic beams. In this case, the non-linear response is generated in the secondary parametric array formed by linear beams scattered from inclusions. Although the strength of this response is controlled by non-linearity of the surrounding medium rather than by non-linearity of inclusions, its measurement can help to obtain better images of rock samples.
Keywords: Body waves Interferometry Ambient noise Microseism Lithosphere Mots cle´s : Ondes de vo... more Keywords: Body waves Interferometry Ambient noise Microseism Lithosphere Mots cle´s : Ondes de volume Interfé romé trie Bruit ambiant Microsé isme Lithosphè re A B S T R A C T
Several geophysical methods exist to delineate the lower interface of a sedimentary basin. Most p... more Several geophysical methods exist to delineate the lower interface of a sedimentary basin. Most popularly employed are gravity and magnetic surveys and surface-wave inversion. While all three methods are successful overall in estimating an average basin depth, they fail to find a more detailed depth variation. As an alternative, we consider three passive seismic techniques, using especially body waves. We analyze 40 hours of data, recorded with 110 stations installed over the Abu Gharadig basin in Egypt. In an earlier study we found the frequency band of 0.09-1.0 Hz to be dominated by body waves. As a first method we apply body-wave seismic interferometry (SI). Using body-wave noise, we extract PP and SS reflections from the basin floor. We estimate the depth of the basin to be around 4.8 km. As a second technique we estimate the resonance spectra of the basin, using the horizontal-to-vertical (H/V) spectral ratio. Using surface-wave noise, we find an extremum that is probably related to the complete sedimentary package. Using this peak, we find a basin depth of 5.4 km. Using S-phase arrivals, we find two extrema in the H/V, which are probably related to the S-wave resonances of two distinct layers in the basin. As a third method we compute receiver functions (RFs). Based on the RFs, we can confirm the presence of a large interface in the upper crust, but we cannot well constrain its depth.
Seismic interferometry involves the crosscorrelation of responses at different receivers to obtai... more 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 seismology͒ or a noise signal ͑as in passive seismology͒, 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 ambient noise and the subsequent tomographic determination of the surfacewave velocity distribution of the subsurface. Seismic interferometry is not restricted to retrieving direct waves between receivers. In a classic paper, Claerbout shows that the autocorrelation of the transmission response of a layered medium gives the plane-wave reflection response of that medium. This is essentially 1D reflected-wave interferometry. Similarly, the crosscorrelation of the transmission responses, observed at two receivers, of an arbitrary inhomogeneous medium gives the 3D reflection response of that medium. One of the main applications of reflected-wave interferometry is retrieving the seismic reflection response from ambient noise and imaging of the reflectors in the subsurface. A common aspect of direct-and reflected-wave interferometry is that virtual sources are created at positions where there are only receivers without requiring knowledge of the subsurface medium parameters or of the positions of the actual sources.
One application of seismic interferometry is to retrieve the impulse response ͑Green's function͒ ... more One application of seismic interferometry is to retrieve the impulse response ͑Green's function͒ from crosscorrelation of ambient seismic noise. Various researchers show results for retrieving the surface-wave part of the Green's function. However, reflection retrieval has proven more challenging. We crosscorrelate ambient seismic noise, recorded along eight parallel lines in the Sirte basin east of Ajdabeya, Libya, to obtain shot gathers that contain reflections. We take advantage of geophone groups to suppress part of the undesired surface-wave noise and apply frequency-wavenumber filtering before crosscorrelation to suppress surface waves further.After comparing the retrieved results with data from an active seismic exploration survey along the same lines, we use the retrieved reflection data to obtain a migrated reflection image of the subsurface.
Surface-wave analysis is a key tool for seismologists, ranging from near-surface characterization... more Surface-wave analysis is a key tool for seismologists, ranging from near-surface characterization in geotechnical applications to global seismology. Even in exploration seismology, where surface waves are regarded as a kind of noise, the fact that they typically represent the bulk of the recorded energy makes an understanding of surface-wave propagation important. On the other hand, the heterogeneity of the near surface can make such analyses difficult since the heterogeneity is responsible for scattering and mode conversion.
In recent years, there has been an increase in the deployment of relatively dense arrays of seism... more In recent years, there has been an increase in the deployment of relatively dense arrays of seismic stations. The availability of spatially densely sampled global and regional seismic data has stimulated the adoption of industry-style imaging algorithms applied to converted-and scattered-wave energy from distant earthquakes, leading to relatively high-resolution images of the lower crust and upper mantle. We use seismic interferometry to extract reflection responses from the coda of transmitted energy from distant earthquakes. In theory, higher-resolution images can be obtained when migrating reflections obtained with seismic interferometry rather than with conversions, traditionally used in lithospheric imaging methods. Moreover, reflection data allow the straightforward application of algorithms previously developed in exploration seismology. In particular, the availability of reflection data allows us to extract from it a velocity model using standard multichannel data-processing methods. However, the success of our approach relies mainly on a favourable distribution of earthquakes. In this paper, we investigate how the quality of the reflection response obtained with interferometry is influenced by the distribution of earthquakes and the complexity of the transmitted wavefields. Our analysis shows that a reasonable reflection response could be extracted if (1) the array is approximately aligned with an active zone of earthquakes, (2) different phase responses are used to gather adequate angular illumination of the array and (3) the illumination directions are properly accounted for during processing. We illustrate our analysis using a synthetic data set with similar illumination and source-side reverberation characteristics as field data recorded during the 2000-2001 Laramie broad-band experiment. Finally, we apply our method to the Laramie data, retrieving reflection data. We extract a 2-D velocity model from the reflections and use this model to migrate the data. On the final reflectivity image, we observe a discontinuity in the reflections. We interpret this discontinuity as the Cheyenne Belt, a suture zone between Archean and Proterozoic terranes.
Empirical Green's functions (EGFs) between receivers can be obtained from seismic interferometry ... more Empirical Green's functions (EGFs) between receivers can be obtained from seismic interferometry through cross-correlation of pairs of ground motion records. Full reconstruction of the Green's function requires diffuse wavefields or a uniform distribution of (noise) sources. In practice, EGFs differ from actual Green's functions because wavefields are not diffuse and the source distribution not uniform. This difference, which may depend on medium heterogeneity, complicates (stochastic) medium characterization as well as imaging and tomographic velocity analysis with EGFs. We investigate how source distribution and scale lengths of medium heterogeneity influence surface wave Green's function reconstruction in the period band of primary microseisms (T = 10-20 s). With data from a broad-band seismograph array in SE Tibet we analyze the symmetry and travel-time properties of surface wave EGFs from correlation of data in different windows: ambient noise, direct surface waves, and surface wave coda. The EGFs from these different windows show similar dispersion characteristics, which demonstrates that the Green's function can be recovered from direct wavefields (e.g., ambient noise or earthquakes) or from wavefields scattered by heterogeneity on a regional scale. Directional bias and signal-to-noise ratio of EGFs can be understood better with (plane wave) beamforming of the energy contributing to EGF construction. Beamforming also demonstrates that seasonal variations in cross-correlation functions correlate with changes in ocean activity.
The recent introduction of novel redatuming techniques, based on the principles of time-reversed ... more The recent introduction of novel redatuming techniques, based on the principles of time-reversed acoustics and source-receiver reciprocity, has allowed seismic measurements collected on one datum to be extrapolated to another datum. Under favourable conditions, this process can approximately remove the complicated overburden structures without any velocity information. We introduce an elastic redatuming scheme for walkaway vertical seismic profiles (WVSPs) based on these principles, using P- and S-wave potentials, which are derived from the spatial derivatives of the measured wavefields. Additional field acquisition is utilized to directly measure these derivatives. We test our elastic redatuming scheme on data simulated with an elastic finite difference algorithm. The elastodynamic Green's functions between multicomponent receivers in a borehole are then extracted from data recorded using multicomponent (P- and S-wave) sources at the surface. The wavefields are redatumed as four parts: two related to the P-wave potential, and another two related to the S-wave potential. These parts are migrated separately and form four independent images of the salt dome flank, providing a more complete elastic description of the subsurface.
Seismic surface wave analysis has provided important insight in the Earth's crustal and upper man... more Seismic surface wave analysis has provided important insight in the Earth's crustal and upper mantle structure and has recently become a standard tool in geotechnical engineering. Most current surface wave inversion methods are aimed at recovering near-surface (shear) velocity profiles from dispersion curves, assuming a (smoothly varying) horizontally layered Earth. In some cases, however, one is interested in the location, strength or shape of local heterogeneities in the shallow subsurface. In this paper we focus on estimating the strength of near-surface heterogeneity from scattered surface waves. This is a non-linear inversion problem as the wavefield in the scatterer also depends on the contrast. For this reason the inversion is cast as an optimization problem in which we minimize the difference between the observed data and the modelled scattered field. The minimization problem is solved using a conjugate gradient algorithm. To accurately estimate the contrast we account for non-linear interactions such as multiple scattering within the scattering domain in the forward problem. To do so, we use a domain-type integral representation to express the near-surface scattered wavefield, which is solved using the method of moments. The entire inversion is carried out in the frequency domain. This way, we may take advantage of the fact that the decay of surface waves with depth depends on frequency. We study 3-D sensitivity kernels for the given inversion problem and observe that sensitivity of the wavefield with respect to heterogeneity in depth depends on frequency in the same way. We therefore, expect to be able to constrain heterogeneity in depth. A numerical example illustrates this and we conclude that it is in principle possible to reliably resolve heterogeneities and estimate their strengths. We compare the results from our algorithm to a similar but more efficient inversion scheme based on the Born approximation and show that, for the shallowest heterogeneities, this inversion can also recover the contrast well.
Summary We present results of applying seismic interferometry to image dipping sediments abutting... more Summary We present results of applying seismic interferometry to image dipping sediments abutting a salt dome. We create a set of synthetic traces representing a multi-level, walk away Vertical Seismic Profile (VSP) for a model composed of a simplified Gulf of Mexico vertical-velocity gradient and an embedded overhanging salt dome. The sediment reflectors in the model dip up towards the salt dome flank. To process these data, we create a set of redatummed traces using seismic interferometry. This is done without having to perform ...
We describe a new shortcut strategy for imaging the sediments and salt edge around a salt flank t... more We describe a new shortcut strategy for imaging the sediments and salt edge around a salt flank through an overburden salt canopy. We tested its performance and capabilities on 2D synthetic acoustic seismic data from a Gulf of Mexico style model. We first redatumed surface shots, using seismic interferometry, from a walkaway vertical seismic profile survey as if the source and receiver pairs had been located in the borehole at the positions of the receivers. This process creates effective downhole shot gathers by completely moving surface shots through the salt canopy, without any knowledge of overburden velocity structure. After redatuming, we can apply multiple passes of prestack migration from the reference datum of the bore-hole. In our example, first-pass migration, using only a simple vertical velocity gradient model, reveals the outline of the salt edge. A second pass of reverse-time, prestack depth migration using full two-way wave equation was performed with an updated velocity model that consisted of the velocity gradient and salt dome. The second-pass migration brings out dipping sediments abutting the salt flank because these reflectors were illuminated by energy that bounced off the salt flank, forming prismatic reflections. In this target-oriented strategy, the computationally fast redatuming process eliminates the need for the traditional complex process of velocity estimation, model building, and iterative depth migration to remove effects of the salt canopy and surrounding overburden. This might allow this strategy to be used in the field in near real time.
When traveling through a complex overburden, upcoming seismic body waves can be disturbed by scat... more When traveling through a complex overburden, upcoming seismic body waves can be disturbed by scattering from local heterogeneities. Currently, surfaceconsistent static and amplitude corrections correct for rapid variations in arrival times and amplitudes of a reflector, but these methods impose strong assumptions on the near-surface model. Observations on synthetic and laboratory experiments of near-surface scattering with densely sampled data suggest that removing noise from near-receiver scattering requires multichannel approaches rather than single-channel, near-surface corrections.
Upgoing body waves that travel through a heterogeneous near-surface region can excite scattered w... more Upgoing body waves that travel through a heterogeneous near-surface region can excite scattered waves. When the scattering takes place close to the receivers, secondary waves interfere with the upcoming reflections, diminishing the continuity of the wavefront. We estimate a near-surface scattering distribution from a subset of a data record and use this scattering distribution to predict the secondary waves of the entire data record with a wave-theoretical model for near-receiver scattering. We then subtract the predicted scattered waves from the record to obtain the wavefield that would have been measured in the absence of near-surface heterogeneities. We apply this method to part of a field data set acquired in an area with significant near-surface heterogeneity. The main result of our processing scheme is that we effectively remove near-surface scattered waves. This, in turn, increases trace-to-trace coherence of reflection events. Moreover, application of our method improves the results obtained from just an application of a dip filter because we remove parts of the scattered wave with apparent velocities that are typically accepted by the pass zone of the dip filter. Based on these results, we conclude that our method for suppressing near-receiver scattered waves works well on densely sampled land data collected in areas with strong near-surface heterogeneity.
When traveling through a complex overburden, upcoming seismic body waves can be disturbed by scat... more When traveling through a complex overburden, upcoming seismic body waves can be disturbed by scattering from local heterogeneities. Currently, surfaceconsistent static and amplitude corrections correct for rapid variations in arrival times and amplitudes of a reflector, but these methods impose strong assumptions on the near-surface model. Observations on synthetic and laboratory experiments of near-surface scattering with densely sampled data suggest that removing noise from near-receiver scattering requires multichannel approaches rather than single-channel, near-surface corrections.
Statics and near‐field scattering. [SEG Technical Program Expanded Abstracts 20, 2029 (2001)]. Xa... more Statics and near‐field scattering. [SEG Technical Program Expanded Abstracts 20, 2029 (2001)]. Xander H. Campman, C. Dwi Riyanti, Gérard C. Herman.
In this paper we present initial results of applying Time-Reversed Acoustics (TRA) technology to ... more In this paper we present initial results of applying Time-Reversed Acoustics (TRA) technology to saltdome flank, seismic imaging. We created a set of synthetic traces representing a multilevel, walkaway VSP for a model composed of a simplified Gulf of Mexico vertical-velocity gradient and an embedded salt dome. We first applied the concepts of TRA to the synthetic traces to create a set of redatummed traces without having to perform velocity analysis, moveout corrections, or complicated processing. Each redatummed trace approximates the output of a zero-offset, downhole source and receiver pair. To produce the final salt-dome flank image, we then applied conventional, poststack, depth migration to the zero-offset section. Our results show a very good image of the salt when compared to an image derived using data from a downhole, zero-offset source and receiver pairs. The simplicity of our TRA implementation provides a virtually automated method to estimate a zero-offset, seismic section as if it had been collected from the reference frame of the borehole containing the VSP survey.
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