Cross‐borehole simulation of wave propagation

Geophysics ◽  
1991 ◽  
Vol 56 (7) ◽  
pp. 1103-1113 ◽  
Author(s):  
Philippe Jean ◽  
Michel Bouchon

Synthetic seismograms are used to study elastic wave propagation in multi‐layered media for cross‐borehole geometries. The calculations are done using the discrete wavenumber method. We compute the wavefield for a series of receiver arrays located at various offsets to follow the evolution of the wavefronts and the distribution of the seismic energy in space. The results show the complexity of the wavefield at large offsets. Trapped waves and conical waves perturb the identification of direct and primary reflected phases. The display of polarization diagrams of the guided waves shows elliptical prograde motions. The source position plays an important role in the energy distribution within the medium. In order to study this dependency, we compare the cases of sources located in relatively low and high‐velocity layers. In the former case, most of the energy is trapped within the source layer and in the neighboring region and propagates horizontally. The S‐converted waves generated at the interfaces bounding the source layer have larger amplitude than the direct P‐wave. When the source is placed in a relatively high‐velocity layer the energy of the P‐wavefront spreads rapidly throughout the medium as the offset increases.

Geophysics ◽  
1992 ◽  
Vol 57 (11) ◽  
pp. 1444-1452 ◽  
Author(s):  
Guy W. Purnell

High‐velocity layers (HVLs) often hinder seismic imaging of deeper reflectors using conventional techniques. A major factor is often the unusual energy partitioning of waves incident at an HVL boundary from lower‐velocity material. Using elastic physical modeling, I demonstrate that one effect of this factor is to limit the range of dips beneath an HVL that can be imaged using unconverted P‐wave arrivals. At the same time, however, partitioning may also result in P‐waves outside the HVL coupling efficiently with S‐waves inside. By exploiting some of the waves that convert upon transmission into and/or out of the physical‐model HVL, I am able to image a much broader range of underlying dips. This is accomplished by acoustic migration tailored (via the migration velocities used) for selected families of converted‐wave arrivals.


2021 ◽  
Author(s):  
◽  
Pauline Maria Galea

<p>A shallow aftershock sequence in the Hawkes Bay region of the North Island, New Zealand (May 1990) was recorded with high quality on an L-shaped, 7-station array of 3-component, short-period seismographs at Wellington, such that the seismic waves travelled almost along strike of the subducted Pacific plate in this region. The arrival times at the stations of the Pn wave pulse from a number of aftershocks could be picked sufficiently accurately for a least-squares inversion to be carried out for wavefront speed, c, and incident azimuth, [theta]. The results show a high apparent velocity, 8.7 [plus or minus] 0.2 km/s, and an azimuth which is shifted by 6.0 [plus or minus] 2.5 degrees east of the true epicentre - station azimuth. The azimuthal anomaly, [delta][theta], has been interpreted as due to lateral refraction of Pn off the subducted slab. The effect of different geometries of the slab on the Pn wavefront characteristics (c and [delta][theta]) at Wellington have been explored through both simple geometrical considerations (in the case of a plane or cylindrical slab) as well as through 3-dimensional ray tracing (in the case of irregular curvature of the slab). It has been shown that a plane or cylindrical slab would require P-wave velocities of about 9.0 km/s to exist within it in order to fit both c and [delta][theta], whereas a model of the slab which departs from a regular cylinder and has a small updip component along strike can fit the observations with P-wave velocities of 8.75 km/s in the high velocity medium. This model has been proposed by Ansell and Bannister (1991) after detailed consideration of the shallow seismicity that defines the slab surface in the lower North Island. Information about the nature of the high velocity medium has been obtained by modeling the waveforms through generation of synthetic seismograms by the reflectivity technique of Kennett (1983). The large number of aftershocks within a small source region, and the sampling of much the same wavepath, meant that a sufficient number of seismograms had very similar and characteristic features that could be modelled. The typical seismogram of the data set had a simple Pn wavepulse, followed immediately by a complex. high frequency (up to 15 Hz) phase (here referred to as Phf) and a high amplitude, lower frequency phase that dominated the P-wavetrain (here referred to as P). A velocity profile that contained a layer of 8.75 km/s material at least 4 km thick, underlying "normal" mantle material of P-velocity 8.2 [plus or minus] 0.2 km/s. and whose surface lies approximately 18 km below the slab surface reproduced the observed seismogram features well. The presence of velocity gradients above and below the layer is not excluded. A gradual decrease in velocity below the layer in fact gives a better fit of the Pn pulse shape. By breaking down the synthetic seismogram into simpler versions. using Kennett's wavefield approximation technique, it has been shown that the Pn wave propagates through the high velocity layer, the Phf phase through the overlying layers as a sequence of reflections and refractions, and the P group as a reverberatory phase in a crustal waveguide, with its energy mostly in the form of free surface reflections and S to P conversion. These results have also been confirmed by ray tracing. Waveform modelling has also clearly shown that a low velocity layer (representing subducted sediment) on the top of the subducted slab produces a highly characteristic imprint on the synthetic seismogram, in the form of an energetic, reverberatory, lower frequency signal late in the P-wavetrain. Wavefield approximations show that this is also a crustal waveguide effect, with a strong component of mode conversion at the free surface, but P - S conversion appears to be the dominant mechanism. Seismograms very similar to such synthetic ones have been observed for the Weber aftershocks recorded at stations along the northern East Coast. The presence of such a low velocity layer in the East Coast region is thus implied, consistently with previous proposals. The petrological implications of the high velocity layer in the subducted Pacific plate are discussed. The most likely explanation is that it represents the maximum P velocity of an anisotropic layer within the Pacific upper mantle. It is proposed that the conditions of stress orientation, pressure and temperature at approximately 36 - 50 km depth in this region induces a strong realignment of olivine crystals with their fast direction along strike of the slab, normal to the maximum compressive stress axis. The upper mantle of the segment of the Pacific ocean just east of the Tonga - Kermadec trench and the North Island has been shown in this study to possess P-wave anisotropy, with the P-velocity reaching a maximum of 8.37 km/s in a direction N60 degrees E. This result was obtained by analysing a large set of ISC travel times from earthquakes along the Tonga - Kermadec - New Zealand subduction zone recorded at stations Niue, Rarotonga and the Chatham Islands. It is suggested that an enhancement of this anisotropy, accompanied by some re-orientation, takes place as the upper mantle medium is subjected to the new stress conditions in the initial stages of subduction.</p>


2021 ◽  
Author(s):  
◽  
Pauline Maria Galea

<p>A shallow aftershock sequence in the Hawkes Bay region of the North Island, New Zealand (May 1990) was recorded with high quality on an L-shaped, 7-station array of 3-component, short-period seismographs at Wellington, such that the seismic waves travelled almost along strike of the subducted Pacific plate in this region. The arrival times at the stations of the Pn wave pulse from a number of aftershocks could be picked sufficiently accurately for a least-squares inversion to be carried out for wavefront speed, c, and incident azimuth, [theta]. The results show a high apparent velocity, 8.7 [plus or minus] 0.2 km/s, and an azimuth which is shifted by 6.0 [plus or minus] 2.5 degrees east of the true epicentre - station azimuth. The azimuthal anomaly, [delta][theta], has been interpreted as due to lateral refraction of Pn off the subducted slab. The effect of different geometries of the slab on the Pn wavefront characteristics (c and [delta][theta]) at Wellington have been explored through both simple geometrical considerations (in the case of a plane or cylindrical slab) as well as through 3-dimensional ray tracing (in the case of irregular curvature of the slab). It has been shown that a plane or cylindrical slab would require P-wave velocities of about 9.0 km/s to exist within it in order to fit both c and [delta][theta], whereas a model of the slab which departs from a regular cylinder and has a small updip component along strike can fit the observations with P-wave velocities of 8.75 km/s in the high velocity medium. This model has been proposed by Ansell and Bannister (1991) after detailed consideration of the shallow seismicity that defines the slab surface in the lower North Island. Information about the nature of the high velocity medium has been obtained by modeling the waveforms through generation of synthetic seismograms by the reflectivity technique of Kennett (1983). The large number of aftershocks within a small source region, and the sampling of much the same wavepath, meant that a sufficient number of seismograms had very similar and characteristic features that could be modelled. The typical seismogram of the data set had a simple Pn wavepulse, followed immediately by a complex. high frequency (up to 15 Hz) phase (here referred to as Phf) and a high amplitude, lower frequency phase that dominated the P-wavetrain (here referred to as P). A velocity profile that contained a layer of 8.75 km/s material at least 4 km thick, underlying "normal" mantle material of P-velocity 8.2 [plus or minus] 0.2 km/s. and whose surface lies approximately 18 km below the slab surface reproduced the observed seismogram features well. The presence of velocity gradients above and below the layer is not excluded. A gradual decrease in velocity below the layer in fact gives a better fit of the Pn pulse shape. By breaking down the synthetic seismogram into simpler versions. using Kennett's wavefield approximation technique, it has been shown that the Pn wave propagates through the high velocity layer, the Phf phase through the overlying layers as a sequence of reflections and refractions, and the P group as a reverberatory phase in a crustal waveguide, with its energy mostly in the form of free surface reflections and S to P conversion. These results have also been confirmed by ray tracing. Waveform modelling has also clearly shown that a low velocity layer (representing subducted sediment) on the top of the subducted slab produces a highly characteristic imprint on the synthetic seismogram, in the form of an energetic, reverberatory, lower frequency signal late in the P-wavetrain. Wavefield approximations show that this is also a crustal waveguide effect, with a strong component of mode conversion at the free surface, but P - S conversion appears to be the dominant mechanism. Seismograms very similar to such synthetic ones have been observed for the Weber aftershocks recorded at stations along the northern East Coast. The presence of such a low velocity layer in the East Coast region is thus implied, consistently with previous proposals. The petrological implications of the high velocity layer in the subducted Pacific plate are discussed. The most likely explanation is that it represents the maximum P velocity of an anisotropic layer within the Pacific upper mantle. It is proposed that the conditions of stress orientation, pressure and temperature at approximately 36 - 50 km depth in this region induces a strong realignment of olivine crystals with their fast direction along strike of the slab, normal to the maximum compressive stress axis. The upper mantle of the segment of the Pacific ocean just east of the Tonga - Kermadec trench and the North Island has been shown in this study to possess P-wave anisotropy, with the P-velocity reaching a maximum of 8.37 km/s in a direction N60 degrees E. This result was obtained by analysing a large set of ISC travel times from earthquakes along the Tonga - Kermadec - New Zealand subduction zone recorded at stations Niue, Rarotonga and the Chatham Islands. It is suggested that an enhancement of this anisotropy, accompanied by some re-orientation, takes place as the upper mantle medium is subjected to the new stress conditions in the initial stages of subduction.</p>


1994 ◽  
Author(s):  
Colin MacBeth ◽  
Enru Liu ◽  
Mark Boyd ◽  
Karen Sweeney

1963 ◽  
Vol 53 (3) ◽  
pp. 593-618
Author(s):  
D. K. Chowdhury ◽  
Peter Dehlinger

Abstract Propagation of direct waves and dispersive long-period waves along a layered system was investigated experimentally by means of two-dimensional ultrasonic models. Velocities of direct and head waves were measured within layers or in a medium adjacent to layers as functions of layer thickness to wave length or source-from-interface distance to wave length. Amplitudes of direct longitudinal, direct shear, and long-period waves were measured on three profiles, each perpendicular to the layers. Three models were used: the first consisted of a low-velocity layer between two thick sheets; the second of a high-velocity layer between two sheets; the third of six alternating high- and low-velocity layers between two sheets. The source was a wave train, simulating a wave from a seismic explosion. The frequency was varied so as to obtain different ratios of layer thickness to wave length. In the single low-velocity layer model the direct longitudinal wave contained a larger amplitude than the dispersive long-period wave in the layer at offset distance of 6 to 10 times the layer thickness. In the single high-velocity layer model the direct longitudinal wave was attenuated rapidly and the amplitudes of the long-period waves were negligigble. In the multilayered model, direct waves had negligible amplitudes at the corresponding distances; nearly all of the energy was in the dispersive long-period waves. In this model the low-velocity layer carried 1 1/2 to 3 times the amplitude observed in the high-velocity layers, whether the source was located in the high- or low-velocity layers. Dispersion of the long-period waves in the multilayered model was pronounced within the low-velocity layers and weak in the high-velocity layers, when the source was either in a high- or low-velocity layer. Dispersion was anomalous when the source was in a low-velocity layer and normal when in a high-velocity layer.


Solid Earth ◽  
2011 ◽  
Vol 2 (1) ◽  
pp. 1-7 ◽  
Author(s):  
I. Flecha ◽  
R. Carbonell ◽  
R. W. Hobbs ◽  
H. Zeyen

Abstract. Subbasalt imaging can be improved by carefully applying pre-stack depth migration. Pre-stack depth migration requires a detailed velocity model and an accurate traveltime calculation. Ray tracing methods are fast but, often fail in calculating traveltimes in complex models, specially, when they feature high velocity contrasts. Finitte difference solutions of the eikonal are more stable and can produce a traveltime field for the whole model avoiding shadow zones. A synthetic test was carried out to check the performance of a new pre-stack depth migration algorithm in a model that features a high velocity layer surrounded by lower velocities. The results reasonably reproduce the original model. The same scheme was used to process long-offset reflection data from the Faroe Shelf where conventional techniques (stack) were insufficient to assess the structure under a basalt layer. Pre-stack depth migration produced an improved image which recovered the main features in the stacked section and allowed to identify some subbasalt coherent events.


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