scholarly journals TWO‐DIMENSIONAL MODEL SEISMOLOGY

Geophysics ◽  
1954 ◽  
Vol 19 (2) ◽  
pp. 202-219 ◽  
Author(s):  
Jack Oliver ◽  
Frank Press ◽  
Maurice Ewing

The solutions of many problems in seismology may be obtained by means of ultrasonic pulses propagating in small scale models. Thin sheets, serving as two dimensional models, are particularly advantageous because of their low cost, availability, ease of fabrication into various configurations, lower energy requirements, and appropriate dilatational‐to‐shear‐velocity ratios. Four examples are presented: flexural waves in a sheet, Rayleigh waves in a low velocity layer overlying a semi‐infinite high velocity layer, Rayleigh waves in a high velocity layer overlying a semi‐infinite low velocity layer, and body and surface waves in a disk.

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.


1959 ◽  
Vol 49 (4) ◽  
pp. 355-364
Author(s):  
H. Takeuchi ◽  
F. Press ◽  
N. Kobayashi

Abstract Variational calculus methods are applied to the problem of dispersion of mantle Rayleigh waves. In the present paper we have worked two models. One is Gutenberg's model with a low-velocity layer around 150 km. depth. The other is a Jeffreys-Bullen model modified above 200 km. depth so as to join smoothly to the explosion-determined velocities just under the Mohorovičić discontinuity. No low-velocity layer is assumed in this model. Both models give almost identical theoretical dispersion curves which agree well with the Ewing-Press observations of mantle Rayleigh waves for periods longer than 250 sec. This result means that the minimum group velocity at about 250 sec. is mainly due to a sharp increase of shear velocity at about 400 km. depth, which is a common feature for the two models. For periods shorter than 250 sec. Gutenberg's model gives results concordant with the observations. The modified Jeffreys-Bullen model disagrees significantly with the observations. This demonstrates the existence of a low-velocity layer in the upper mantle.


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>


Geophysics ◽  
1981 ◽  
Vol 46 (7) ◽  
pp. 1003-1008 ◽  
Author(s):  
K. L. Kaila ◽  
H. C. Tewari ◽  
V. G. Krishna

We present an indirect method for determining the thickness of a low‐velocity layer (LVL) underlying a high‐velocity layer (HVL) in seismic prospecting. Comparison of the average velocity‐depth function determined from the first arrival refraction data with that obtained from reflection data in the same region, especially below the LVL, makes it possible to recognize the presence of the LVL and to estimate its probable thickness. The applicability of the method has been demonstrated in a field case where the presence of an LVL is indicated by geologic evidence. It has been shown that thickness estimates of an LVL and an HVL can be made reliably in situations where the velocity in the LVL can be accurately estimated from nearby exposures or in a drilled well. For the field case analyzed, a thickness of 0.75 km was estimated for an LVL (probably Mesozoic sediments) underlying a 0.25 km thick HVL (probably basalt). The velocity of propagation in the LVL was taken from seismic data on nearby exposed Mesozoics as 4.0 km/sec, and the velocity of the HVL is 5.4 km/sec, based on the refraction data. In areas where the velocity in the LVL cannot be inferred accurately, an upper limit of this velocity can be obtained which permits estimation of the maximum possible thickness of the LVL. In the field example presented, we show that the velocity in the LVL cannot exceed 4.17 km/sec.


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>


2013 ◽  
Vol 5 (1) ◽  
pp. 699-736
Author(s):  
M. Grad ◽  
T. Tiira ◽  
S. Olsson ◽  
K. Komminaho

Abstract. The problem of the asthenosphere for old Precambrian cratons, including East European Craton and its part – the Baltic Shield, is still discussed. To study the seismic lithosphere-asthenosphere boundary (LAB) beneath the Baltic Shield we used records of 9 local events with magnitudes in the range 2.7–5.9. The relatively big number of seismic stations in the Baltic Shield with a station spacing of 30–100 km permits for relatively dense recordings, and is sufficient in lithospheric scale. For modelling of the lower lithosphere and asthenosphere, the original data were corrected for topography and the Moho depth for each event and each station location, using a reference model with a 46 km thick crust. Observed P and S arrivals are significantly earlier than those predicted by the iasp91 model, which clearly indicates that lithospheric P and S velocities beneath the Baltic Shield are higher than in the global iasp91 model. For two northern events at Spitsbergen and Novaya Zemlya we observe a low velocity layer, 60–70 km thick asthenosphere, and the LAB beneath Barents Sea was found at depth of about 200 km. Sections for other events show continous first arrivals of P waves with no evidence for "shadow zone" in the whole range of registration, which could be interpreted as absence of asthenosphere beneath the central part of the Baltic Shield, or that LAB in this area occurs deeper (>200 km). The relatively thin low velocity layer found beneath southern Sweden, 15 km below the Moho, could be interpreted as small scale lithospheric inhomogeneities, rather than asthenosphere. Differentiation of the lid velocity beneath the Baltic Shield could be interpreted as regional inhomogeneity. It could also be interpreted as anisotropy of the Baltic Shield lithosphere, with fast velocity close to the east-west direction, and slow velocity close to the south-north direction.


2021 ◽  
Vol 40 (8) ◽  
pp. 601-609
Author(s):  
Ivan Javier Sánchez-Galvis ◽  
Jheyston Serrano ◽  
Daniel A. Sierra ◽  
William Agudelo

The accurate simulation of seismic surface waves on complex land areas requires elastic models with realistic near-surface parameters. The SEAM Phase II Foothills model, proposed by the SEG Advanced Modeling (SEAM) Corporation, is one of the most comprehensive efforts undertaken by the geophysics community to understand complex seismic wave propagation in foothills areas. However, while this model includes a rough topography, alluvial sediments, and complex geologic structures, synthetic data from the SEAM consortium do not reproduce the qualitative characteristics of the scattering energy that is generally interpreted as the “ground roll energy cone” on shot records of real data. To simulate the scattering, a near-surface elastic model in mountainous areas ideally must include the following three elements: (1) rough topography and bedrock, (2) low-velocity layer, and (3) small-scale heterogeneities (size approximately Rayleigh wavelength). The SEAM Foothills model only includes element (1) and, to a lesser extent, element (2). We represent a heterogeneous near surface as a random medium with two parameters: the average size of the heterogeneities and fractional fluctuation. A parametric analysis shows the influence of each parameter on the synthetic data and how similar it is compared to real data acquired in a foothills area in Colombia. We perform the analysis in the shot gather panel and dispersion image. Our study shows that it is necessary to include the low-velocity layer and small-scale distributed heterogeneities in the shallow part of the SEAM model to get synthetic data with realistic scattered surface-wave energy.


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