Surface motion due to a point source in a semi-infinite elastic medium*

1954 ◽  
Vol 44 (4) ◽  
pp. 571-596
Author(s):  
Edmund Pinney
Keyword(s):  
Point Source ◽  
Elastic Medium ◽  
Elastic Solid ◽  
Point Sources ◽  
P Wave ◽  
Tabular Form ◽  
Internal Point ◽  
S Wave ◽  
Surface Motion

Abstract The theory of the motion of the surface of a semi-infinite elastic solid due to an impulsive internal point source is developed, both for P-wave and S-wave point sources. The resulting motions have been computed numerically for the case λ = μ and are presented both in tabular form and graphically.

The use of singular integrals in wave propagation problems; with application to the point source in a semi-infinite elastic medium

1963 ◽  
Vol 276 (1365) ◽  
pp. 204-237 ◽  
Keyword(s):  
Free Surface ◽  
Point Source ◽  
Elastic Medium ◽  
Constant Velocity ◽  
Singular Integrals ◽  
Plane Waves ◽  
Elastic Solid ◽  
Fundamental Solutions ◽  
General Point ◽  
Set Up

This is an investigation of the field due to a general point source of energy in an isotropic, elastic solid with a free surface. The paper is divided into three parts. In part I we are concerned with the development of new plane wave representations for the fundamental solutions of elastodynamics. There are two types of situation involved; we have the simpler type involved in the case of a steady point source which moves steadily with any constant velocity in an elastic medium, this type involves superposition of plane waves with respect to a single parameter, and we have the more complicated transient problem in which a point source is set up at a given moment, and thereafter moves at constant velocity, without change of strength. In part II we make use of the new representation for the field of a steadily moving source in the calculation of fields and displacements in the presence of a free surface and in part III we do the same for the transient source. We discuss in some detail the application of the new approach to the case of a vertical load, to a horizontal load, and to a couple of arbitrary orientation, and we give a general discussion of the singularities to be expected for the general point source.

Sources of Nitrogen and Phosphorus in the Catchment Area of Neusiedlersee/Fertö, Austria/Hungary

1993 ◽  
Vol 28 (3-5) ◽  
pp. 101-110 ◽  
Author(s):  
W. v. d. Emde ◽  
H. Fleckseder ◽  
N. Matsché ◽  
F. Plahl-Wabnegg ◽  
G. Spatzierer ◽  
...  
Keyword(s):  
Point Source ◽  
Catchment Area ◽  
Management Practice ◽  
Water Erosion ◽  
Nonpoint Source ◽  
Point Sources ◽  
Source Control ◽  
Nitrogen And Phosphorus ◽  
Catchment Areas ◽  
The One

Neusiedlersee (in German) / Fertö tó (in Hungarian) is a shallow lake at the Austro-Hungarian border. In the late 1970s, the question arose what to do in order to protect the lake against eutrophication. A preliminary report established the need for point-source control as well as gave first estimates for non-point source inputs. The proposed point-source control was quickly implemented, non-point sources were - among other topics - studied in detail in the period 1982 - 1986. The preliminary work had shown, based on integrated sampling and data from literature, that the aeolic input outweighed the one via water erosion (work was for totP only). In contrast to this, the 1982 - 1986 study showed that (a) water erosion by far dominates over aeolic inputs and (b) the size of nonpoint-source inputs was assessed for the largest catchment area in pronounced detail, whereas additional estimates were undertaken for smaller additional catchment areas. The methods as well as the results are presented in the following. The paper concludes with some remarks on the present management practice of nonpoint-source inputs.

scholarly journals Post-collisional mantle delamination in the Dinarides implied from staircases of Oligo-Miocene uplifted marine terraces

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Philipp Balling ◽  
Christoph Grützner ◽  
Bruno Tomljenović ◽  
Wim Spakman ◽  
Kamil Ustaszewski
Keyword(s):  
Balkan Peninsula ◽  
Receiver Functions ◽  
P Wave ◽  
S Wave ◽  
Slab Geometry ◽  
Surface Uplift ◽  
River Incision ◽  
Marine Terraces ◽  
Convergence System ◽  
Internal Dinarides

AbstractThe Dinarides fold-thrust belt on the Balkan Peninsula resulted from convergence between the Adriatic and Eurasian plates since Mid-Jurassic times. Under the Dinarides, S-wave receiver functions, P-wave tomographic models, and shear-wave splitting data show anomalously thin lithosphere overlying a short down-flexed slab geometry. This geometry suggests a delamination of Adriatic lithosphere. Here, we link the evolution of this continental convergence system to hitherto unreported sets of extensively uplifted Oligocene–Miocene (28–17 Ma) marine terraces preserved at elevations of up to 600 m along the Dinaric coastal range. River incision on either side of the Mediterranean-Black Sea drainage divide is comparable to the amounts of terrace uplift. The preservation of the uplifted terraces implies that the most External Dinarides did not experience substantial deformation other than surface uplift in the Neogene. These observations and the contemporaneous emplacement of igneous rocks (33–22 Ma) in the internal Dinarides suggest that the Oligo-Miocene orogen-wide uplift was driven by post-break-off delamination of the Adriatic lithospheric mantle, this was followed by isostatic readjustment of the remaining crust. Our study details how lithospheric delamination exerts an important control on crustal deformation and that its crustal signature and geomorphic imprint can be preserved for millions of years.

scholarly journals S-wave experiments for the exploration of a deep geothermal carbonate reservoir in the German Molasse Basin

2021 ◽  
Vol 9 (1) ◽  
Author(s):  
Britta Wawerzinek ◽  
Hermann Buness ◽  
Hartwig von Hartmann ◽  
David C. Tanner
Keyword(s):  
Upper Jurassic ◽  
Carbonate Reservoir ◽  
P Wave ◽  
Seismic Survey ◽  
Seismic Exploration ◽  
Molasse Basin ◽  
S Wave ◽  
Induced Earthquakes ◽  
Conversion Point ◽  
Facies Classification

AbstractThere are many successful geothermal projects that exploit the Upper Jurassic aquifer at 2–3 km depth in the German Molasse Basin. However, up to now, only P-wave seismic exploration has been carried out. In an experiment in the Greater Munich area, we recorded S-waves that were generated by the conventional P-wave seismic survey, using 3C receivers. From this, we built a 3D volume of P- to S-converted (PS) waves using the asymptotic conversion point approach. By combining the P-volume and the resulting PS-seismic volume, we were able to derive the spatial distribution of the vp/vs ratio of both the Molasse overburden and the Upper Jurassic reservoir. We found that the vp/vs ratios for the Molasse units range from 2.0 to 2.3 with a median of 2.15, which is much higher than previously assumed. This raises the depth of hypocenters of induced earthquakes in surrounding geothermal wells. The vp/vs ratios found in the Upper Jurassic vary laterally between 1.5 and 2.2. Since no boreholes are available for verification, we test our results against an independently derived facies classification of the conventional 3D seismic volume and found it correlates well. Furthermore, we see that low vp/vs ratios correlate with high vp and vs velocities. We interpret the latter as dolomitized rocks, which are connected with enhanced permeability in the reservoir. We conclude that 3C registration of conventional P-wave surveys is worthwhile.

Inverse design of layered periodic wave barriers based on deep learning

2021 ◽  
pp. 146442072110168
Author(s):  
Chen-Xu Liu ◽  
Gui-Lan Yu
Keyword(s):  
Deep Learning ◽  
Activation Function ◽  
Periodic Wave ◽  
P Wave ◽  
Soil Parameters ◽  
S Wave ◽  
Output Frequency ◽  
Great Generality ◽  
Typical Range ◽  
Deep Learning Model

This study presents an approach based on deep learning to design layered periodic wave barriers with consideration of typical range of soil parameters. Three cases are considered where P wave and S wave exist separately or simultaneously. The deep learning model is composed of an autoencoder with a pretrained decoder which has three branches to output frequency attenuation domains for three different cases. A periodic activation function is used to improve the design accuracy, and condition variables are applied in the code layer of the autoencoder to meet the requirements of practical multi working conditions. Forty thousand sets of data are generated to train, validate, and test the model, and the designed results are highly consistent with the targets. The presented approach has great generality, feasibility, rapidity, and accuracy on designing layered periodic wave barriers which exhibit good performance in wave suppression in targeted frequency range.

P- and S-wave attenuation logs from monopole sonic data

Geophysics ◽  
2000 ◽  
Vol 65 (3) ◽  
pp. 755-765 ◽  
Author(s):  
Xinhua Sun ◽  
Xiaoming Tang ◽  
C. H. (Arthur) Cheng ◽  
L. Neil Frazer
Keyword(s):  
Wave Attenuation ◽  
Fluid Velocity ◽  
P Wave ◽  
Reservoir Rock ◽  
Rock Properties ◽  
S Wave ◽  
Intrinsic Attenuation ◽  
Modified Method ◽  
Receiver Array ◽  
Attenuation Profiles

In this paper, a modification of an existing method for estimating relative P-wave attenuation is proposed. By generating synthetic waveforms without attenuation, the variation of geometrical spreading related to changes in formation properties with depth can be accounted for. With the modified method, reliable P- and S-wave attenuation logs can be extracted from monopole array acoustic waveform log data. Synthetic tests show that the P- and S-wave attenuation values estimated from synthetic waveforms agree well with their respective model values. In‐situ P- and S-wave attenuation profiles provide valuable information about reservoir rock properties. Field data processing results show that this method gives robust estimates of intrinsic attenuation. The attenuation profiles calculated independently from each waveform of an eight‐receiver array are consistent with one another. In fast formations where S-wave velocity exceeds the borehole fluid velocity, both P-wave attenuation ([Formula: see text]) and S-wave attenuation ([Formula: see text]) profiles can be obtained. P- and S-wave attenuation profiles and their comparisons are presented for three reservoirs. Their correlations with formation lithology, permeability, and fractures are also presented.

Fracture detection using P-wave and S-wave vertical seismic profiling at The Geysers

Geophysics ◽  
1988 ◽  
Vol 53 (1) ◽  
pp. 76-84 ◽  
Author(s):  
E. L. Majer ◽  
T. V. McEvilly ◽  
F. S. Eastwood ◽  
L. R. Myer
Keyword(s):  
Fractured Rock ◽  
Geothermal Field ◽  
P Wave ◽  
Velocity Variation ◽  
Fracture Detection ◽  
S Wave ◽  
Fracture Geometry ◽  
Seismic Profiling ◽  
Vertical Seismic Profiling ◽  
The Geysers

In a pilot vertical seismic profiling study, P-wave and cross‐polarized S-wave vibrators were used to investigate the potential utility of shear‐wave anisotropy measurements in characterizing a fractured rock mass. The caprock at The Geysers geothermal field was found to exhibit about an 11 percent velocity variation between SH-waves and SV-waves generated by rotating the S-wave vibrator orientation to two orthogonal polarizations for each survey level in the well. The effect is generally consistent with the equivalent anisotropy expected from the known fracture geometry.

Polarization and coherence of 5 to 30 Hz seismic wave fields at a hard-rock site and their relevance to velocity heterogeneities in the crust

1990 ◽  
Vol 80 (2) ◽  
pp. 430-449 ◽  
Author(s):  
William Menke ◽  
Arthur L. Lerner-Lam ◽  
Bruce Dubendorff ◽  
Javier Pacheco
Keyword(s):  
Hard Rock ◽  
Scale Effects ◽  
Spatial Coherence ◽  
Compressional Wave ◽  
P Wave ◽  
Transverse Motion ◽  
S Wave ◽  
Chemical Explosions ◽  
Aperture Arrays ◽  
The Waves

Abstract Except for its very onset, the P wave of earthquakes and chemical explosions observed at two narrow-aperture arrays on hard-rock sites in the Adirondack Mountains have a nearly random polarization. The amount of energy on the vertical, radial, and transverse components is about equal over the frequency range 5 to 30 Hz, for the entire seismogram. The spatial coherence of the seismograms is approximately exp(−cfΔx), where c is in the range 0.4 to 0.7 km−1Hz−1, f is frequency and Δx is the distance between array elements. Vertical, radial, and transverse components were quite coherent over the aperture of the array, indicating that the transverse motion of the compressional wave is a property of relatively large (106 m3) volumes of rock, and not just an anomaly caused by a malfunctioning instrument, poor instrument-rock coupling, or out-crop-scale effects. The spatial coherence is approximately independent of component, epicentral azimuth and range, and whether P- or S-wave coda is being considered, at least for propagation distances between 5 and 170 km. These results imply a strongly and three-dimensionally heterogeneous crust, with near-receiver scattering in the uppermost crust controlling the coherence properties of the waves.

Direct shear-wave seismic survey in Sanhu area, Qaidam Basin, west China

2022 ◽  
Vol 41 (1) ◽  
pp. 47-53
Author(s):  
Zhiwen Deng ◽  
Rui Zhang ◽  
Liang Gou ◽  
Shaohua Zhang ◽  
Yuanyuan Yue ◽  
...  
Keyword(s):  
Shear Wave ◽  
Reservoir Characterization ◽  
Qaidam Basin ◽  
P Wave ◽  
Data Sets ◽  
Direct Shear ◽  
Subsurface Structure ◽  
S Wave ◽  
West China ◽  
Wave Data

The formation containing shallow gas clouds poses a major challenge for conventional P-wave seismic surveys in the Sanhu area, Qaidam Basin, west China, as it dramatically attenuates seismic P-waves, resulting in high uncertainty in the subsurface structure and complexity in reservoir characterization. To address this issue, we proposed a workflow of direct shear-wave seismic (S-S) surveys. This is because the shear wave is not significantly affected by the pore fluid. Our workflow includes acquisition, processing, and interpretation in calibration with conventional P-wave seismic data to obtain improved subsurface structure images and reservoir characterization. To procure a good S-wave seismic image, several key techniques were applied: (1) a newly developed S-wave vibrator, one of the most powerful such vibrators in the world, was used to send a strong S-wave into the subsurface; (2) the acquired 9C S-S data sets initially were rotated into SH-SH and SV-SV components and subsequently were rotated into fast and slow S-wave components; and (3) a surface-wave inversion technique was applied to obtain the near-surface shear-wave velocity, used for static correction. As expected, the S-wave data were not affected by the gas clouds. This allowed us to map the subsurface structures with stronger confidence than with the P-wave data. Such S-wave data materialize into similar frequency spectra as P-wave data with a better signal-to-noise ratio. Seismic attributes were also applied to the S-wave data sets. This resulted in clearly visible geologic features that were invisible in the P-wave data.

An exact anelastic model for the free-surface relfection of P and S-I waves

1989 ◽  
Vol 79 (3) ◽  
pp. 842-859
Author(s):  
R. D. Borcherdt ◽  
G. Glassmoyer
Keyword(s):  
Free Surface ◽  
Volumetric Strain ◽  
Major Axis ◽  
P Wave ◽  
Reflection Coefficients ◽  
S Wave ◽  
Low Loss ◽  
Surface Reflection ◽  
Pierre Shale ◽  
Homogeneous Wave

Abstract Exact anelastic solutions incorporating inhomogeneous waves are used to model numerically S-I and P waves incident on the free surface of a low-loss anelastic half-space. Anelastic free-surface reflection coefficients are computed for the volumetric strain and displacement components of inhomogeneous wave fields. For the problem of an incident homogeneous S-I wave in Pierre shale, the largest strain and displacement amplitudes for the reflected P wave occur at angles of incidence for which the particle motion for the reflected inhomogeneous P wave is elliptical (minor/major axis = 0.6), the specific absorption (QP−1) is greater (300 per cent) and the velocity is less (25 per cent) than those for a corresponding homogeneous P wave, the direction of phase propagation is not parallel to the free surface, and the amplitude of the wave shows a significant increase with depth (6 per cent in one wavelength). Energy reflection coefficients computed for this low-loss anelastic model show that energy flow due to interaction of the incident and reflected waves reach maxima (30 per cent of the incident energy) near large but nongrazing angles of incidence. For the problem of an incident homogeneous P wave in Pierre shale, the inhomogeneity of the reflected S wave is shown not to contribute to significant variations in wave field characteristics over those that would be expected for a homogeneous wave.

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