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.

Seismic reflectivity of hydraulic fractures approximated by thin fluid layers

Geophysics ◽  
2013 ◽  
Vol 78 (4) ◽  
pp. T79-T87 ◽  
Author(s):  
A. Oelke ◽  
D. Alexandrov ◽  
I. Abakumov ◽  
S. Glubokovskikh ◽  
R. Shigapov ◽  
...  
Keyword(s):  
Analytical Solutions ◽  
Fluid Layer ◽  
Synthetic Data ◽  
P Wave ◽  
Hydraulic Fractures ◽  
Reflection Coefficients ◽  
S Wave ◽  
Reservoir Properties ◽  
Thin Fluid ◽  
Theoretical Results

We have analyzed the angle-dependent reflectivity of microseismic wavefields at a hydraulic fracture, which we modeled as an ideal thin fluid layer embedded in an elastic, isotropic solid rock. We derived full analytical solutions for the reflections of an incident P-wave, the P-P and P-S reflection coefficients, as well as for an incident S-wave, and the S-S and S-P reflection coefficients. The rather complex analytical solutions were then approximated and we found that these zero-thickness limit approximations are in good agreement with the linear slip model, representing a fracture at slip contact. We compared the analytical solutions for the P-P reflections with synthetic data that were derived using finite-difference modeling and found that the modeling confirmed our theoretical results. For typical parameters of microseismic monitoring by hydraulic fracturing, e.g., a layer thickness of [Formula: see text] and frequencies of [Formula: see text], the reflection coefficients depend on the Poisson’s ratio. Furthermore, the reflection coefficients of an incident S-wave are remarkably high. Theoretical results suggested that it is feasible to image hydraulic fractures using microseismic events as a source and to solve the inverse problem, that is, to interpret reflection coefficients extracted from microseismic data in terms of reservoir properties.

Downhole seismic logging for high‐resolution reflection surveying in unconsolidated overburden

Geophysics ◽  
1998 ◽  
Vol 63 (4) ◽  
pp. 1371-1384 ◽  
Author(s):  
J. A. Hunter ◽  
S. E. Pullan ◽  
R. A. Burns ◽  
R. L. Good ◽  
J. B. Harris ◽  
...  
Keyword(s):  
High Resolution ◽  
Seismic Velocity ◽  
P Wave ◽  
Unconsolidated Sediments ◽  
Dynamic Shear Modulus ◽  
S Wave ◽  
Interface Shear ◽  
Similar Frequency ◽  
Surface Reflection ◽  
First Arrival

Downhole seismic velocity logging techniques have been developed and applied in support of high‐resolution reflection seismic surveys. For shallow high‐resolution reflection surveying within unconsolidated overburden, velocity‐depth control can sometimes be difficult to achieve; as well, unambiguous correlation of reflections with overburden stratigraphy is often problematic. Data obtained from downhole seismic logging can provide accurate velocity‐depth functions and directly correlate seismic reflections to depth. The methodologies described in this paper are designed for slimhole applications in plastic‐cased boreholes (minimum ID of 50 mm) and with source and detector arrays that yield similar frequency ranges and vertical depth resolutions as the surface reflection surveys. Compressional- (P-) wave logging uses a multichannel hydrophone array with 0.5-m detector spacings in a fluid‐filled borehole and a high‐frequency, in‐hole shotgun source at the surface. Overlapping array positions downhole results in redundant first‐arrival data (picked using interactive computer techniques), which can be processed to provide accurate interval velocities. The data also can be displayed as a record suite, showing reflections and directly correlating reflection events with depths. Example applications include identification of gas zones, lithological boundaries within unconsolidated sediments, and the overburden‐bedrock interface. Shear- (S-) wave logging uses a slimhole, well‐locked, three‐component (3-C) geophone pod and a horizontally polarized, hammer‐and‐loaded‐plate source at ground surface. The pod is moved in successive 0.5- or 1-m intervals downhole with no redundancy of overlapping data as in the P-wave method. First‐arrival data can be obtained by picking the crossover onset of polarized energy or by closely examining particle‐motion plots using all three components of motion. In unconsolidated sediments, shear‐wave velocity contrasts can be associated with changes in material density or dynamic shear modulus, which in turn can be related to consolidation. Example applications include identification of a lithological boundary for earthquake hazard applications and mapping massive ice within permafrost materials.

scholarly journals Rotation, Initial Stress, Gravity and Electromagnetic Field Effect on P Wave Reflection from Stress-Free Surface Elastic Half-Space with Voids under Three Thermoelastic Models

2020 ◽  
Vol 22 (1) ◽  
pp. 313-328 ◽  
Author(s):  
S. M. Abo-Dahab ◽  
S. Z. Rida ◽  
R. A. Mohamed ◽  
A. A. Kilany
Keyword(s):  
Free Surface ◽  
Gravity Field ◽  
Initial Stress ◽  
Complex Modulus ◽  
Plane Waves ◽  
Relaxation Times ◽  
Thermal Relaxation ◽  
Generalized Thermoelasticity ◽  
P Wave ◽  
Reflection Coefficients

AbstractThe present paper is devoted to investigate the influence of the rotation, thermal field, initial stress, gravity field, electromagnetic and voids on the reflection of P wave under three models of generalized thermoelasticity: Classical and Dynamical coupled model (CD), Lord-Shulman model (LS), Green-Lindsay model (GL), The boundary conditions at stress-free thermally insulated surface are satisfied to obtain Algebraic system of four equations in the reflection coefficients of various reflected waves. It is shown that there exist four plane waves; P1, P2, P3 and P4. In addition, the reflection coefficients from insulated and isothermal stress-free surface for the incident P wave are obtained. Finally, numerical values of the complex modulus of the reflection coefficients are visualized graphically to display the effects of the rotation, initial stress, gravity field magnetic field, thermal relaxation times and voids parameters.

Amplitude effect of the free surface in elastic reverse-time extrapolation

Geophysics ◽  
2008 ◽  
Vol 73 (5) ◽  
pp. S177-S184 ◽  
Author(s):  
Robert Sun ◽  
George A. McMechan
Keyword(s):  
Free Surface ◽  
Computational Model ◽  
P Wave ◽  
Surface Boundary ◽  
Reverse Time ◽  
S Wave ◽  
Elastic Data ◽  
Converted Waves ◽  
Incident Waves ◽  
Time Extrapolation

We evaluate the physical validity of surface boundary conditions of the computational model in reverse-time extrapolation of 3D, three-component (3-C) elastic seismic data acquired at the earth’s free surface by using mathematical derivations and numerical simulations. Reverse-time extrapolation of elastic data assumes that only the incident P- or S-waves are reconstructed during extrapolation into the computational grid. However, superposition of the (upgoing) incident waves and the (downgoing) reflected and converted waves generated at the free surface also is recorded in data acquisition and is input into reverse-time extrapolation. In elastic reverse-time extrapolation, the computational model needs to have an absorbing top boundary. When the 3D, 3-C elastic data are inserted into the computational model during reverse-time extrapolation, the originally incident P- or S-wave is reconstructed. In addition, the free-surface P-to-P reflected and P-to-S converted waves recombine to reconstruct a second incident P-wave, and the free-surface S-to-S reflected and S-to-P converted waves recombine to reconstruct a second incident S-wave. Therefore, 3D elastic reverse-time extrapolation reconstructs the incident waves with displacement amplitudes increased by a fixed factor of exactly two when free-surface reflections and conversions are in the data. In this implementation, reconstructed (virtual) waves propagating upward from the free surface enter an absorbing zone and disappear.

scholarly journals The 30 June 2017 North Sea Earthquake: Location, Characteristics, and Context

2020 ◽  
Vol 110 (2) ◽  
pp. 937-952
Author(s):  
Annie E. Jerkins ◽  
Hasbi Ash Shiddiqi ◽  
Tormod Kværna ◽  
Steven J. Gibbons ◽  
Johannes Schweitzer ◽  
...  
Keyword(s):  
North Sea ◽  
Moment Tensor ◽  
P Wave ◽  
Double Difference ◽  
High Signal ◽  
Seismic Events ◽  
S Wave ◽  
Surface Reflection ◽  
Moment Tensor Solution ◽  
Seismicity Pattern

ABSTRACT The Mw 4.5 southern Viking graben earthquake on 30 June 2017 was one of the largest seismic events in the Norwegian part of the North Sea during the last century. It was well recorded on surrounding broadband seismic stations at regional distances, and it generated high signal-to-noise ratio teleseismic P arrivals at up to 90° with good azimuthal coverage. Here, the teleseismic signals provide a unique opportunity to constrain the event hypocenter. Depth phases are visible globally and indicate a surface reflection in the P-wave coda some 4 s after the initial P arrival, giving a much better depth constraint than regional S-P time differences provide. Moment tensor inversion results in a reverse thrust faulting mechanism. The fit between synthetic and observed surface waves at regional distances is improved by including a sedimentary layer. Synthetic teleseismic waveforms generated based on the moment tensor solution, and a near-source 1D velocity model indicates a depth of 7 km. Correlation detectors using the S-wave coda from the main event were run on almost 30 yr of continuous multichannel seismic data searching for repeating signals. In addition to a magnitude 1.9 aftershock 33 min later, and a few magnitude ∼1 events in the following days, a magnitude 2.5 earthquake on 13 November 2016 was the only event found to match the 30 June 2017 event well. Using double-difference techniques, we find that the two largest events are located within 1 km of the main event. We present a Bayesloc probabilistic multiple event location including the 30 June event and all additional seismic events in the region well recorded on the regional networks. The Bayesloc relocation gave a more consistent seismicity pattern and moved several of the events more toward the west. The results of this study are also discussed within the regional seismotectonic frame of reference.

scholarly journals Reflection and Propagation of Magneto-Thermoelastic Plane Waves at Free Surfaces of a Rotating Micropolar Fibre-Reinforced Medium under G-L Theory

2020 ◽  
Vol 25 (2) ◽  
pp. 190-199
Author(s):  
Augustine Igwebuike Anya ◽  
Aftab Khan
Keyword(s):  
Magnetic Field ◽  
Free Surface ◽  
Plane Waves ◽  
P Wave ◽  
Graphical Form ◽  
Reflection Coefficients ◽  
Transverse Displacement ◽  
Thermoelastic Medium ◽  
Solution Approach ◽  
Reflection Of Waves

This article is concerned with the investigation of reflection of waves at the free surface of a rotating micropolar fibre-reinforced thermoelastic medium, in the presence of a magnetic field using Green and Lindsay theory. It is observed that when a P-wave is incident on the free surface of rotating micropolar fibre-reinforced thermoelastic medium in the presence of a magnetic field, four waves are reflected; quasi-longitudinal displacement (qLD), quasi-transverse displacement (qTD), quasi-transverse micro-rotational (qTM) and quasi-thermal waves. The normal modes method, also called the harmonic solution approach, is used simultaneously with Snell's laws and Maxwell's equation, governing electromagnetic fields, in the determination of a solution for the micropolar fibre-reinforced modelled problem. Amplitude ratios or reflection coefficients, which correspond to reflected waves in vertical and horizontal components, are presented analytically. Moreover, the reflection coefficients are presented using numerically simulated results in graphical form for a particular chosen material. We observe that the micropolar fibre-reinforced, rotation, and magneto-thermoelastic field parameters, have varied degree of effects on the propagation and reflection of waves in the medium. The study should be helpful in understanding the behaviour of propagation and reflection of rotating micropolar fibre-reinforced magneto-thermoelastic machination fields and on future works about behaviour of seismic waves.

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.

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