Three‐dimensional elastic modeling by the Fourier method

Geophysics ◽  
1988 ◽  
Vol 53 (9) ◽  
pp. 1184-1193 ◽  
Author(s):  
Moshe Reshef ◽  
Dan Kosloff ◽  
Mickey Edwards ◽  
Chris Hsiung
Keyword(s):  
Wave Velocity ◽  
Three Dimensional ◽  
P Wave ◽  
Velocity Variation ◽  
Difference Operators ◽  
Time Step ◽  
Current Time ◽  
Partial Differentiation ◽  
Wide Range ◽  
Spatial Grid

Earlier work on three‐dimensional forward modeling is extended to elastic waves using the equations of conservation of momentum and the stress‐strain relations for an isotropic elastic medium undergoing infinitesimal deformation. In addition to arbitrary compressional (or P‐wave) velocity and density variation in lateral and vertical directions, elastic modeling permits shear (or S‐wave) velocity variation as well. The elastic wave equation is solved using a generalization of the method for the acoustic case. Computation of each time step begins by computing six strain components by performing nine spatial partial differentiation operations on the three displacement components from the previous time step. The six strains and two Lamé constants are linearly combined to yield six stress components. Nine spatial partial differentiation operations on the six stresses, three body forces, and density are used to compute second partial time derivatives of the three displacement components. Time stepping to obtain the three displacement components for the current time step is performed with second‐order difference operators. The modeling includes an optional free surface above the spatial grid. An absorbing boundary is applied on the lateral and bottom edges of the spatial grid. This modeling scheme is implemented on a four‐processor CRAY X‐MP computer system using the solid‐state storage device (SSD). Using parallel processing with four CPUs, a reasonable geologic model can be computed within a few hours. The modeling scheme provides a variety of seismic source types and many possible output displays. These features enable the modeling of a wide range of seismic surveys. Numerical and analytic results are presented.

scholarly journals Research on prediction method of S-wave velocity based on deep learning

2021 ◽  
Vol 2083 (4) ◽  
pp. 042065
Author(s):  
Guojie Yang ◽  
Shuhua Wang
Keyword(s):  
Deep Learning ◽  
Wave Velocity ◽  
Prediction Method ◽  
P Wave ◽  
Learning Technology ◽  
S Wave ◽  
Advantages And Disadvantages ◽  
Wave Prediction ◽  
Wide Range ◽  
Velocity Prediction

Abstract Aiming at the s-wave velocity prediction problem, based on the analysis of the advantages and disadvantages of the empirical formula method and the rock physics modeling method, combined with the s-wave velocity prediction principle, the deep learning method is introduced, and a deep learning-based logging s-wave velocity prediction method is proposed. This method uses a deep neural network algorithm to establish a nonlinear mapping relationship between reservoir parameters (acoustic time difference, density, neutron porosity, shale content, porosity) and s-wave velocity, and then applies it to the s-wave velocity prediction at the well point. Starting from the relationship between p-wave and s-wave velocity, the study explained the feasibility of applying deep learning technology to s-wave prediction and the principle of sample selection, and finally established a reliable s-wave prediction model. The model was applied to s-wave velocity prediction in different research areas, and the results show that the s-wave velocity prediction technology based on deep learning can effectively improve the accuracy and efficiency of s-wave velocity prediction, and has the characteristics of a wide range of applications. It can provide reliable s-wave data for pre-stack AVO analysis and pre-stack inversion, so it has high practical application value and certain promotion significance.

scholarly journals The Local Earthquake Tomography of Erzurum (Turkey) Geothermal Area

2019 ◽  
Vol 23 (3) ◽  
pp. 209-223 ◽  
Author(s):  
Caglar Ozer ◽  
Mehmet Ozyazicioglu
Keyword(s):  
Wave Velocity ◽  
Seismic Velocity ◽  
Three Dimensional ◽  
P Wave ◽  
Geothermal Area ◽  
S Wave ◽  
Velocity Models ◽  
Local Earthquake Tomography ◽  
P Wave Velocity ◽  
Local Earthquake

Erzurum and its surroundings are one of the seismically active and hydrothermal areas in the Eastern part of Turkey. This study is the first approach to characterize the crust by seismic features by using the local earthquake tomography method. The earthquake source location and the three dimensional seismic velocity structures are solved simultaneously by an iterative tomographic algorithm, LOTOS-12. Data from a combined permanent network comprising comprises of 59 seismometers which was installed by Ataturk University-Earthquake Research Center and Earthquake Department of the Disaster and Emergency Management Authority  to monitor the seismic activity in the Eastern Anatolia, In this paper, three-dimensional Vp and Vp/Vs characteristics of Erzurum geothermal area were investigated down to 30 km by using 1685 well-located earthquakes with 29.894 arrival times, consisting of 17.298 P- wave and 12.596 S- wave arrivals. We develop new high-resolution depth-cross sections through Erzurum and its surroundings to provide the subsurface geological structure of seismogenic layers and geothermal areas. We applied various size horizontal and vertical checkerboard resolution tests to determine the quality of our inversion process. The basin models are traceable down to 3 km depth, in terms of P-wave velocity models. The higher P-wave velocity areas in surface layers are related to the metamorphic and magmatic compact materials. We report that the low Vp and high Vp/Vs values are observed in Yedisu, Kaynarpinar, Askale, Cimenozu, Kaplica, Ovacik, Yigitler, E part of Icmeler, Koprukoy, Uzunahmet, Budakli, Soylemez, Koprukoy, Gunduzu, Karayazi, Icmesu, E part of Horasan and Kaynak regions indicated geothermal reservoir.

Physical modeling and analysis of P-wave attenuation anisotropy in transversely isotropic media

Geophysics ◽  
2007 ◽  
Vol 72 (1) ◽  
pp. D1-D7 ◽  
Author(s):  
Yaping Zhu ◽  
Ilya Tsvankin ◽  
Pawan Dewangan ◽  
Kasper van Wijk
Keyword(s):  
Attenuation Coefficient ◽  
Symmetry Axis ◽  
Wave Attenuation ◽  
Transversely Isotropic ◽  
P Wave ◽  
Velocity Variation ◽  
Ratio Method ◽  
Fracture Detection ◽  
Wide Range ◽  
Attenuation Anisotropy

Anisotropic attenuation can provide sensitive attributes for fracture detection and lithology discrimination. This paper analyzes measurements of the P-wave attenuation coefficient in a transversely isotropic sample made of phenolic material. Using the spectral-ratio method, we estimate the group (effective) attenuation coefficient of P-waves transmitted through the sample for a wide range of propagation angles (from [Formula: see text] to [Formula: see text]) with the symmetry axis. Correction for the difference between the group and phase angles and for the angular velocity variation help us to obtain the normalized phase attenuation coefficient [Formula: see text] governed by the Thomsen-style attenuation-anisotropy parameters [Formula: see text] and [Formula: see text]. Whereas the symmetry axis of the angle-dependent coefficient [Formula: see text] practically coincides with that of the velocity function, the magnitude of the attenuation anisotropy far exceeds that of the velocity anisotropy. The quality factor [Formula: see text] increases more than tenfold from the symmetry axis (slow direction) to the isotropy plane (fast direction). Inversion of the coefficient [Formula: see text] using the Christoffel equation yields large negative values of the parameters [Formula: see text] and [Formula: see text]. The robustness of our results critically depends on several factors, such as the availability of an accurate anisotropic velocity model and adequacy of the homogeneous concept of wave propagation, as well as the choice of the frequency band. The methodology discussed here can be extended to field measurements of anisotropic attenuation needed for AVO (amplitude-variation-with-offset) analysis, amplitude-preserving migration, and seismic fracture detection.

Laboratory characterization of coal P-wave velocity variation during adsorption of methane under tri-axial stress condition

Fuel ◽  
2020 ◽  
Vol 272 ◽  
pp. 117698
Author(s):  
Shuangjiang Zhu ◽  
Fubao Zhou ◽  
Jianhong Kang ◽  
Youpai Wang ◽  
Haijian Li ◽  
...  
Keyword(s):  
Wave Velocity ◽  
Stress Condition ◽  
Axial Stress ◽  
P Wave ◽  
Velocity Variation ◽  
Laboratory Characterization ◽  
P Wave Velocity ◽  
Adsorption Of Methane

scholarly journals A new compositionally based thermal conductivity model for plutonic rocks

2019 ◽  
Vol 219 (2) ◽  
pp. 1377-1394 ◽  
Author(s):  
S Jennings ◽  
D Hasterok ◽  
J Payne
Keyword(s):  
Thermal Conductivity ◽  
Wave Velocity ◽  
Geometric Model ◽  
Limited Range ◽  
P Wave ◽  
Similar Degree ◽  
Primary Control ◽  
Element Geochemistry ◽  
P Wave Velocity ◽  
Wide Range

SUMMARY Thermal conductivity is a physical parameter crucial to accurately estimating temperature and modelling thermally related processes within the lithosphere. Direct measurements are often impractical due to the high cost of comprehensive sampling or inaccessibility and thereby require indirect estimates. In this study, we report 340 new thermal conductivity measurements on igneous rocks spanning a wide range of compositions using an optical thermal conductivity scanning device. These are supplemented by a further 122 measurements from the literature. Using major element geochemistry and modal mineralogy, we produce broadly applicable empirical relationships between composition and thermal conductivity. Predictive models for thermal conductivity are developed using (in order of decreasing accuracy) major oxide composition, CIPW normative mineralogy and estimated modal mineralogy. Four common mixing relationships (arithmetic, geometric, square-root and harmonic) are tested and, while results are similar, the geometric model consistently produces the best fit. For our preferred model, $k_{\text{eff}} = \exp ( 1.72 \, C_{\text{SiO}_2} + 1.018 \, C_{\text{MgO}} - 3.652 \, C_{\text{Na}_2\text{O}} - 1.791 \, C_{\text{K}_2\text{O}})$, we find that SiO2 is the primary control on thermal conductivity with an RMS of 0.28 W m−1 K−1or ∼10 per cent. Estimates from normative mineralogy work to a similar degree but require a greater number of parameters, while forward and inverse modelling using estimated modal mineralogy produces less than satisfactory results owing to a number of complications. Using our model, we relate thermal conductivity to both P-wave velocity and density, revealing systematic trends across the compositional range. We determine that thermal conductivity can be calculated from P-wave velocity in the range 6–8 km s−1 to within 0.31 W m−1 K−1 using $k({V_p}) = 0.5822 \, V_p^2 - 8.263 \, V_p + 31.62$. This empirical model can be used to estimate thermal conductivity within the crust where direct sampling is impractical or simply not possible (e.g. at great depths). Our model represents an improved method for estimating lithospheric conductivity than present formulas which exist only for a limited range of compositions or are limited by infrequently measured parameters.

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