Synthetic full‐waveform acoustic logs in cased boreholes, II—Poorly bonded casing

Geophysics ◽  
1986 ◽  
Vol 51 (4) ◽  
pp. 902-913 ◽  
Author(s):  
Kenneth M. Tubman ◽  
C. H. Cheng ◽  
S. P. Cole ◽  
M. Nafi Toksöz
Keyword(s):  
Wave Propagation ◽  
Elastic Wave ◽  
Theoretical Study ◽  
Fluid Layer ◽  
Body Wave ◽  
P Wave ◽  
Full Waveform ◽  
Fluid Layers ◽  
First Arrival ◽  
Wave Arrival

A generalization of the technique of Tubman et al. (1984) allows the inclusion of intermediate fluid layers in the theoretical study of elastic wave propagation in a layered borehole. The number and location of fluid layers are arbitrary. The only restrictions are that the central cylinder is fluid and the outermost formation is solid. Synthetic full‐waveform microseismograms in poorly bonded cased holes can be generated, allowing investigation of free pipe and cement sheathed pipe with no bond to the formation. If there is a fluid layer between the steel and the cement, the steel is free to ring. The first arrival in this situation is from the casing, even with an extremely thin fluid layer or microannulus. The amplitude and duration of the pipe signal depend upon the thickness of the fluid layer. While the first arrival is from the casing, the formation body‐wave energy is present. The character of the waveform will vary as the formation parameters vary. If the duration of the steel arrival is small, it is possible to distinguish the formation P-wave arrival. If the fluid layer is between the cement and the formation, then the steel is well bonded to the cement but the cement is not bonded to the formation. In this case the thicknesses of the fluid and cement layers are important in determining the nature of the first arrival. If there is a large amount of cement bonded to the steel, the cement can damp out the ringing of the pipe and make it possible to distinguish formation arrivals. If there is less cement bonded to the steel, the cement does not damp out the steel ringing but the cement rings along with the steel and the first arrival is from the combination of the steel and the cement. The velocity of this wave depends upon the velocities and thicknesses of the steel and cement layers.

scholarly journals Recording seismic reflections using rigidly interconnected geophones

Geophysics ◽  
2001 ◽  
Vol 66 (6) ◽  
pp. 1838-1842 ◽  
Author(s):  
C. M. Schmeissner ◽  
K. T. Spikes ◽  
D. W. Steeples
Keyword(s):  
Wave Propagation ◽  
Data Acquisition ◽  
Seismic Reflection ◽  
Spatial Sampling ◽  
P Wave ◽  
Signal Distortion ◽  
Reflection And Refraction ◽  
First Arrival ◽  
The Cost ◽  
Seismic Reflections

Ultrashallow seismic reflection surveys require dense spatial sampling during data acquisition, which increases their cost. In previous efforts to find ways to reduce these costs, we connected geophones rigidly to pieces of channel iron attached to a farm implement. This method allowed us to plant the geophones in the ground quickly and automatically. The rigidly interconnected geophones used in these earlier studies detected first‐arrival energy along with minor interfering seismic modes, but they did not detect seismic reflections. To examine further the feasibility of developing rigid geophone emplacement systems to detect seismic reflections, we experimented with four pieces of channel iron, each 2.7 m long and 10 cm wide. Each segment was equipped with 18 geophones rigidly attached to the channel iron at 15‐cm intervals, and the spikes attached to all 18 geophones were pushed into the ground simultaneously. The geophones detected both refracted and reflected energy; however, no significant signal distortion or interference attributable to the rigid coupling of the geophones to the channel iron was observed in the data. The interfering seismic modes mentioned from the previous experiments were not detected, nor was any P‐wave propagation noted within the channel iron. These results show promise for automating and reducing the cost of ultrashallow seismic reflection and refraction surveys.

Approximation of pure acoustic seismic wave propagation in TTI media

Geophysics ◽  
2011 ◽  
Vol 76 (5) ◽  
pp. WB97-WB107 ◽  
Author(s):  
Chunlei Chu ◽  
Brian K. Macy ◽  
Phil D. Anno
Keyword(s):  
Wave Propagation ◽  
Wave Equation ◽  
Elastic Wave ◽  
Wave Equations ◽  
Computational Cost ◽  
P Wave ◽  
Anisotropy Axis ◽  
S Wave ◽  
Time Migration ◽  
Tti Media

Pseudoacoustic anisotropic wave equations are simplified elastic wave equations obtained by setting the S-wave velocity to zero along the anisotropy axis of symmetry. These pseudoacoustic wave equations greatly reduce the computational cost of modeling and imaging compared to the full elastic wave equation while preserving P-wave kinematics very well. For this reason, they are widely used in reverse time migration (RTM) to account for anisotropic effects. One fundamental shortcoming of this pseudoacoustic approximation is that it only prevents S-wave propagation along the symmetry axis and not in other directions. This problem leads to the presence of unwanted S-waves in P-wave simulation results and brings artifacts into P-wave RTM images. More significantly, the pseudoacoustic wave equations become unstable for anisotropy parameters [Formula: see text] and for heterogeneous models with highly varying dip and azimuth angles in tilted transversely isotropic (TTI) media. Pure acoustic anisotropic wave equations completely decouple the P-wave response from the elastic wavefield and naturally solve all the above-mentioned problems of the pseudoacoustic wave equations without significantly increasing the computational cost. In this work, we propose new pure acoustic TTI wave equations and compare them with the conventional coupled pseudoacoustic wave equations. Our equations can be directly solved using either the finite-difference method or the pseudospectral method. We give two approaches to derive these equations. One employs Taylor series expansion to approximate the pseudodifferential operator in the decoupled P-wave equation, and the other uses isotropic and elliptically anisotropic dispersion relations to reduce the temporal frequency order of the P-SV dispersion equation. We use several numerical examples to demonstrate that the newly derived pure acoustic wave equations produce highly accurate P-wave results, very close to results produced by coupled pseudoacoustic wave equations, but completely free from S-wave artifacts and instabilities.

Experimental study on the effects of fractures on elastic wave propagation in synthetic layered rocks

Geophysics ◽  
2016 ◽  
Vol 81 (4) ◽  
pp. D441-D451 ◽  
Author(s):  
Tianyang Li ◽  
Ruihe Wang ◽  
Zizhen Wang ◽  
Yuzhong Wang
Keyword(s):  
Wave Propagation ◽  
Fractal Dimension ◽  
Power Spectrum ◽  
Elastic Wave ◽  
Power Law ◽  
Layered Media ◽  
Physical Models ◽  
P Wave ◽  
Fracture Density ◽  
S Wave

Fractures greatly increase the difficulty of oil and gas exploration and development in reservoirs consisting of interlayered carbonates and shales and increase the uncertainty of highly efficient development. The presence of fractures or layered media is also widely known to affect the elastic properties of rocks. The combined effects of fractures and layered media are still unknown. We have investigated the effects of fracture structure on wave propagation in interlayered carbonate and shale rocks using physical models based on wave theory and the similarity principle. We have designed and built two sets of layered physical models with randomly embedded predesigned vertically aligned fractures according to the control variate principle. We have measured the P- and S-wave velocities and attenuation and analyzed the effects of fracture porosity and aspect ratio (AR) on velocity, attenuation, and power spectral dimension of the P- and S-waves. The experimental results indicated that under conditions of low porosity ([Formula: see text]), Han’s empirical velocity-porosity relations and Wang’s attenuation-porosity relation combined with Wyllie’s time-average model are a good prediction for layered physical models with randomly embedded fractures. When the porosity is constant, the effect of different ARs on elastic wave properties can be described by a power law function. We have calculated the power spectrum fractal dimension [Formula: see text] of the transmitted signal in the frequency domain, which can supplement the S-wave splitting method for estimating the degree of anisotropy. The simple power law relation between the power spectrum fractal dimension of the P-waveform and fracture density suggests the possible use of P-waves for discriminating fracture density. The high precision and low error of this processing method give new ideas for rock anisotropy evaluation and fracture density prediction when only P-wave data are available.

Pore-scale modeling of elastic wave propagation in carbonate rocks

Geophysics ◽  
2015 ◽  
Vol 80 (1) ◽  
pp. D51-D63 ◽  
Author(s):  
Zizhen Wang ◽  
Ruihe Wang ◽  
Ralf J. Weger ◽  
Tianyang Li ◽  
Feifei Wang
Keyword(s):  
Porous Media ◽  
Wave Propagation ◽  
Elastic Wave ◽  
Pore Structure ◽  
Wave Velocity ◽  
Carbonate Rocks ◽  
P Wave ◽  
Pore Scale ◽  
Scale Modeling ◽  
P Wave Velocity

The relationship between P-wave velocity and porosity in carbonate rocks shows a high degree of variability due to the complexity of the pore structure. This variability introduces high uncertainties to seismic inversion, amplitude variation with offset analysis, porosity estimation, and pore-pressure prediction based on velocity data. Elastic wave propagation in porous media is numerically modeled on the pore scale to investigate the effects of pore structure on P-wave velocities in carbonate rocks. We built 2D models of porous media using pore structure information and the similarity principle. Then, we simulated normal incidence wave propagation using finite element analysis. Finally, the velocity was determined from received modeled signals by means of crosscorrelation. The repeatability and accuracy of this modeling process was verified carefully. Based on the modeling results, a simple formulation of Sun’s frame flexibility factor ([Formula: see text]), aspect ratio (AR, the ratio of the major axis to the minor axis), and pore density was developed. The numerical simulation results indicated that the P-wave velocity increases as a power function as the AR increases. Pores with small AR ([Formula: see text]) or large [Formula: see text] created softening effects that decrease P-wave velocity significantly. The P-wave velocity of carbonate rocks was dispersive; it depends on the ratio of the wavelength to pore size ([Formula: see text]). Such scale-dependent dispersion was more evident for carbonate rocks with higher porosity, lower AR, and/or lower P-wave impedance of pore fluids. The P-wave velocity of carbonate rocks with complicated pore geometries (low AR, high [Formula: see text], small [Formula: see text]) was much lower than that of rocks with simple pore geometries (high AR, small [Formula: see text], large [Formula: see text]) at low and high [Formula: see text]. The pore-scale modeling of elastic wave properties of porous rocks may explain the poor velocity-porosity correlation in carbonate rocks.

A rectangular-grid lattice spring model for modeling elastic waves in Poisson’s solids

Geophysics ◽  
2018 ◽  
Vol 83 (2) ◽  
pp. T69-T86 ◽  
Author(s):  
Muming Xia ◽  
Hui Zhou ◽  
Hanming Chen ◽  
Qingchen Zhang ◽  
Qingqing Li
Keyword(s):  
Wave Propagation ◽  
Elastic Wave ◽  
Elastic Waves ◽  
Heterogeneous Media ◽  
Elastic Wave Propagation ◽  
P Wave ◽  
Numerical Dispersion ◽  
Spring Model ◽  
Rectangular Grid ◽  
Lattice Spring Model

The lattice spring model (LSM) combined with the velocity Verlet algorithm is a newly developed scheme for modeling elastic wave propagation in solid media. Unlike conventional wave equations, LSM is established on the basis of micromechanics of the subsurface media, which enjoys better dynamic characteristics of elastic systems. We develop a rectangular-grid LSM scheme for elastic waves simulation in Poisson’s solids, and the direction-dependent elastic constants are deduced to keep the isotropy of the discrete grid. The stability condition and numerical dispersion properties of LSM are discussed and compared with other numerical methods. The 2D and 3D numerical simulations are carried out using the rectangular-grid LSM, as well as the second- and fourth-order accuracy staggered finite-difference method (FDM). Wavefields obtained by LSM are fairly similar with those by analytical solution and FDM, which demonstrates the correctness of the proposed scheme and its capability of modeling elastic wave propagation in heterogeneous media. Moreover, we perform plane P-wave simulation through a semi-infinite cavity model via LSM and FDM, the recorded wavefield snapshots indicate that our proposed rectangular-grid LSM obtains more reasonable wavefield details compared with those of FDM, especially in media with high compliance and structure complexity. Our main contribution lies in offering an alternative simulation scheme for modeling elastic wave propagation in media with some kinds of complexities, which conventional FDM may fail to simulate.

Synthetic full waveform acoustic logs in cased boreholes

Geophysics ◽  
1984 ◽  
Vol 49 (7) ◽  
pp. 1051-1059 ◽  
Author(s):  
Kenneth M. Tubman ◽  
C. H. Cheng ◽  
M. Nafi Toksöz
Keyword(s):  
Rayleigh Wave ◽  
Arbitrary Number ◽  
Fluid Layer ◽  
Body Wave ◽  
Model Parameters ◽  
Combined Effects ◽  
Interface Waves ◽  
Full Waveform ◽  
Propagator Matrix ◽  
Model Geometry

A general expression is derived for the dispersion relations and the impulse response of a radially layered borehole. The model geometry consists of a central fluid cylinder surrounded by an arbitrary number of solid annuli. A Thomson‐Haskell type propagator matrix is used to relate stresses and displacements across the layers. Although the model is completely general, the geometries considered here are restricted to those of a cased hole. Layers of steel, cement, and formation surround the innermost fluid layer. Synthetic microseismograms containing all body and interface waves are calculated for a variety of model parameters. Formation body wave arrivals are relatively unaffected by the presence of a casing. They may, however, be hard to identify cement velocities are close to or larger than those of the formation. The Stoneley and pseudo‐Rayleigh wave arrivals are strongly influenced by the casing parameters. They respond to the combined effects of the steel, the cement, and the formation.

Amplitude and frequency characteristics of elastic wave types generated by the underground nuclear detonation, Boxcar

1969 ◽  
Vol 59 (6) ◽  
pp. 2283-2293
Author(s):  
W. W. Hays
Keyword(s):  
Surface Wave ◽  
Elastic Wave ◽  
Wave Amplitude ◽  
Body Wave ◽  
Time Windows ◽  
Maximum Amplitude ◽  
Propagation Distance ◽  
Dominant Frequency ◽  
Frequency Characteristics ◽  
P Wave

abstract Elastic wave types generated by the Boxcar underground nuclear detonation were identified and analyzed to determine their amplitude and frequency characteristics as a function of distance. The amplitude characteristics of the identified wave types were determined to vary with source to recording station distance and frequency. Within each body wave subset, the refracted wave amplitude decays most rapidly and the reflected wave amplitude least rapidly with distance. Fourier amplitude spectra of the P, S, and surface wave time windows exhibit maxima which occur at different spectral frequencies for stations on rock, ranging from a dominant frequency of about 0.8 Hz for the P-wave window to about 0.25 Hz for the surface wave window. The frequency of the maximum amplitude of each of the three wave mode window spectral sets is essentially unaffected by increase in propagation distance over the distance range 22.2-79.1 km.

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