A theoretical study on formation shear radial profiling in well-bonded cased boreholes using sonic dispersion data based on a parameterized perturbation model

Geophysics ◽  
2012 ◽  
Vol 77 (3) ◽  
pp. WA197-WA210 ◽  
Author(s):  
Jiaqi Yang ◽  
Bikash K. Sinha ◽  
Tarek M. Habashy
Keyword(s):  
Shear Velocity ◽  
Radial Variation ◽  
Perturbation Model ◽  
Root Finding ◽  
Dispersion Data ◽  
Radial Extent ◽  
Layered Formation ◽  
Search Routine ◽  
Borehole Waves ◽  
Cased Borehole

Interpretation of sonic data can be challenging in the presence of a steel casing that has a strong influence on elastic waves propagating along a borehole. The cement annulus behind the casing together with drilling-induced near-wellbore alteration causes radial heterogeneity in the propagating medium. It is necessary to study the influence of such heterogeneities on borehole waves and estimate the radial extent of near-wellbore alteration in terms of radial variation of velocities away from the casing. To this end, we based our study on the model of a fluid-filled well-bonded cased borehole surrounded by a cylindrically layered formation. The formation is isotropic and purely elastic, and can be either fast or slow. Borehole monopole and dipole dispersions for this kind of model can be obtained from a root finding mode-search routine. A modified perturbation model based on Hamilton’s principle is used to predict changes in borehole dispersions caused by formation heterogeneities. A two-layer formation model as the reference state is introduced, which always provides normal dispersive reference dispersion for calculations of perturbation integrals for fast and slow formations. Radial variations of the formation shear velocity can be expressed in terms of a parametric exponential profile. Consequently, estimation of these parameters in the assumed profile yields the radial variation of the formation shear slowness away from the casing. Numerical results using synthetic examples are presented to demonstrate the validity of this radial profiling methodology.

scholarly journals Mantle Rayleigh waves from the Kamchatka earthquake of November 4, 1952*

1954 ◽  
Vol 44 (3) ◽  
pp. 471-479
Author(s):  
Maurice Ewing ◽  
Frank Press
Keyword(s):  
Internal Friction ◽  
Rayleigh Waves ◽  
Shear Velocity ◽  
Velocity Curve ◽  
The Core ◽  
Long Period ◽  
A Value ◽  
The Earth ◽  
Dispersion Data ◽  
Kamchatka Earthquake

Abstract Mantle Rayleigh waves from the Kamchatka earthquake of November 4, 1952, are analyzed. The new Palisades long-period vertical seismograph recorded orders R6–R15, the corresponding paths involving up to seven complete passages around the earth. The dispersion data for periods below 400 sec. are in excellent agreement with earlier results and can be explained in terms of the known increase of shear velocity with depth in the mantle. Data for periods 400-480 sec. indicate a tendency for the group velocity curve to level off, suggesting that these long waves are influenced by a low or vanishing shear velocity in the core. Deduction of internal friction in the mantle from wave absorption gives a value 1/Q = 370 × 10−5 for periods 250-350 sec. This is a little over half the value reported earlier for periods 140-215 sec.

Estimation of formation shear and borehole-fluid slownesses using sonic dispersion data in well-bonded cased boreholes

Geophysics ◽  
2011 ◽  
Vol 76 (6) ◽  
pp. E187-E197 ◽  
Author(s):  
Jiaqi Yang ◽  
Bikash K. Sinha ◽  
Tarek M. Habashy
Keyword(s):  
Frequency Band ◽  
Accurate Estimate ◽  
Model Parameters ◽  
Inversion Algorithm ◽  
Dispersion Data ◽  
Open Hole ◽  
Cased Borehole ◽  
Contrast Inversion

New inversion algorithms have been developed for estimating the formation shear and borehole-fluid slownesses, using either the borehole Stoneley or dipole flexural dispersion in well-bonded cased boreholes surrounded by a fast or slow isotropic and purely elastic formation. Two inversion algorithms have been developed for each type of formation. The first algorithm inverts either the measured borehole Stoneley or flexural dispersion at select frequencies for the formation shear slowness when all other model parameters are known. The second algorithm inverts either the borehole Stoneley or flexural dispersion for both the formation shear and borehole-fluid compressional slownesses. Optimal bandwidths for the inversion of the Stoneley and dipole flexural dispersions for the formation shear slowness range from about 5 to 8 kHz. The well-bonded cased borehole dispersion sensitivity to formation shear slowness becomes larger at these higher frequencies than in an open-hole. Moreover, the Stoneley dispersion sensitivity to the borehole-fluid compressional slowness is so large that it becomes necessary to input an extremely accurate estimate of fluid compressional slowness in the inversion algorithm. Inverted formation shear slowness from the Stoneley data in a fast formation exhibits an uncertainty of about 3%, whereas the input borehole-fluid slowness has an uncertainty of 0.5%. Given a certain amount of uncertainty in the borehole-fluid slowness, one can then estimate possible variances in the inverted formation shear slowness. In contrast, inversion of the flexural dispersion for formation shear slowness is less sensitive to the input borehole-fluid compressional slowness in the preferred frequency band of 5 to 8 kHz. Inverted formation shear slownesses in slow formations that use either the Stoneley or flexural dispersion are also far less sensitive to uncertainties in the borehole-fluid compressional slowness.

Inversion of the shear velocity of the cement in cased borehole through ultrasonic flexural waves

Geophysics ◽  
2017 ◽  
Vol 82 (2) ◽  
pp. D57-D68 ◽  
Author(s):  
Feilong Xu ◽  
Hengshan Hu
Keyword(s):  
Wave Velocity ◽  
Error Rate ◽  
Shear Velocity ◽  
P Wave ◽  
Inversion Method ◽  
Flexural Waves ◽  
S Wave ◽  
Additional Time ◽  
Full Waveforms ◽  
Cased Borehole

Young’s elastic modulus and Poisson’s ratio of the cement in a cased borehole are important in the prediction of the cement sheath integrity under hydraulic fracturing. Although these mechanical properties can be derived in principle from the bulk velocities, the inversion of these velocities of the cement from the received full waveforms remains a challenging problem, especially the S-wave velocity. We have developed an inversion method based on the round-trip traveltimes of the leaked flexural waves (TTL) to invert the bulk velocities of the medium behind the casing. The traveltime difference between the casing wave and the delayed casing wave is the additional time for the leaked wave to travel in the interlayer to the formation and back to the casing. To demonstrate the effectiveness of this method, synthetic full waveforms with a changing interlayer are calculated when an ultrasonic acoustic beam is incident obliquely on the casing. The traveltimes of the wave packets are picked from the envelope curve of the full waveform and then used to invert the bulk velocities in the TTL method. The inverted S-wave velocity of cement is quite accurate with an error rate smaller than 3%, no matter whether the cement is of the ordinary, heavy, or light type. When the interlayer is mud, the P-wave is inverted with an error rate of less than 2%. The P-wave velocity is inverted roughly with an error rate of approximately 10% when the medium behind the casing is light cement.

Inversion of Rg waveforms recorded in southern Spain

1997 ◽  
Vol 87 (4) ◽  
pp. 847-865
Author(s):  
Manuel Navarro ◽  
Victor Corchete ◽  
José Badal ◽  
José A. Canas ◽  
Luis Pujades ◽  
...  
Keyword(s):  
Group Velocity ◽  
Velocity Structure ◽  
Group Velocity Dispersion ◽  
Shear Velocity ◽  
Dispersion Analysis ◽  
Southern Spain ◽  
Mountain Range ◽  
Low Velocity ◽  
Dispersion Data ◽  
Group Velocities

Abstract Group velocity dispersion measurements of Rg waves generated either by blasts or by local earthquakes are used to investigate the shallow crustal structure of Almería (southern Spain). In principle, the usable frequency range of 250 to 2000 mHz allows determination of structures to depths of about 4 km. For this purpose, the main operations are a detailed dispersion analysis of high-frequency Rayleigh waves propagating along very short paths and the inversion of Rg-wave group velocities. A total of 21 seismic events were studied. These events had small magnitudes (2.0 to 2.5 approximately) and very shallow focal depths (about 100 m) and were taken from a set of 214 events that occurred in 1991 during a Spanish-Italian seismic experiment. The events were recorded at seven single-component stations belonging to the Regional Seismic Network of Andalucía at approximate distances of between 15 and 57 km from the source. These events were grouped into six seismic sources according to specific criteria. We used digital filtering techniques providing a significant improvement in signal-to-noise ratio to determine ray-path group velocities, and we inverted dispersion data via generalized inversion. In order to obtain refined dispersion data, we have carried out a further regionalization of group velocities, and thus six small subregions have been resolved in group velocities. The highest group velocity values, from 1.93 to 2.25 km sec−1, correspond to the Filabres mountain range, which is an area containing materials of the Nevado-Filábride complex of Paleozoic and Triassic age. On the other hand, low velocity values, between 1.39 and 1.56 km sec−1, correspond to the Alhamilla mountain range, which belongs to the Alpujárride complex and contains conglomerates of the Cambrian and Tortonian periods. The velocities obtained for the neogene-quaternary basin of the Andarax river, with materials of the Tortonian and Pliocene periods, are also very low, between 1.35 and 1.68 km sec−1. We inverted the regionalized group velocities in order to obtain the shear velocity structure of the region for depths down to 4 km. According to the regional Earth models that we obtained, we find clear variations in velocity both laterally and vertically for several zones with different composition. The Filabres mountain range shows high shear velocity values: 2.14 to 2.83 km sec−1. In the opposite end, we have the Andarax basin that presents the lowest shear velocity values, consistent with its sedimentary structure: 1.56 to 2.55 km sec−1. Intermediate shear-wave velocities characterize the remaining regions: the Tabernas-Sorbas basin, the Gádor mountain range, and the volcanic region of Nijar-Cape of Gata. Although the relationship between lateral changes in Rg dispersion and geologic structure may not be straightforward, in this study, we have observed a correlation between those changes and the sharply contrasting geology between adjacent geological formations.

Mapping formation shear-velocity variation by inverting logging-while-drilling quadrupole-wave dispersion data

Geophysics ◽  
2013 ◽  
Vol 78 (6) ◽  
pp. D491-D498 ◽  
Author(s):  
Yuan-Da Su ◽  
Xiao-Ming Tang ◽  
Chun-Xi Zhuang ◽  
Song Xu ◽  
Long Zhao
Keyword(s):  
Velocity Profile ◽  
High Frequency ◽  
Shear Velocity ◽  
Wave Dispersion ◽  
Physical Principle ◽  
Equivalent Model ◽  
Velocity Variation ◽  
Inversion Method ◽  
Dispersion Data ◽  
Logging While Drilling

The logging-while-drilling (LWD) quadrupole wave is a dispersive wave mode guided along the borehole with a drill collar. The wave is sensitive to the formation alteration caused by drilling. We inverted LWD quadrupole-wave dispersion data to estimate a radial shear-velocity profile away from the wellbore. We also explored the nonuniqueness of the inverse problem and solved it by using a constrained inversion method. This was done by constraining the high-frequency portion of the model dispersion curve with another curve calculated using the near-borehole velocity. The constraint condition is based on the physical principle that a high-frequency LWD quadrupole wave has a shallow penetration depth and is therefore sensitive to the near-borehole shear velocity. Particularly, we found that a monotonically continuous velocity profile can be well approximated using a one-zone equivalent model, allowing for a drastic simplification of the inversion process. We used theoretical modeling and real data examples to validate the method for the LWD wave data. The quadrupole dispersion data and the inversion results clearly demonstrated that formation alteration can occur even while the well is being drilled.

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