Compressional Attenuation Research Articles

Determination of formation shear attenuation from dipole sonic log data

ABSTRACT Formation S-wave attenuation, when combined with compressional attenuation, serves as a potential hydrocarbon indicator for seismic reservoir characterization. Sonic flexural wave measurements provide a direct means for obtaining the in situ S-wave attenuation at log scale. The key characteristic of the flexural wave is that it propagates at the formation shear slowness and experiences shear attenuation at low frequency. However, in a fast formation, the dipole log consists of refracted P- and S-waves in addition to the flexural wave. The refracted P-wave arrives early and can be removed from the dipole waveforms through time windowing. However, the refracted S-wave, which is often embedded in the flexural wave packet, is difficult to separate from the dipole waveforms. The additional energy loss associated with the refracted S-wave results in the estimated dipole attenuation being higher than the shear attenuation at low frequency. To address this issue, we have developed a new method for accurately determining the formation shear attenuation from the dipole sonic log data. The method uses a multifrequency inversion of the frequency-dependent flexural wave attenuation based on energy partitioning. We first developed our method using synthetic data. Application to field data results in a shear attenuation log that is consistent with lithologic interpretation of other available logs.

Three-Dimensional Compressional Attenuation Model (QP) for the Salton Trough, Southern California

Abstract I present a frequency‐independent 3D seismic attenuation model (indicated by ) for the crust of the Salton trough and the adjacent regions in southeastern southern California. The simul2000 tomographic algorithm was used to invert the frequency‐independent attenuation operator t * values measured from amplitude spectra of 23,378 P ‐wave arrivals of 1203 events through a recently developed 3D velocity model. The Q P model has a uniform horizontal grid spacing of 5 km, and the vertical‐node intervals range between 2 and 5 km down to 27 km depth. In general, the Q P values increase with depth and agree with the surface geology in the shallow depth layers. Low Q P values are observed in the Imperial Valley, California, which are consistent with the sedimentary deposits and may also reflect the presence of pore fluid in the active fault zones, whereas greatly elevated Q P values are shown in the surrounding crystalline ranges. The new Q P model provides an important complement to the existing velocity models for interpreting structural heterogeneity and fluid saturation of rocks in the study area. Online Material: Figures of checkerboard resolution tests, Q P versus V P , and Q P versus heat flow.

Borehole study of compressional and shear attenuation of basalt flows penetrated by the Brugdan and William wells on the Faroes shelf

ABSTRACTWe investigated the seismic attenuation of compressional (P‐) and converted shear (S‐) waves through stacked basalt flows using short‐offset vertical seismic profile (VSP) recordings from the Brugdan (6104/21–1) and William (6005/13–1A) wells in the Faroe‐Shetland Trough. The seismic quality factors (Q) were evaluated with the classical spectral ratio method and a root‐mean‐square time‐domain amplitude technique. We found the latter method showed more robust results when analysing signals within the basalt sequence. For the Brugdan well we calculated effective Q estimates of 22–26 and 13–17 for P‐ and S‐waves, respectively, and 25–33 for P‐waves in the William well. An effective QS/QP ratio of 0.50–0.77 was found from a depth interval in the basalt flow sequence where we expect fully saturated rocks. P‐wave quality factor estimates are consistent with results from other VSP experiments in the North Atlantic Margin, while the S‐wave quality factor is one of the first estimates from a stacked basalt formation using VSP data. Synthetic modelling demonstrates that seismic attenuation for P‐ and S‐waves in the stacked basalt flow sequence is mainly caused by one‐dimensional scattering, while intrinsic absorption is small.

Seabed geoacoustic characterization with a vector sensor array

This paper proposes a vector sensor measurement model and the related Bartlett estimator based on particle velocity measurements for generic parameter estimation, illustrating the advantages of the Vector Sensor Array (VSA). A reliable estimate of the seabed properties such as sediment compressional speed, density and compressional attenuation based on matched-field inversion (MFI) techniques can be achieved using a small aperture VSA. It is shown that VSAs improve the resolution of seabed parameter estimation when compared with pressure sensor arrays with the same number of sensors. The data considered herein was acquired by a four-element VSA in the 8-14 kHz band, during the Makai Experiment in 2005. The results obtained with the MFI technique are compared with those obtained with a method proposed by C. Harrison, which determines the bottom reflection loss as the ratio between the upward and downward beam responses. The results show a good agreement and are in line with the historical information for the area. The particle velocity information provided by the VSA increases significantly the resolution of seabed parameter estimation and in some cases reliable results are obtained using only the vertical component of the particle velocity.

Fractional wave equation for compressional and shear waves.

This study has been motivated by the observed difference in the range of the power law attenuation exponent for compressional and shear waves. Usually compressional attenuation increases with frequency to a power between 1 and 2, while shear wave attenuation often is described with powers less than 1. Another motivation is the apparent lack of partial differential equations with desirable properties such as causality that describe such wave propagation. Starting with a constitutive equation which is generalized Hooke’s law with a loss term containing a fractional derivative, one can derive a causal fractional wave equation previously given by Caputo (1967) and Wismer (2006). In the low ωτ (low‐frequency) case, this equation has an attenuation with a power law in the range from 1 to 2. This is consistent with, e.g., attenuation in tissue. In the often neglected high ωτ (high‐frequency) case, it describes attenuation with a power law between 0 and 1, consistent with what is observed in, e.g., dynamic elastography. Thus a unifying wave equation derived properly from constitutive equations can describe both cases. Recent results on fractional random media will also be discussed as they give similar characteristics from a microperspective.

A unifying fractional wave equation for compressional and shear waves

This study has been motivated by the observed difference in the range of the power-law attenuation exponent for compressional and shear waves. Usually compressional attenuation increases with frequency to a power between 1 and 2, while shear wave attenuation often is described with powers less than 1. Another motivation is the apparent lack of partial differential equations with desirable properties such as causality that describe such wave propagation. Starting with a constitutive equation which is a generalized Hooke's law with a loss term containing a fractional derivative, one can derive a causal fractional wave equation previously given by Caputo [Geophys J. R. Astron. Soc. 13, 529-539 (1967)] and Wismer [J. Acoust. Soc. Am. 120, 3493-3502 (2006)]. In the low omegatau (low-frequency) case, this equation has an attenuation with a power-law in the range from 1 to 2. This is consistent with, e.g., attenuation in tissue. In the often neglected high omegatau (high-frequency) case, it describes attenuation with a power-law between 0 and 1, consistent with what is observed in, e.g., dynamic elastography. Thus a unifying wave equation derived properly from constitutive equations can describe both cases.

Attenuation of shear and compressional waves in surficial sediments.

Recent in situ measurements of shear and compressional wave attenuation in sediments provide an appropriate data set to develop empirical relationships among seafloor acoustic and physical properties. Compressional wave attenuation increases with increasing mean grain size and bulk density and with decreasing porosity, whereas the relationships among shear wave attenuation and these physical properties display the opposite trends. The ratio of shear to compressional attenuation ranges from 25 to 60, with the highest values occurring in fine‐grained, high‐porosity sediments. Empirical relationships defined by regressions of compressional and shear wave speeds on sediment physical properties have high confidence levels. However, confidence levels for the prediction of attenuation are poor due to a combination of measurement technique, spatial variability, and presence of strong near‐surface gradients.

Geoacoustic inversion using adaptive neuro-fuzzy inference system

The geoacoustic parameters form significant input for underwater acoustic propagation studies and geoacoustic modeling. Conventional inversion techniques commonly used as indirect approach for extraction of geoacoustic parameters from acoustic or seismic data are computationally intensive and time-consuming. In the present study, we have tried to exploit the advantage of soft computing techniques like, reasoning ability of fuzzy logic and learning abilities of neural networks, in inversion studies. The network model based on the combined approach called adaptive neuro-fuzzy inference system (ANFIS), is found to be very promising in inversion of the acoustic data. The network model once built is capable of invert a few thousand data sets instantaneously, to a reasonably good accuracy. In the case of conventional approaches, repetition of the entire inversion process with each new data set is required. A limited number of sensor’s data are sufficient for simulation of the network model and provides an advantage to use short hydrophone array data. Inversion results of a few hundred test data sets, representing different geoacoustic environments, show the prediction error is much less than 0.01 g/cc, 10 m/s, 10 m and 0.1 against first layer’s density, compressional sound speed, thickness and attenuation respectively for a three-layer geoacoustic model. However, the error is relatively large for the second- and third-layer parameters, which need to be improved. The model is efficient, robust and inexpensive.

Seismic attenuation from VSP data in methane hydrate-bearing sediments

Recent seismic surveys have shown that the presence of methane hydrate (MH) in sediments has significant influence on seismic attenuation. I have used vertical seismic profile (VSP) data from a Nankai Trough exploratory well, offshore Tokai in central Japan, to estimate compressional attenuation in MH-bearing sediments at seismic frequencies of 30–110 Hz. The use of two different measurement methods (spectral ratio and centroid frequency shift methods) provides an opportunity to validate the attenuation measurements. The sensitivity of attenuation analyses to different depth intervals, borehole irregularities, and different frequency ranges was also examined to validate the stability of attenuation estimation. I found no significant compressional attenuation in MH-bearing sediments at seismic frequencies. Macroscopically, the peaks of highest attenuation in the seismic frequency range correspond to low-saturation gas zones. In contrast, high compressional attenuation zones in the sonic frequency range (10–20 kHz) are associated with the presence of methane hydrates at the same well locations. Thus, this study demonstrated the frequency-dependence of attenuation in MH-bearing sediments; MH-bearing sediments cause attenuation in the sonic frequency range rather than the seismic frequency range. As a possible reason why seismic frequencies in the 30–110 Hz range were not affected in MH-bearing sediments, I point out the effect of thin layering of MH-bearing zones.

Using Triplet Arrays for Broadband Reverberation Analysis and Inversions

Some directional characteristics of observed clutter and reverberation are presented using line arrays with cardioid elements. It is shown that the cardioid arrays break the left/right ambiguity for reverberation sources above ~600-700 Hz. Data analysis uses a cardioid beamforming algorithm developed by researchers at the NATO Undersea Research Centre (NURC, La Spezia, Italy) but the normalization for this algorithm is derived by the author. It is shown that this normalized algorithm has an upper frequency limitation not previously noted. Reverberation data are taken from two recent experiments. One was the 2004 Boundary Characterization Experiment near the Malta Plateau. The area is rich in clutter objects like wrecks and mud-volcanoes and has some subbottom features that may be important. Sources were monostatic coherent pulses and impulsive sources. The receiver was the NURC cardioid array. The other experiment was the U.S. Office of Naval Research's 2003 Geoclutter effort to study shallow-water bottom reverberation and clutter in the STRATAFORM area off New Jersey. Sources were bistatic coherent pulses. The receiver was the five-octave research array (FORA). The STRATAFORM has benign surface morphology but strong clutter is observed. Some highlights of the reverberant returns from that area are discussed that include returns from probable fish schools. From these two data sets, it is shown that up to 15-20-dB left/right discrimination is attainable on broadside cardioid beams in the 1200-1750-Hz region for both linear frequency modulation (LFM) pulses and sound-underwater-source (SUS) broadband data. Also, a (previously developed) constrained simulated annealing (SA) inversion technique is applied to the directional reverberation data from the NURC array. A two-layer fluid model of the bottom is assumed. The algorithm is best at estimating compressional speeds, layer thickness, and attenuations in that order. Extracted bottom parameters at the site are compared with independent inversion results previously reported by Holland. Inverting reverberation from directional arrays is shown to give somewhat better quality results since, unlike standard line arrays, the reverberation data apply to only one bearing along the seafloor.

Seismic wave attenuation in methane hydrate‐bearing sediments: Vertical seismic profiling data from the Nankai Trough exploratory well, offshore Tokai, central Japan

Data from two vertical seismic profiles (VSPs) from the Nankai Trough exploratory well, offshore Tokai, central Japan, are used to estimate compressional attenuation in methane hydrate (MH)‐bearing sediments at seismic frequencies of 30–110 Hz. We compare spectral ratio and centroid frequency shift methods for measuring attenuation. To isolate intrinsic attenuation from total attenuation, attenuation is computed from multiples using one‐dimensional synthetic VSP data from sonic and density logs. The use of two different measurement methods and two VSPs recorded at just 100 m separation provides an opportunity to validate the attenuation measurements. No significant compressional attenuation was observed in MH‐bearing sediments at seismic frequencies. Macroscopically, the peaks of highest attenuation in the seismic frequency range correspond to low‐saturation gas zones. In contrast, high compressional attenuation zones in the sonic frequency range (10–20 kHz) are affected by the presence of methane hydrates in the same well locations. Thus this study demonstrated the frequency dependence of attenuation in MH‐bearing sediments; MH‐bearing sediments cause attenuation in the sonic frequency range rather than the seismic frequency range.

Geoacoustic Uncertainties From Viscoelastic Inversion of Seabed Reflection Data

This paper applies nonlinear Bayesian inversion to seabed reflection data to estimate viscoelastic parameters of the upper sediments. The inversion provides maximum a posteriori probability (MAP) parameter estimates with uncertainties quantified in terms of marginal probability distributions, variances, and credibility intervals; interparameter relationships are quantified by correlations and joint marginal distributions. The inversion is applied to high-resolution reflectivity data from two sites in the Strait of Sicily. One site is characterized by low-speed sediments, resulting in data with a well-defined angle of intromission; the second is characterized by high-speed sediments, resulting in a critical angle. Data uncertainties are quantified using several approaches, including maximum-likelihood (ML) estimation, treating uncertainties as nuisance parameters in the inversion, and analysis of experimental errors. Statistical tests are applied to the data residuals to validate the assumed uncertainty distributions. Excellent results (i.e., small uncertainties) are obtained for sediment compressional-wave speed, compressional attenuation, and density; shear parameters are less well determined although low shear-wave speeds are indicated. The Bayesian analysis provides a quantitative comparison of inversion results for the two sites in terms of the resolution of specific geoacoustic parameters, and indicates that the geoacoustic information content is significantly higher for intromission data

Bayesian inversion of frequency-averaged reflection data

This paper presents a nonlinear Bayesian inversion of high-resolution seabed reflection data to estimate visco-elastic parameters of the upper sediments. The inversion is applied to data from two sites in the Strait of Sicily. One site is characterized by low-velocity, silty-clay sediments, resulting in data with a well-defined angle of intromission. The second site is characterized by high-velocity clayey sand, resulting in a critical angle. The data were frequency averaged from 500–2000 Hz and inverted for visco-elastic parameters of a half-space seabed model. The likelihood function employed in the inversion is based on the assumption of independent, Gaussian-distributed data errors, with the standard deviation included as a nuisance parameter in the inversion. Statistical tests are applied to the data residuals a posteriori to validate these assumptions. Good results are obtained for sediment compressional-wave velocity, compressional attenuation, and density; shear parameters are less-well determined although low shear-wave velocities are indicated. The Bayesian analysis provides a quantitative comparison of inversion results for the two sites in terms of the resolution of specific geoacoustic parameters, and indicates that the geoacoustic information content is significantly higher for angle-of-intromission data.

Attenuation measurements from sonic waveform logs in methane hydrate‐bearing sediments at the Nankai Trough exploratory well off Tokai, central Japan

I have used full waveform logs from the Nankai Trough exploratory well off central Japan to estimate both compressional and shear attenuation in sediments containing methane hydrate (MH). The attenuation estimates are based on a median frequency shift to the amplitude spectrum of the recorded waveforms. This paper is concerned with attenuation at sonic frequencies of 10–20 kHz for compressional waves and 500–1000 Hz for shear waves. I observed that the presence of MH increases the host sediments' seismic attenuation, and shear attenuation may be more helpful than compressional attenuation in detecting or characterizing MH‐bearing sediments as compressional attenuation is affected by the presence of gas. Moreover, the ratio of compressional to shear attenuation is found to be a more sensitive indicator of the presence of low‐saturation gas than the corresponding velocity ratio.

Sediment tomography in the Middle Atlantic Bight

Sediment properties such as compressional speed and attenuation have been extracted using the modal dispersion of explosive signals in the Middle Atlantic Bight. Data collected during the Shelf Break PRIMER experiment are used to generate sediment sound speed profiles along various propagation paths. Compressional speeds are inverted using traveltime of modes 1 to 9 from 10 Hz to 225 Hz. Compressional attenuation is inverted using modal amplitude ratios. Gravity cores taken at the experimental site give direct mesurements of compressional speed and attenuation for comparison. A posteriori estimates of resolution are evaluated. Nonlinear inversion techniques based on a Genetic Algorithm and Levenberg–Marquardt methods are used. Methods for increasing the efficiency of the inversion algorithm are also investigated. [Work supported by ONR.]

Using the Biot theory to establish a baseline geoacoustic model for seafloor sediments

By modeling the soft, fine-grained sediments of Eckernförde Bay, Germany, as porous viscoelastic materials filled with a viscous fluid, the Biot theory is used to establish a baseline geoacoustic model that is useful as a starting point for studies of scattering and other phenomena caused by the introduction of free gas into the sediment. The basic parameters of the model are derived from a wide variety of field measurements made during the Coastal Benthic Boundary Layer research program. The low permeability revealed by these measurements indicated that the overall fluid mobility would be small and therefore it would be necessary to include the effects of local fluid motion in “hidden” coordinate systems in order to model the dispersion and attenuation that is observed over a wide fre-quency range. This was accomplished by using a very general viscoelastic model (Cole–Cole model) to describe the response of the skeletal frame in a water environment. By adjusting the three free parameters of this model it was possible to match both overall attenuation and velocity in both high- and low-frequency ranges, however, because of the fact that compressional attenuation and velocity were only measured at two relatively high frequencies and shear wave attenuation determined only at low frequency, it is not clear whether the best rheological model was chosen to model the skeletal frame. This suggests that more specially designed experimental studies are desirable if the objective is to define the most general baseline model, applicable over a wide frequency range.

A radial model of anelasticity consistent with long-period surface-wave attenuation

Abstract A new global model of radial variations in intrinsic shear and compressional attenuation, Qμ(r) and Qκ(r), is presented. The model, called QL6, is derived from recent observations of long-period (150 < T < 300 sec) Rayleigh- and Love-wave attenuation and an extensive set of mode decay observations compiled from the literature. Our preferred model consists of six layers of constant Q, where the parameterization of Qμ(r) follows that of the anelastic component of the preliminary reference earth model (PREM). Relative to the commonly used models of PREM and QM1, lower values of Qμ are required in the upper 200 km of the mantle to explain observations of Love-wave attenuation. The observations require a finite level of compressional attenuation, preferentially located in the upper mantle. An analysis using continuous spline-basis functions supports the layered parameterization—with the recovered model possessing strong gradients in Qμ at the 670-km discontinuity; at the bottom of the asthenosphere; and to a lesser extent, at the base of the lithosphere. However, the continuous model does not have a significant discontinuity in Qμ at the 400-km phase boundary.

A new wideband (1 mHz to 100 Hz) seismic spectrometer

A new instrument has been developed to measure the compressional attenuation and Young’s modulus of rocks in the seismic-frequency range. This instrument has been calibrated over a frequency range from 1 mHz to 100 Hz at a strain of about 2.5×10−6. The attenuation of the sample is calculated from a relative phase measurement between a low-attenuation reference material and the sample. The Young’s modulus of the sample is calculated from the displacement amplitude of the sample relative to the displacement amplitude of the reference material. Use of this instrument has allowed the investigation of the dependence of a rock’s attenuation and Young’s modulus on its fluid content.

Effects of heterogeneities and anisotropy on sonic and ultrasonic attenuation in rocks

We compare the attenuation obtained by the resonant bar technique in the sonic frequency range (3–10 kHz) with that obtained by the pulse transmission technique in the ultrasonic frequency range (500 kHz) on a set of 30 rocks, including sandstones and limestones. The sonic and ultrasonic measurements were performed under high effective pressure on adjacent water‐saturated samples from each rock block. Compressional ultrasonic attenuation was typically larger than extensional sonic attenuation, particularly in limestones. This is attributed to the presence of density heterogeneities, that can be seen on X‐ray scanner imagery. Heterogeneities at the scale of the ultrasonic wavelength produce diffraction of the waves, and as a consequence, high attenuation values. At ultrasonic frequencies, large apparent shear attenuation values, compared to compressional attenuation values, are explained by shear wave splitting.

Microscopic mechanism of attenuation of compressional ultrasonic waves in tissue-mimicking phantom materials

An investigation was performed to determine whether the sound-attenuation-insuspensions theory of Allegra and Hawley can be used to explain the compressional (longitudinal wave) attenuation of ultrasonically tissue-mimicking materials commonly used in phantoms for testing the performance of medical ultrasound systems. These materials are composed of microscopic graphite particles suspended in a gel. The theory was first tested using materials containing spherical glass beads instead of graphite particles because these materials more closely fit the geometric conditions assumed in the theory. For the glass bead type materials as well as the graphite particle type materials, the attenuation coefficients predicted using the Allegra and Hawley model agreed rather well with experimental measurements over the diagnostic frequency range.