Logarithmic Spectral Ratio Research Articles

T* Revise Attenuation Tomography for Q Estimation

Seismic attenuation is often calculated by attenuated travel time tomography. The accuracy of this method is controlled by the precision of attenuated travel time. In this paper, a novel T* revise in attenuated travel time tomography method for Q inversion was developed. The attenuated travel time was calculated from seismic data by using a logarithmic spectral ratio inversion strategy. In the inversion process, multiple offset traces were used for multiple attenuated travel time calculations. The proposed method produced more accurate results compared to those of the conventional approach without the requirement of choosing an optimistic frequency band. The accuracy of the proposed method was improved by avoiding the effect of overburden. Both synthetic and real data examples prove the viability and effectiveness of the proposed method.

Seismic Attenuation Estimation Using an Enhanced Log Spectral Ratio Method

Seismic attenuation estimation is a significant task for characterizing reservoirs and improving the resolution of seismic data. The logarithmic spectral ratio (LSR) is one of the widely used tools for seismic attenuation estimation. However, how to select a suitable frequency bandwidth for the LSR is a difficult task, especially for field data. Moreover, field data are often contained kinds of noises, which makes seismic attenuation estimation difficult and unstable. We proposed an enhanced LSR (ELSR) workflow to estimate seismic attenuation. First, we built a sparse S-transform (SST) to obtain a sparse time-frequency (TF) spectrum of the analyzed seismic trace. Then, based on the SST spectrum, we introduced an ELSR workflow to estimate seismic attenuation. It should be noticed that we provided an adaptive frequency band selection for the LSR. To demonstrate the effectiveness of the proposed workflow, we apply it on both synthetic and field data. Compared with the results from several traditional attenuation estimation methods, the proposed ELSR provides a more stable and more accurate attenuation estimation result and offers the potentials in improving the resolution of post-stacked seismic data.

Q Estimation via the Discriminant Method Based on Error Modeling

Seismic attenuation is one of the crucial attributes for seismic resolution enhancement and reservoir characterization, which is often described by quality factor Q. Among the commonly used methods for Q estimation, the frequency based method is demonstrated for effectively estimating Q factor, mainly including the frequency shift (FS) based, and the spectral correlation (SC), and the logarithm spectral ratio (LSR) based methods. However, the frequency spectrum of the received wave may be affected by the closely adjacent reflections, which may result in an unreliable Q estimation. To handle this limitation, the error modeling based discriminative approach in machine learning is proposed in this study. We utilize the seismic wave first received to construct the classifier based on the reproducing kernel Hilbert spaces representer theorem, then give an effect Q estimation by applying the classifier to the wave second received. Furthermore, to improve the robustness of the estimation results, the error models of the classifier are introduced. The loss functions are proposed to correspond to the distributions of the error models, from which two different implementations of Q estimation are derived. When applying to the synthetic data, the corresponding results show that the proposed method greatly improves the robustness and accuracy of the conventional methods. Field data test is also provided and demonstrates the effectiveness of our proposed method.

First arrivalQtomography based on an adjoint-state method

AbstractUnder the assumption of invariant ray path in a weakly dissipative (high quality factor Q) subsurface medium, a tomographic inversion approach composed of two cascading applications of first arrival traveltime and Q tomography is proposed for compensating amplitude loss caused by near-surface anomalies, such as unconsolidated soils or the overburden gas cloud. To improve the computational efficiency, these two related tomography methods were adopted with an adjoint-state technique. First, arrival traveltime tomography will be performed to provide an inverted velocity model as one of the inputs for the following first arrival Q tomography. Then, the synthetic first break generated by the inverted velocity model will be used as a stable guidance of accessing the scopes of first arrival waveforms in the time domain where the potential attenuated time information is contained. The attenuated time will be estimated through a logarithmic spectral ratio linear regression corresponding to frequency-dependent propagation responses of different wave types. All these estimated attenuated times will be applied with reference signals to generate synthetic attenuated seismic data in the time domain, and their discrepancies with real data will be evaluated using similarity coefficients. The ones with larger values will be selected as optimal attenuated time inputs for the following Q tomographic inversion. Examples of both synthetic and field data reveal the feasibility and potential of this method.

Estimation of near‐surface Q factor under constraint of layered velocity based on uphole survey data

ABSTRACTTo improve the resolution of seismic data, it is important to accurately estimate the near‐surface quality factor, Q, which provides a measure of seismic wave attenuation. In view of the unique advantages provided by uphole surveys when investigating near‐surface structures, they are widely employed to estimate the near‐surface Q factor. However, the Q factor estimated using the traditional spectral ratio method is not always precise and provides larger oscillations in the estimated Q factors due to errors associated with first‐break picking and velocity estimation. Following on the traditional logarithmic spectral ratio method, a new method called the logarithmic spectral ratio integral method was proposed to estimate the layer Q factor using uphole survey data. It calculates first the weighted integral of the logarithmic spectral ratio in an effective frequency interval between non‐adjacent traces, then makes a linear regression between the inter‐trace travel moveout and the weighted integral of logarithmic spectral ratio under the constraint of velocity stratification. The result of model analysis shows that under an ideal condition (without first‐break picking errors), the layer Q values estimated by the logarithmic spectral ratio integral method are fairly consistent with the true layer‐specific Q values in the model. In addition, the Q values estimated from field‐measured data and data from forward modelling with 10% random noise added, both have smaller mean relative errors than the results using traditional spectral ratio method and the double‐linear regression method. A case study is employed and the results show that the layer Q factor estimated using the new method correlates well with the velocity stratification and is thus applicable for use with various uphole survey observation systems. Furthermore, all results indicate that the logarithmic spectral ratio integral method delivers a more precise and stable estimation of the layered Q than the other methods, and the anti‐noise characteristics are stronger.

Seismic Attenuation Estimation Using the Centroid Frequency Shift and Divergence

Quality factor $Q$ can be used for hydrocarbon detection and reservoir characterization. The commonly used methods for $Q$ estimation include the logarithm spectral ratio (LSR) method, the centroid frequency shift (CFS) method, and the peak frequency shift (PFS) method. However, all these methods are existing limitations respectively. The LSR method is sensitive to random noise. The CFS and PFS methods are lack of applicability owing to their assumptions of the source wavelet type. To overcome these limitations, we derived a new formula without any wavelet assumption. This formula establishes a relationship between the $Q$ factor and the spectral centroid downshift concisely through the Jeffery divergence. The proposed method is named the generalized centroid frequency shift (GCFS) method. Compared with the conventional methods, the proposed method can achieve higher accuracy and better antinoise performance. In addition, the proposed method is suitable for various source wavelet types. Synthetic and field examples demonstrate the effectiveness and potential of the proposed method.

$Q$ Estimation by Combining ISD With LSR Method Based on Shaping-Regularized Inversion

The quality factor $Q$ is an indispensable parameter for studying wave propagation in viscoelastic media. $Q$ can not only be implemented for improving the quality of wave records but can also be used for directly indicating frequency-dependent anomalies induced by fluids, so it is widely used in seismic exploration and clinical medicine. $Q$ estimation here refers to the extraction of $Q$ information from seismic data; it has aroused lots of attention but is still somewhat controversial due to the limitations of existing methods. In this letter, combined with a logarithmic spectral ratio (LSR) algorithm, we have introduced a sparse-constrained inversion spectral decomposition (ISD) method for average- $Q$ estimation (LSR-ISD), and have used shaping regularization to solve for the spectrum ratio. Then, through regularized linear inversion, average- $Q$ was converted to an interval- $Q$ value. Finally, we have applied this method to synthetic data and field data. Numerical examples and field data application demonstrate that the proposed method produces a series of results with high resolution and good stability.

Seismic Attenuation for Characterization of Gas Hydrate Reservoir in Krishna-Godavari Basin, Eastern Indian Margin

ABSTRACT Gas hydrates have received global attention as a possible alternative non-conventional energy resource. Hence, the detection, characterization and quantification of gas hydrates are very important for evaluating the resource potential. Presence of gas hydrates in sediments above the bottom simulating reflector or BSR is associated with low attenuation or high quality factor (Q), whereas, free gas bearing sediments below the BSR exhibit high attenuation or low seismic Q. Here the logarithm spectral ratio (LSR) method is applied to marine seismic reflection data along two cross lines (18 and 46) in the Krishna-Godavari (KG) basin in eastern Indian margin, where gas hydrates have already been established by drilling/coring. The interval Qs is calculated for three sedimentary layers (A, B, and C) bounded by the seafloor, BSR, one reflector above and another reflector below the BSR at some common depth points (CDPs) to study the attenuation characteristics of sediments across the BSR. The estimated average interval Q (160) for the hydrate bearing sediments (layer B) is much higher than the average interval Q (80) for both the loose clayey sediments (Layer A) and underlying free gas saturated sediments (layer C). This demonstrates that estimation of seismic quality factor Q can be used for characterization of gas hydrate reservoir.

Q estimation and its application in the 3D shallow weathering zone

Attenuation in the shallow weathering zone is relatively strong, causing severe energy loss during wave propagation. It is difficult to estimate accurate [Formula: see text] values in the shallow weathering zone, and the influence of shallow weathering zone is seldom considered into attenuation estimation and compensation in the deep part. We achieved [Formula: see text] value estimation where there exist microlog data in the shallow weathering zone using the generalized S transform (GST); then, we establish an empirical formula using the velocity and [Formula: see text] value estimated with microlog data; finally, the [Formula: see text] value in the 3D shallow weathering zone can be obtained using the established formula and the velocity information. During the first procedure, the GST is used to provide reasonable time-frequency resolution, and linear regression is used in the obtained logarithmic spectral ratio to get the estimated [Formula: see text] value. An empirical formula is established using the estimated [Formula: see text] value and the velocity where there exists microlog data in the second procedure. In the third step, [Formula: see text] estimation in the whole shallow weathering zone can be obtained using the established formula and the velocity information, which can overcome the inaccuracy of spatial interpolation with the estimated [Formula: see text] factors where there exist different twin-well microlog data. Attenuation compensation to seismic data obtained from the deep part is carried out to prove the effectiveness of the estimated [Formula: see text] in the shallow weathering zone. After compensation, the resolution of seismic data is effectively increased, which demonstrates the validity of the estimated [Formula: see text] values in the shallow weathering zone. Synthetic data and field data examples demonstrate the validity of our method.

Q estimation of seismic data using the generalized S-transform

Quality factor, Q, is a parameter that characterizes the energy dissipation during seismic wave propagation. The reservoir pore is one of the main factors that affect the value of Q. Especially, when pore space is filled with oil or gas, the rock usually exhibits a relative low Q value. Such a low Q value has been used as a direct hydrocarbon indicator by many researchers. The conventional Q estimation method based on spectral ratio suffers from the problem of waveform tuning; hence, many researchers have introduced time-frequency analysis techniques to tackle this problem. Unfortunately, the window functions adopted in time-frequency analysis algorithms such as continuous wavelet transform (CWT) and S-transform (ST) contaminate the amplitude spectra because the seismic signal is multiplied by the window functions during time-frequency decomposition. The basic assumption of the spectral ratio method is that there is a linear relationship between natural logarithmic spectral ratio and frequency. However, this assumption does not hold if we take the influence of window functions into consideration. In this paper, we first employ a recently developed two-parameter generalized S-transform (GST) to obtain the time-frequency spectra of seismic traces. We then deduce the non-linear relationship between natural logarithmic spectral ratio and frequency. Finally, we obtain a linear relationship between natural logarithmic spectral ratio and a newly defined parameter γ by ignoring the negligible second order term. The gradient of this linear relationship is 1/Q. Here, the parameter γ is a function of frequency and source wavelet. Numerical examples for VSP and post-stack reflection data confirm that our algorithm is capable of yielding accurate results. The Q-value results estimated from field data acquired in western China show reasonable comparison with oil-producing well location.

Q factor estimation based on the method of logarithmic spectral area difference

We have developed a novel method for [Formula: see text] estimation. As a seismic wave propagates through subsurface viscoelastic media, seismic attenuation decreases the amplitude and reduces the bandwidth, which leads to variation of the logarithmic spectral area of seismic wave. According to this property, we have derived an analytical relation between [Formula: see text] factor and the logarithmic spectral area difference of seismic wave. To improve the accuracy of [Formula: see text] estimation, we took account of the amplitude loss due to energy partitioning from transmission. Tests of the method on synthetic models determined the validity of our method, and it was insensitive to different types of noises and evaluated density. A further comparison between the presented method and two widely used [Formula: see text] estimation methods, namely, the logarithmic spectral ratio and centroid frequency shifting methods, with a synthetic model containing random noise demonstrated that our method is the more robust, in these situations, among the three approaches. Then, we also compared the effect of bandwidth and time-window selection on the [Formula: see text] estimation for these three methods, and the result revealed that our method is less sensitive to the bandwidth and time window than the other two methods. Application of this method to real zero-offset vertical seismic profile data shows a reasonable correlation between estimated interval-[Formula: see text] and interval velocities, which further indicates the validity of the method.

ESTIMATION OF QUALITY FACTOR Q FROM THE INSTANTANEOUS FREQUENCY AT THE ENVELOPE PEAK OF A SEISMIC SIGNAL

In this paper, we derive an approximate equation combining the quality factor Q, the travel time of a wave, and the variation of the instantaneous frequency (IF) at the envelope peaks of two successive seismic wavelets, along the wave-propagating direction, based on the theory of one-way wave propagation in a 1D viscoelastic medium. We then propose a method (called the WEPIF method) to estimate Q by measuring the variations of the wavelet envelope peak IF (WEPIF) with the travel time of seismic wavelet. For zero-offset VSP data and poststack seismic data, we describe how to implement the WEPIF method in detail. A test on synthetic VSP data shows that the WEPIF method is less sensitive to interference from the reflector than the logarithm spectral ratio and the centroid frequency shift methods. Applied to field VSP data, the WEPIF method gives a Q-curve with nearly the same distribution as the results from a known well. Applied to poststack seismic data, it produces a Q-profile that indicates an intense absorption zone corresponding to the excellent gas-bearing reservoir. This allows us to predict a potential high-productivity gas well. Drilling confirmed this prediction. The WEPIF method can be applied to poststack seismic data and zero-offset VSP data.

Seismic wave attenuation beneath the Australasian region

The attenuation of seismic waves is strongly influenced by temperature and rheological changes, and so provides an important supplement to information from seismic wavespeeds. Differential attenuation measurements are made for seismic waves refracted through the mantle beneath the Australasian region and are then used to construct 3D images of the attenuation of shear and compressional waves. The differential attenuation between different seismic phases is estimated using a spectral ratio method in the frequency band 0.25–1.0 Hz using a multi-taper method. Over this band the attenuation is nearly independent of frequency so that the logarithmic spectral ratio is a linear function of frequency. Differential measurements are made either between P and S phases on the same record or between stations for P and S waves separately. Images of seismic attenuation for the Australasian region are produced using a tomographic inversion, with the fast marching method employed to trace ray paths in an initial 3-D model derived from surface wave tomography. There is a deep seated horizontal contrast between central Australia and the eastern seaboard. The crustal and lithospheric mantle beneath the Archean and Proterozoic rocks in the west and in the middle of the continent have low seismic attenuation, whereas the Phanerozoic material in the east is more attenuative. Regions with recent volcanism, most likely associated with hot spots such as near Bass Strait and the Coral Sea, display high seismic attenuation anomalies. There is a strong contrast in attenuation between the relatively low loss lithosphere and the high loss asthenosphere beneath with a change by a factor of 6–10. Anisotropy in attenuation is slight even though some would be expected from the radial anisotropy seen in shear wavespeed in the lithosphere.

Seismic Quality Factors Estimation From Spectral Correlation

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> This letter describes a method for estimating seismic quality <formula formulatype="inline"><tex Notation="TeX">$(Q)$</tex> </formula> factors from spectral correlation (SC). For a linear frequency attenuation model, the SC coefficient is examined between the amplitude spectrum of a reference pulse multiplied by an absorption filter and that of a target pulse, and then, the <formula formulatype="inline"><tex Notation="TeX">$Q$</tex></formula> factor can be determined from the absorption filter which yields the maximum SC coefficient. In this way, <formula formulatype="inline"><tex Notation="TeX">$Q$</tex></formula> -factor estimation is converted into an optimization problem which can be quickly implemented by the Newton iteration scheme. Synthetic tests with different source signatures show that the SC method is free of the type of source wavelet. Noisy tests indicate that the SC method has higher noise resistance than the logarithm spectral ratio and the centroid frequency shifting methods. Field test indicates that the depth range of lower <formula formulatype="inline"><tex Notation="TeX">$Q$</tex></formula> values estimated by the SC method well corresponds to the distribution of gas reservoirs. With better <formula formulatype="inline"><tex Notation="TeX">$Q$</tex></formula>-factor evaluation, the SC method may become a more practical tool for gas reservoir characterization than before. </para>

Least‐squares inversion of in‐situ sonicQmeasurements: Stability and resolution

We minimize the effect of noise and increase both the reliability and the resolution of attenuation estimates obtained from multireceiver full‐waveform sonics. Multiple measurements of effective attenuation were generated from full‐waveform sonic data recorded by an eight‐receiver sonic tool in a gas‐bearing sandstone reservoir using two independent techniques: the logarithmic spectral ratio (LSR) and the instantaneous frequency (IF) method. After rejecting unstable estimates [receiver separation &lt;2 ft (0.61 m)], least‐squares inversion was used to combine the multiple estimates into high‐resolution attenuation logs. The procedure was applied to raw attenuation data obtained with both the LSR and IF methods, and the resulting logs showed that the attenuation estimates obtained for the maximum receiver separation of 3.5 ft (1.07 m) provide a smoothed approximation of the high‐resolution measurements. The approximation is better for the IF method, with the normalized crosscorrelation factor between the low‐ and high‐resolution logs being 0.90 for the IF method and 0.88 for the LSR method.

Compressional‐wave Q estimation from full‐waveform sonic data

There is significant evidence that the anelastic loss of seismic energy is linked to petrophysical properties such as porosity, permeability and clay content. Thus, reliable estimation of anelastic attenuation from seismic data can lead to improved methods for the prediction of petrophysical properties. This paper is concerned with methods for the estimation of attenuation at sonic frequencies (5–30 KHz) from in situ data. Two independent methods have been developed and tested for estimating compressional‐wave attenuation from full‐waveform sonic data. A well‐established technique, the logarithm spectral ratio (LSR) method, is compared with a new technique, the instantaneous frequency (IF) method. The LSR method uses the whole spectrum of the seismic pulse whilst the IF method uses a carefully estimated value of instantaneous frequency which is representative of the centre frequency of the pulse. In the former case, attenuation estimation is based on the relative variation of amplitudes at different frequencies, whilst in the latter case it is based on the shift of the centre frequency of the pulse to lower values during anelastic wave propagation. The IF method does not assume frequency independence of Q which is a necessary assumption for the LSR method, and it provides a stable frequency log, the peak instantaneous frequency (PIF) log, which may be used as an indicator for attenuation under certain limitations. The development and implementation of the two methods is aimed at minimizing the effect of secondary arrivals, such as leaky modes, and involved a series of parameter tests. Testing of the two methods using full‐waveform sonic data of variable quality, obtained from a gas‐bearing sandstone reservoir, showed that the IF method is in general more stable and suitable for full‐waveform sonic data compared with the LSR method. This was evident especially in data sets with high background noise levels and wave‐interference effects. For good quality data, the two methods gave results that showed good agreement, whilst comparison with other log types further increased confidence in the results obtained. A significant decrease (approximately 5 KHz) in the PIF values was observed in the transition from an evaporite/shale sequence to the gas‐bearing sandstone. Average Q values of 54 and 51 were obtained using good quality data from a test region within the gas‐saturated sandstone reservoir, using the LSR and IF methods, respectively.

Relationships among compressional wave attenuation, porosity, clay content, and permeability in sandstones

Anelastic attenuation is the process by which rocks convert compressional waves into heat and thereby modify the amplitude and phase of the waves. Understanding the causes of compressional wave attenuation is important in the acquisition, processing, and interpretation of high‐resolution seismic data, and in deducing the physical properties of rocks from seismic data. We have measured the attenuation coefficients of compressional waves in 42 sandstones at a confining pressure of 40 MPa (equivalent to a depth of burial of about 1.5 km) in a frequency range from 0.5 to 1.5 MHz. The compressional wave measurements were made using a pulse‐echo method in which the sample (5 cm diameter, 1.8 cm to 3.5 cm long) was sandwiched between perspex (lucite) buffer rods inside the high‐pressure rig. The attenuation of the sample was estimated from the logarithmic spectral ratio of the signals (corrected for beam spreading) reflected from the top and base of the sample. The results show that for these samples, compressional wave attenuation (α, dB/cm) at 1 MHz and 40 MPa is related to clay content (C, percent) and porosity (ϕ, percent) by α=0.0315ϕ+0.241C−0.132 with a correlation coefficient of 0.88. The relationship between attenuation and permeability is less well defined: Those samples with permeabilities less than 50 md have high attenuation coefficients (generally greater than 1 dB/cm) while those with permeabilities greater than 50 md have low attenuation coefficients (generally less than 1 dB/cm) at 1 MHz at 40 MPa. These experimental data can be accounted for by modifications of the Biot theory and by consideration of the Sewell/Urick theory of compressional wave attenuation in porous, fluid‐saturated media.