利用基于子波估计的频谱校正方法提高Q值估计精度(英文)

用Q值刻画的地震衰减在地震信号处理和解释中具有很广泛的应用。利用反射地震资料进行Q值估计需要解决地震子波和反射系数序列耦合的问题。从反射地震资料中去除反射系数序列的影响,这个过程称为频谱校正。本文提出了一种基于子波估计的求取Q值的方法,进而设计了一个反Q滤波器。该方法利用反射地震资料的高阶统计量进行子波估计,并利用所估计子波实现频谱校正。我们利用合成数据实验给出了质心频移法与频谱比法这两种常用的Q值估计方法在不同参数设置下的性能。人工合成数据和实际数据处理表明,利用本文提出的方法进行频谱校正后,可以得到可靠的Q值估计。经过反Q滤波,地震数据的高频部分得到了有效地恢复。     

零偏移距VSP资料层Q反演及其应用研究(英文)

地层品质因子Q的可用于地震资料高分辨率处理,而从VSP资料下行直达波更容易获取准确的地层品质因子。通过对零偏移距VSP资料的监控子波和下行初至波的频谱进行综合分析,仿照Ricker子波频谱的表达式,本文提出了震源子波频谱新的表达式。在震源子波频谱新的表达式基础上,我们介绍了改进的频谱拟合法和改进的谱比法的层Q值反演方法及相应的处理流程。基于本文提出的层Q值反演方法,利用实际的零偏移距VSP资料的下行直达波,反演稳定的层Q值,并用于零偏移距VSP资料及井旁地面地震资料的反Q滤波振幅补偿处理,提高了地震资料的分辨率。     

Modelling of GPR waves for lossy media obeying a complex power law of frequency for dielectric permittivity

The attenuation of ground‐penetrating radar (GPR) energy in the subsurface decreases and shifts the amplitude spectrum of the radar pulse to lower frequencies (absorption) with increasing traveltime and causes also a distortion of wavelet phase (dispersion). The attenuation is often expressed by the quality factor Q. For GPR studies, Q can be estimated from the ratio of the real part to the imaginary part of the dielectric permittivity. We consider a complex power function of frequency for the dielectric permittivity, and show that this dielectric response corresponds to a frequency‐independent‐Q or simply a constant‐Q model. The phase velocity (dispersion relationship) and the absorption coefficient of electromagnetic waves also obey a frequency power law. This approach is easy to use in the frequency domain and the wave propagation can be described by two parameters only, for example Q and the phase velocity at an arbitrary reference frequency. This simplicity makes it practical for any inversion technique. Furthermore, by using the Hilbert transform relating the velocity and the absorption coefficient (which obeys a frequency power law), we find the same dispersion relationship for the phase velocity. Both approaches are valid for a constant value of Q over a restricted frequency‐bandwidth, and are applicable in a material that is assumed to have no instantaneous dielectric response. Many GPR profiles acquired in a dry aeolian environment have shown a strong reflectivity inside dunes. Changes in water content are believed to be the origin of this reflectivity. We model the radar reflections from the bottom of a dry aeolian dune using the 1D wavelet modelling method. We discuss the choice of the reference wavelet in this modelling approach. A trial‐and‐error match of modelled and observed data was performed to estimate the optimum set of parameters characterizing the materials composing the site. Additionally, by combining the complex refractive index method (CRIM) and/or Topp equations for the bulk permittivity (dielectric constant) of moist sandy soils with a frequency power law for the dielectric response, we introduce them into the expression for the reflection coefficient. Using this method, we can estimate the water content and explain its effect on the reflection coefficient and on wavelet modelling.     

Improving the resolution of seismic traces based on the secondary time–frequency spectrum

The resolution of seismic data is critical to seismic data processing and the subsequent interpretation of fine structures. In conventional resolution improvement methods, the seismic data is assumed stationary and the noise level not changes with space, whereas the actual situation does not satisfy this assumption, so that results after resolution improvement processing is not up to the expected effect. To solve these problems, we propose a seismic resolution improvement method based on the secondary time–frequency spectrum. First, we propose the secondary time-frequency spectrum based on S transform (ST) and discuss the reflection coefficient sequence and time-dependent wavelet in the secondary time–frequency spectrum. Second, using the secondary time–frequency spectrum, we design a twodimensional filter to extract the amplitude spectrum of the time-dependent wavelet. Then, we discuss the improvement of the resolution operator in noisy environments and propose a novel approach for determining the broad frequency range of the resolution operator in the time–frequency–space domain. Finally, we apply the proposed method to synthetic and real data and compare the results of the traditional spectrum-modeling deconvolution and Q compensation method. The results suggest that the proposed method does not need to estimate the Q value and the resolution is not limited by the bandwidth of the source. Thus, the resolution of the seismic data is improved sufficiently based on the signal-to-noise ratio (SNR).     

The estimation of spectra from time‐frequency transforms for use in attenuation studies

We introduce the signal dependent time–frequency distribution, which is a time–frequency distribution that allows the user to optimize the tradeoff between joint time–frequency resolution and suppression of transform artefacts. The signal‐dependent time–frequency distribution, as well as the short‐time Fourier transform, Stockwell transform, and the Fourier transform are analysed for their ability to estimate the spectrum of a known wavelet used in a tuning wedge model. Next, the signal‐dependent time–frequency distribution, and fixed‐ and variable‐window transforms are used to estimate spectra from a zero‐offset synthetic seismogram. Attenuation is estimated from the associated spectral ratio curves, and the accuracy of the results is compared. The synthetic consisted of six pairs of strong reflections, based on real well‐log data, with a modeled intrinsic attenuation value of 1000/Q = 20. The signal‐dependent time–frequency distribution was the only time–frequency transform found to produce spectra that estimated consistent attenuation values, with an average of 1000/Q = 26±2; results from the fixed‐ and variable‐window transforms were 24±17 and 39±10, respectively. Finally, all three time–frequency transforms were used in a pre‐stack attenuation estimation method (the pre‐stack Q inversion algorithm) applied to a gather from a North Sea seismic dataset, to estimate attenuation between nine different strong reflections. In this case, the signal‐dependent time‐frequency distribution produced spectra more consistent with the constant‐Q model of attenuation assumed in the pre‐stack attenuation estimation algorithm: the average L1 residuals of the spectral ratio surfaces from the theoretical constant‐Q expectation for the signal‐dependent time‐frequency distribution, short‐time Fourier transform, and Stockwell transform were 0.12, 0.21, and 0.33, respectively. Based on the results shown, the signal‐dependent time‐frequency distribution is a time–frequency distribution that can provide more accurate and precise estimations of the amplitude spectrum of a reflection, due to a higher attainable time–frequency resolution.     

THE DETERMINATION OF THE SEISMIC QUALITY FACTOR Q FROM VSP DATA: A COMPARISON OF DIFFERENT COMPUTATIONAL METHODS1

Ten methods for the computation of attenuation have been investigated, namely: amplitude decay, analytical signal, wavelet modelling, phase modelling, frequency modelling, rise-time, pulse amplitude, matching technique, spectral modelling and spectral ratio. In particular, we have studied the reliability of each of these methods in estimating correct values of Q using three synthetic VSP seismograms for plane P-waves with different noise contents. The investigations proved that no single method is generally superior. Rather, some methods are more suitable than others in specific situations depending on recording, noise or geology. The analytical signal method has been demonstrated to be superior if true amplitude recordings are available. Otherwise spectral modelling or, in the ‘ noise-free’ case the spectral ratio method, is optimal. Finally, two field VSPs in sediments are investigated. Only in the case of the highest quality VSP can significant information be deduced from the computed attenuation.     

Source/receiver array directivity effects on marine seismic attenuation measurements

Attenuation of seismic waves, quantified by the seismic quality factor Q, holds important information for seismic interpretation, due to its sensitivity to rock and fluid properties. A recently published study of Q, based on surface seismic reflection data, used a modified spectral ratio approach (QVO), but both source and receiver responses were treated as isotropic, based on simple raypath arguments. Here, this assumption has been tested by computing apparent attenuation generated by frequency-dependent directivity of typical marine source and receiver arrays and acquisition geometries. Synthetic wavelet spectra were computed for reflected rays, summed over the first Fresnel zone, from the base of a single interval, 50–3000 m thick and velocity 2000 m/s, overlying a 2200 m/s half-space, and for offsets of 71–2071 m. The source and receiver geometry were those of an actual survey. The modelled spectra are clearly affected by directivity, most strongly because of surface ghosts. In general, the strong high-frequency component, produced by the array design, leads to apparently negative attenuation in individual reflection events, though this is dependent on offset and target depth. For shallow targets (less than 400–500 ms two-way traveltime (TWT) depth), apparent Q-values as extreme as ?50 to ?100 were obtained. For deeper target depths, the directivity effect is far smaller. The implications of the model study were tested on real data. QVO was applied to 20 true-spectrum-processed CMPs, in a shallow (405–730 ms TWT) and a deeper (1000–1300 ms TWT) interval, firstly using a measured far-field source signature (effectively isotropic), and secondly using computed directivity effects instead. Mean interval Q^?1-values for the deeper interval, 0.029 ± 0.011 and 0.027 ± 0.018 for conventional and directional processing, respectively, suggested no directivity influence on attenuation estimation. For the shallow interval (despite poor spectral signal-to-noise ratios and hence scattered attenuation estimates), directional processing removed directivity-generated irregularities from the spectral ratios, resulting in an improvement from Q^?1_int = ?0.036 ± 0.130 to a realistic Q^?1_int = 0.012 ± 0.030: different at 94% confidence level. Equivalent Q-values are: for the deeper interval, 35 and 37 for conventional and directional processing, respectively, and ?28 and 86 for the shallow interval. These results support the conclusions of the model studies, i.e. that source/receiver directivity has a negligible effect except for shallow targets (e.g. TWT depth ≤ 500 ms) imaged with conventional acquisition geometry. In such cases directivity corrections to spectra are strongly recommended.     

Some remarks on Q-compensated sparse deconvolution without knowing the quality factor Q

The subsurface media are not perfectly elastic, thus anelastic absorption, attenuation and dispersion (aka Q filtering) effects occur during wave propagation, diminishing seismic resolution. Compensating for anelastic effects is imperative for resolution enhancement. Q values are required for most of conventional Q-compensation methods, and the source wavelet is additionally required for some of them. Based on the previous work of non-stationary sparse reflectivity inversion, we evaluate a series of methods for Q-compensation with/without knowing Q and with/without knowing wavelet. We demonstrate that if Q-compensation takes the wavelet into account, it generates better results for the severely attenuated components, benefiting from the sparsity promotion. We then evaluate a two-phase Q-compensation method in the frequency domain to eliminate Q requirement. In phase 1, the observed seismogram is disintegrated into the least number of Q-filtered wavelets chosen from a dictionary by optimizing a basis pursuit denoising problem, where the dictionary is composed of the known wavelet with different propagation times, each filtered with a range of possible values. The elements of the dictionary are weighted by the infinity norm of the corresponding column and further preconditioned to provide wavelets of different values and different propagation times equal probability to entry into the solution space. In phase 2, we derive analytic solutions for estimates of reflectivity and Q and solve an over-determined equation to obtain the final reflectivity series and Q values, where both the amplitude and phase information are utilized to estimate the Q values. The evaluated inversion-based Q estimation method handles the wave-interference effects better than conventional spectral-ratio-based methods. For Q-compensation, we investigate why sparsity promoting does matter. Numerical and field data experiments indicate the feasibility of the evaluated method of Q-compensation without knowing Q but with wavelet given.     

Q estimation based on the centroid frequency and standard deviation of frequency-weighted-exponential function

The quality factor Q is a vital parameter for quantitatively describing the attenuation information of underground reservoirs, which is of great significance for hydrocarbon detection and reservoir characterization. A frequency-weighted-exponential (FWE) method utilizing the symmetry index and the characteristic frequency can obtain this parameter. Unfortunately, the constant symmetry index assumption of it reduces the accuracy of Q values under the non-standard FWE shape. Selecting an optimal symmetry index is also a problem for this method. Hence, the basic idea of a novel Q estimation method is to substitute the symmetry index with the standard deviation of the source and attenuated wavelet spectrums. The added standard deviation varies with the degree of attenuation under different wavelet shapes, which can reduce the effects of the constant assumption. Meanwhile, it is simple to calculate this parameter directly from the spectrums. In this way, the proposed method has wider applicability to various wavelets. The synthetic records show the better performance of the novel method in improving the accuracy of Q values and the resistance to random noise than the FWE method. Furthermore, the results of matching wavelets exhibit the applicability of the proposed method in real data, and the quadratic spectrum simulation method improves the stability of the spectrums. Finally, real data experiments indicate the effectiveness of the proposed method after the above two processing means.     

Using wavelet‐domain adaptive filtering to improve signal‐to‐noise ratio of nuclear magnetic resonance log data from tight gas sands

In tight gas sands, the signal‐to‐noise ratio of nuclear magnetic resonance log data is usually low, which limits the application of nuclear magnetic resonance logs in this type of reservoir. This project uses the method of wavelet‐domain adaptive filtering to denoise the nuclear magnetic resonance log data from tight gas sands. The principles of the maximum correlation coefficient and the minimum root mean square error are used to decide on the optimal basis function for wavelet transformation. The feasibility and the effectiveness of this method are verified by analysing the numerical simulation results and core experimental data. Compared with the wavelet thresholding denoise method, this adaptive filtering method is more effective in noise filtering, which can improve the signal‐to‐noise ratio of nuclear magnetic resonance data and the inversion precision of transverse relaxation time T₂ spectrum. The application of this method to nuclear magnetic resonance logs shows that this method not only can improve the accuracy of nuclear magnetic resonance porosity but also can enhance the recognition ability of tight gas sands in nuclear magnetic resonance logs.     

EXPERIMENTAL COMPARISON BETWEEN SPECTRAL RATIO AND RISE TIME TECHNIQUES FOR ATTENUATION MEASUREMENT*

Two techniques for the measurement of attenuation–spectral ratio and rise time techniques–were tested and compared in the laboratory. The spectral ratio technique proved to be reliable and easy to implement for intermediate values (5 < Q < 50) of attenuation. For low (Q > 50) and high attenuations, the spectral ratio technique is inaccurate. Calculating the rise time on simulated signals, we found a relation between rise time τ and the ratio travel-time to quality factor T/Q which could be approximated in intervals by the linear relation τ=τ+C*T/Q. The constants τ and C depend on the absolute value of T/Q and on the initial source signal. The rise time technique, performed on the first quarter period of the signal, enables high attenuations (Q < 5) to be measured. The determination of the relation between τ and T/Q is possible if one knows the initial source. We theoretically approximate this relation through a simulation using a realistic propagation model. With laboratory measurements made on Fontainebleau sandstone, we show that the rise time technique using the theoretical relation τ=τ(T/Q) gives comparable values of Q to those obtained from the spectral ratio technique. In borehole seismics, where it is often difficult to remove undesired signals, the rise time technique applied with the right (τ, T/Q) relation is the best method to use.     

ON ERRORS OF FIT AND ACCURACY IN MATCHING SYNTHETIC SEISMOGRAMS AND SEISMIC TRACES*

A synthetic seismogram that closely resembles a seismic trace recorded at a well may not be at all reliable for, say, stratigraphic interpretation around the well. The most accurate synthetic seismogram is, in general, not the one that displays the smallest errors of fit to the trace but the one that best estimates the noise on the trace. If the match is confined to a short interval of interest or if the seismic reflection wavelet is allowed to be unduly long, there is considerable danger of forcing a spurious fit that treats the noise on the trace as part of the seismic reflection signal instead of making a genuine match with the signal itself. This paper outlines tests that allow an objective and quantitative evaluation of the accuracy of any match and illustrates their application with practical examples. The accuracy of estimation is summarized by the normalized mean square error (NMSE) in the estimated reflection signal, which is shown to be (/n)(P_N/P_S) where P_S/P_N is the signal-to-noise power ratio and n is the spectral smoothing factor. That is, the accuracy varies directly with the ratio of the power in the signal (taken to be the synthetic) to that in the noise on the seismic trace, and the smoothing acts to improve the accuracy of the predicted signal. The construction of confidence intervals for the NMSE is discussed. Guidelines for the choice of the spectral smoothing factor n are given. The variation of wavelet shape due to different realizations of the noise component is illustrated, and the use of confidence intervals on wavelet phase is recommended. Tests are described for examining the normality and stationarity of the errors of fit and their independence of the estimated reflection signal.     

Anisotropic P-wave attenuation measured from a multi-azimuth surface seismic reflection survey

A system of aligned vertical fractures produces azimuthal variations in stacking velocity and amplitude variation with offset, characteristics often reported in seismic reflection data for hydrocarbon exploration. Studies of associated attenuation anisotropy have been mostly theoretical, laboratory or vertical seismic profiling based. We used an 11 common‐midpoint‐long portion of each of four marine surface‐seismic reflection profiles, intersecting each other at 45° within circa 100 m of a common location, to measure the azimuthal variation of effective attenuation, Q⁻¹_eff and stacking velocity, in a shallow interval, about 100 m thick, in which consistently orientated vertical fracturing was expected due to an underlying salt diapirism. We found qualitative and quantitative consistency between the azimuthal variation in the attenuation and stacking velocity, and published amplitude variation with offset results. The 135° azimuth line showed the least apparent attenuation (1000 Q⁻¹_eff= 16 ± 7) and the fastest stacking velocity, hence we infer it to be closest to the fracture trend: the orthogonal 45° line showed the most apparent attenuation (1000Q⁻¹_eff= 52 ± 15) and slowest stacking velocity. The variation of Q⁻¹_eff with azimuth φ is well fitted by 1000Q⁻¹_eff = 34 − 18cos[2(φ+40°)] giving a fracture direction of 140 ± 23° (±1SD, derived from ‘bootstrapping’ fits to all 11⁴ combinations of individual common‐midpoint/azimuth measurements), compared to 134 ± 47° from published amplitude variation with offset data. The effects of short‐window spectral estimation and choices of spectral ratio bandwidth and offset ranges used in attenuation analysis, individually give uncertainties of up to ±13° in fracture direction. This magnitude of azimuthal variation can be produced by credible crack geometries (e.g., dry cracks, radius 6.5 m, aspect ratio 3 × 10⁻⁵, crack density 0.2) but we do not claim these to be the actual properties of the interval studied, because of the lack of well control (and its consequences for the choice of theoretical model and host rock physical properties) and the small number of azimuths available here.     

Estimating quality factor from surface seismic data: A comparison of current approaches

The performances of the spectral ratio (SR), frequency centroid shift (FCS), and frequency peak shift (FPS) methods to estimate the effective quality factor Q are compared. These methods do not demand true amplitude data and their implementations were done following an “as simple as possible” approach to highlight their intrinsic potentials and limitations. We use synthetic zero-offset seismic data generated with a simple layer-cake isotropic model. The methods can be ranked from simple to complex in terms of automation as: FPS, FCS and SR. This is a consequence of: (i) peak identification consists basically of a sorting procedure, (ii) centroid estimation involves basically the evaluation of two well-behaved integrals, and (iii) implementation of the SR method involves at least choosing a usable frequency bandwidth and fitting a gradient. The methods can be ranked from robust to sensitive in the presence of noise content in the sequence SR, FCS, and FPS. This is consequence of: (i) the gradient estimate associated to the SR method averages out the noise content in the entire usable frequency bandwidth, (ii) in the presence of moderate-to-high noise level, the centroid estimation is biassed towards overestimating Q due to noise contribution in the tail of the amplitude spectrum, and (iii) peak identification is unstable due to local noise fluctuation in the amplitude spectrum around the peak frequency. Regarding the stability of the estimates relative to the attenuation amount, SR and FCS methods show similar behaviours, whereas FPS method presents an inferior performance. This fact is an indirect consequence of the sensitivity of FPS method to the noise content because the higher is the attenuation the lower is the signal-to-noise ratio. Finally, regarding the robustness of the methods to the presence of dipping layers, only SR and FCS methods provide good estimates, at least to typical dips in non-faulted sedimentary layers, with the estimates obtained with SR method being more accurate that those obtained with FCS method. Except in relation to the automation complexity, which is less important than the performances of the methods, SR method was superior or showed similar performance to FCS method in all scenarios we tried.     

Pulse-like versus non-pulse-like ground motion records: Spectral shape comparisons and record selection strategies

Pulse-like records are well recognized for their potential to impose higher demands on structures when compared with ordinary records. The increased severity of the structural response usually caused by pulse-like records is commonly attributed to the spectral increment around the pulse period. By comparing the building response to sets of spectrally equivalent pulse-like and ordinary records, we show that there are characteristics of pulse-like records beyond the shape of the acceleration response spectrum that affect the results of nonlinear dynamic analysis. Nevertheless, spectral shape together with the ratio of pulse period to the first-mode structural period, T_p/T₁, are confirmed as “sufficient” predictors for deformation and acceleration response metrics in a building, conditioned on the seismic intensity. Furthermore, the average spectral acceleration over a period range, AvgSA, is shown to incorporate to a good proxy for spectral shape, and together with T_p/T₁, form an efficient and sufficient intensity measure for response prediction to pulse-like ground motions. Following this latter route, we propose a record selection scheme that maintains the consistency of T_p with the hazard of the site but uses AvgSA to account for the response sensitivity to spectral shape.     

基于经验参考场地的广义线性反演方法

为了克服广义线性反演方法（GIT）中理想的参考场地难以找到的局限性,本文将四分之一波长法计算的平均场地放大系数和谱衰减法计算的高频衰减参数作为GIT方法的经验参考场地（ERS）。以2008年5月至8月间28个强震动台站记录的95个汶川8.0级地震余震的615组强震动记录为例,通过与其他方法的比较,验证了ERS-GIT的合理性,并讨论了各类方法之间差异的原因。结果显示,ERS-GIT方法、传统GIT方法和非参数化GIT方法计算得到的平均应力降依次为1.15 MPa,0.78 MPa和0.52 MPa;ERS-GIT方法和传统GIT方法得到的品质因子分别为Q（f）=75.02f^1.27和Q（f）=65.56f^1.22。以场地的卓越频率为分界,ERS-GIT方法得到的局部场地响应在长周期和高频部分分别与H/V谱比法和传统GIT方法更为接近。     

<Emphasis Type="Italic">Q</Emphasis>-type bursts in magnetic oscillations of ELF range as a phenomenon reflecting the properties of the global Earth-ionosphere resonator

The observation results of Q-type bursts in the measurements of the horizontal component of the noise magnetic field in the range of the first Schumann resonance in polar regions (Lovozero high-latitude observatory) are presented. Automatic selection of Q-type bursts from the experimental data series is implemented on the basis of a waveform recognition algorithm. The resonant nature of Q-bursts is shown. The possibility of selecting such events in magnetic excitation conditions is highlighted. The global resonator quality upon decreasing the selected waveform amplitudes is estimated. The data obtained by this method are compared with estimates on the basis of Fourier analysis and values known from the world literature. The possible reasons for disagreements of the estimates are analyzed, including the problem of selecting the function approximating the spectrum, the problem of accounting for the background, and the possible irregularity of the spectrum. It is shown that Q-type bursts, besides the quality, allow estimating the resonant frequency of the first oscillation mode; however, the accuracy of such estimation is lower as compared to the results of Fourier analysis methods.     

The Q value variations in the preparing process of rock rupture

In this paper, the "spectral amplitude ratio method" (SAR), "energy method" (EN) and "coda wave method" (CW) are used to calculate theQ value variations of gneiss in the preparing rupture process. The obtained results show that the variation state ofQ values by SAR features the shape of relative stability—gradual increment to the maximum—then decrement and final rupture. The variation state ofQ values by EN is just contrary to that by SAR, i. e. with the shape of stability—decrement—increment—and final rupture. The varation state ofQ values by CW is similar to that by EN, its main frequency features the shape of relatively high value—decrement to the minimum—increment—and final rupture. But to the high frequency (higher than the main frequency), the variation state ofQ values features the shape of the stable value-increment to the maximum-decrement-and final rupture. At the same time, the results by coda wave amplitude spectrum show that, when stress reaches 70% of rupture stress, the high frequency component of S wave rapidly reduces (Q _c increasing); at the time of impending the main rupture, the main frequency component reduces with a large scale (Q _c increasing again), this may be the reason which causes the different variation states of two codaQ values. The result of amplitude spectra of P, S (initial wave) waves also show that with the appearance of microcracks the frequency band of S wave turn to be narrow, the high frequency component is reduced quickly, i. e. the S wave spectra have different variation states with different frequency components. That is why theQ _s obtained by different methods have different variation characteristics.     

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.     

HOMOMORPHIC FILTERING — THEORY AND PRACTICE*

The application of homomorphic filtering in marine seismic reflection work is investigated with the aims to achieve the estimation of the basic wavelet, the wavelet deconvolution and the elimination of multiples. Each of these deconvolution problems can be subdivided into two parts: The first problem is the detection of those parts in the cepstrum which ought to be suppressed in processing. The second part includes the actual filtering process and the problem of minimizing the random noise which generally is enhanced during the homomorphic procedure. The application of homomorphic filters to synthetic seismograms and air-gun measurements shows the possibilities for the practical application of the method as well as the critical parameters which determine the quality of the results. These parameters are:

• a) the signal-to-noise ratio (SNR) of the input data
• b) the window width and the cepstrum components for the separation of the individual parts
• c) the time invariance of the signal in the trace.

In the presence of random noise the power cepstrum is most efficient for the detection of wavelet arrival times. For wavelet estimation, overlapping signals can be detected with the power cepstrum up to a SNR of three. In comparison with this, the detection of long period multiples is much more complicated. While the exact determination of the water reverberation arrival times can be realized with the power cepstrum up to a multiples-to-primaries ratio of three to five, the detection of the internal multiples is generally not possible, since for these multiples this threshold value of detectibility and arrival time determination is generally not realized. For wavelet estimation, comb filtering of the complex cepstrum is most valuable. The wavelet estimation gives no problems up to a SNR of ten. Even in the presence of larger noise a reasonable estimation can be obtained up to a SNR of five by filtering the phase spectrum during the computation of the complex cepstrum. In contrast to this, the successful application of the method for the multiple reduction is confined to a SNR of ten, since the filtering of the phase spectrum for noise reduction cannot be applied. Even if the threshold results are empirical, they show the limits fór the successful application of the method.