共查询到20条相似文献，搜索用时 15 毫秒
1.
B. URSIN 《Geophysical Prospecting》1979,27(1):1-15
In the mathematical theory of seismic signal detection and parameter estimation given, the seismic measurements are assumed to consist of a sum of signals corrupted by additive Gaussian white noise uncorrelated to the signals. Each signal is assumed to consist of a signal pulse multiplied by a space-dependent amplitude function and with a space-dependent arrival time. The signal pulse, amplitude, and arrival time are estimated by the method of maximum likelihood. For this signal-and-noise model, the maximum likelihood method is equivalent to the method of least squares which will be shown to correspond to using the signal energy as coherency measure. The semblance coefficient is equal to the signal energy divided by the measurement energy. For this signal model we get a more general form of the semblance coefficient which reduces to the usual expression in the case of a constant signal amplitude function. The signal pulse, amplitude, and arrival time can be estimated by a simple iterative algorithm. The effectiveness of the algorithm on seismic field data is demonstrated. 相似文献
2.
Singular value decomposition (SVD) is applied to the identification of seismic reflections by using two different models: the impulse response model, where a seismic trace is assumed to consist of a known signal pulse convolved with a reflection coefficient series plus noise, and the delayed pulse model, where the seismic signal is assumed to consist of a small number of delayed pulses of known shape and with unknown amplitudes and arrival times. SVD clearly shows how least-squares estimation of the reflection coefficients may become unstable, since a division by the singular values is required. Two methods for stabilizing this procedure are investigated. The inverse of the singular values may be replaced by zeros when they are less than a given threshold. This is called the SVD cut-off method. Alternatively, we may use ridge regression which in filter design corresponds to assuming white noise. Statistical methods are used to compute an optimal SVD cut-off level and also to compute an optimal weighting parameter in ridge regression. Numerical studies indicate that the use of SVD cut-off or ridge regression stabilizes the least-squares procedure, but that the results are inferior to maximum-likelihood estimation where the noise is assumed to be filtered white noise. For the delayed pulse model, we use a linearization procedure to iteratively update the estimates of both the reflection amplitudes and the arrival times. In each step, the optimal SVD cut-off method is used. Confidence regions for the estimated reflection amplitudes and arrival times are also computed. Synthetic data examples demonstrate the effectiveness of this method. In a real data example, the maximum-likelihood method assuming an impulse response model is first used to obtain initial estimates of the number of reflections and their amplitudes and traveltimes. Then the iterative procedure is used to obtain improved estimates of the reflection amplitudes and traveltimes. 相似文献
3.
Reiter , E.C., Toksoz , M.N. and Purdy , G.M. 1992. A semblance-guided median filter. Geophysical Prospecting 41 , 15–41. A slowness selective median filter based on information from a local set of traces is described and implemented. The filter is constructed in two steps, the first being an estimation of a preferred slowness and the second, the selection of a median or trimmed mean value to replace the original data point. A symmetric window of traces defining the filter aperture is selected about each trace to be filtered and the filter applied repeatedly to each time point. The preferred slowness is determined by scanning a range of linear moveouts within the user-specified slowness passband. Semblance is computed for each trial slowness and the preferred slowness selected from the peak semblance value. Data points collected along this preferred slowness are then sorted from lowest to highest and in the case of a pure median filter, the middle point(s) selected to replace the original data point. The output of the filter is therefore quite insensitive to large amplitude noise bursts, retaining the well-known beneficial properties of a traditional 1D median filter. Energy which is either incoherent over the filter aperture or lies outside the slowness passband, may be additionally suppressed by weighting the filter output by the measured peak semblance. This approach may be used as a velocity filter to estimate coherent signal within a specified slowness passband and reject coherent energy outside this range. For applications of this type, other velocity estimators may be used in place of our semblance measure to provide improved velocity estimation and better filter performance. The filter aperture may also be extended to provide increased velocity estimation, but will result in additional lateral smearing of signal. We show that, in addition to a velocity filter, our approach may be used to improve signal-to-noise ratios in noisy data. The median filter tends to suppress the amplitude of random background noise and semblance weighting may be used to reduce the amplitude of background noise further while enhancing coherent signal. We apply our method to vertical seismic profile data to separate upgoing and downgoing wavefields, and also to large-offset ocean bottom hydrophone data to enhance weak refracted and post-critically reflected energy. 相似文献
4.
H.
ZDEMIR 《Geophysical Prospecting》1981,29(5):702-714
Optimum multichannel filters can be designed to process seismic events falling on hyperbolic moveout curves using the conventional least-squares method. Contrary to the linear moveout filters, autocorrelation and crosscorrelation functions inherent in the normal equations have to be computed numerically. However, computation times of filter coefficients are comparable to linear moveout operators. For a given source-receiver geometry and assuming straight ray-path, relative moveout of a seismic reflection event is dependent on the two way arrival time and rms velocity. Consequently, to avoid overlapping of pass and reject moveout windows, hyperbolic moveout filters have to be designed over time gates rather than for the whole record lengths. Hyperbolic and hyperbolic-linear moveout filters applied to synthetic and field seismic reflection traces show good signal-to-noise (S/N) ratio improvements. Results of some combined synthetic and field data examples are presented. 相似文献
5.
提出一种在时间域采用最大熵谱反褶积提取台站接收函数的方法，以最大熵作为自相关函数和互相关函数的递推准则，利用Toeplitz方程及Levinson递推算法，得到预测误差滤波系数的递推公式，从而计算台站接收函数．外推运算过程中，反射系数总是小于1，保证了最大熵谱反褶积的稳定性．时窗外数据熵极大提高了接收函数的分辨率．合成地震图与实测地震图的检验表明, 最大熵谱反褶积是一种在时间域测定台站接收函数的有效方法． 相似文献
6.
In this paper, we discuss high‐resolution coherence functions for the estimation of the stacking parameters in seismic signal processing. We focus on the Multiple Signal Classification which uses the eigendecomposition of the seismic data to measure the coherence along stacking curves. This algorithm can outperform the traditional semblance in cases of close or interfering reflections, generating a sharper velocity spectrum. Our main contribution is to propose complexity‐reducing strategies for its implementation to make it a feasible alternative to semblance. First, we show how to compute the multiple signal classification spectrum based on the eigendecomposition of the temporal correlation matrix of the seismic data. This matrix has a lower order than the spatial correlation used by other methods, so computing its eigendecomposition is simpler. Then we show how to compute its coherence measure in terms of the signal subspace of seismic data. This further reduces the computational cost as we now have to compute fewer eigenvectors than those required by the noise subspace currently used in the literature. Furthermore, we show how these eigenvectors can be computed with the low‐complexity power method. As a result of these simplifications, we show that the complexity of computing the multiple signal classification velocity spectrum is only about three times greater than semblance. Also, we propose a new normalization function to deal with the high dynamic range of the velocity spectrum. Numerical examples with synthetic and real seismic data indicate that the proposed approach provides stacking parameters with better resolution than conventional semblance, at an affordable computational cost. 相似文献
7.
Seismograms predicted from acoustic or elastic earth models depend very non-linearly on the long wavelength components of velocity. This sensitive dependence demands the use of special variational principles in waveform-based inversion algorithms. The differential semblance variational principle is well-suited to velocity inversion by gradient methods, since its objective function is smooth and convex over a large range of velocity models. An extension of the adjoint state technique yields an accurate estimate of the differential semblance gradient. Non-linear conjugate gradient iteration is quite successful in locating the global differential semblance minimum, which is near the ordinary least-squares global minimum when coherent data noise is small. Several examples, based on the 2D primaries-only acoustic model, illustrate features of the method and its performance. 相似文献
8.
We propose a two-dimensional, non-linear method for the inversion of reflected/converted traveltimes and waveform semblance designed to obtain the location and morphology of seismic reflectors in a lateral heterogeneous medium and in any source-to-receiver acquisition lay-out. This method uses a scheme of non-linear optimization for the determination of the interface parameters where the calculation of the traveltimes is carried out using a finite-difference solver of the Eikonal equation, assuming an a priori known background velocity model. For the search for the optimal interface model, we used a multiscale approach and the genetic algorithm global optimization technique. During the initial stages of inversion, we used the arrival times of the reflection phase to retrieve the interface model that is defined by a small number of parameters. In the successive steps, the inversion is based on the optimization of the semblance value determined along the calculated traveltime curves. Errors in the final model parameters and the criteria for the choice of the best-fit model are also estimated from the shape of the semblance function in the model parameter space. The method is tested and validated on a synthetic dataset that simulates the acquisition of reflection data in a complex volcanic structure. This study shows that the proposed inversion approach is a valid tool for geophysical investigations in complex geological environments, in order to obtain the morphology and positions of embedded discontinuities. 相似文献
9.
H.
ZDEM&#x;R 《Geophysical Prospecting》1985,33(6):828-860
A seismic trace is modeled as a moving average (MA) process both in signal and noise: a signal wavelet convolved with a reflection coefficient series plus colored random noise. Seismic reflection coefficients can be estimated from seismic traces using suitable estimation algorithms if the input wavelet is known and vice versa. The maximum likelihood (ML) algorithm is used to estimate the system order and the reflection coefficients. The system order is related to the arrival time of the latest signal in a complex seismic reflection event. The least-squares (LS) method does not provide such information. The ML algorithm makes assumptions only about the Gaussian nature of the noise. It is better suited for seismic applications since the LS method inherits the white noise assumption. The Gauss-Newton (G-N) and Newton-Raphson (N-R) optimization algorithms are used to obtain the ML and the LS estimates. Reflection coefficient estimations are affected by the choice of sampling rate of seismic data. Theoretically, the optimum choice in system identification is the Nyquist rate. Experience with synthetic data confirms the theory. In practice, good estimates of reflection coefficients are possible only up to certain pulse separations (or, equivalently, orders). This is mostly due to numerical problems with the optimization algorithms used and partly due to the limited bandwidth of seismic signals. Good estimates from data simulated using three airgun array pulses recorded with 6–128 Hz filter setting are possible up to about 40.0 ms pulse separations. Successful estimations from pinchout and thin layer simulations and well controlled offshore “bright-spots” are given. 相似文献
10.
HUANG Guangyuan 《中国科学D辑(英文版)》2001,44(2):159-165
Some new imaging formulas for seismic reflection wave and their theoretical basis are given. Phenomena of wave propagation
should be characterized by instantaneous spectrum and expressed by complex function of three variables (time, space and frequency)
in mathematics. Various physical parameters of medium are also complex functions of two variables (space and frequency). The
relationship between reflection coefficient of medium and spectrum of reflected wave is given. Multi-reflection and filter
of formations are considered in inversion formulas. Problems in classical convolution model and wave equation are illustrated.
All these inversion formulas can be used to image underground medium by wavelet transform and method of “3-basic colors”.
Different colors mean different media. 相似文献
11.
The Earth center of mass (geocenter) time series with the sampling interval of one week are determined from Satellite Laser Ranging (SLR), Global Navigation Satellite System (GNSS) and Doppler Orbitography and Radiopositioning Integrated by Satellite (DORIS) observations. The 3D geocenter time series were projected onto XY, YZ and ZX planes of the International Terrestrial Reference Frame (ITRF), thus, three complex-valued time series can be analyzed for each observation technique. The signal to noise ratio in these geocenter time series is very small and detectable oscillations are rather broadband, however, the annual oscillation can be noticed in each one of them. The wavelet transform technique with the Morlet wavelet function was applied to compute the mean and spectra-temporal polarization functions from the prograde (positive periods) and retrograde (negative periods) spectra of the examined complex-valued time series. The sign of the polarization function determines turning direction in the elliptical motion. If this function is positive or negative for oscillation with a chosen period, then this oscillation is prograde or retrograde, respectively. To estimate the significance level of polarization functions, corresponding to time series data length, the Monte Carlo experiment was performed using complex-valued white noise data. In order to detect similarity between elliptic oscillations in two different time series the spectra-temporal wavelet semblance function was computed. This function reveals that in the XY equatorial plane there is phase agreement between retrograde annual oscillation for SLR and GNSS techniques, and between prograde annual oscillation for DORIS and two other techniques. To construct a model of geocenter motion from GNSS and SLR center of mass time series the wavelet based semblance filtering method was applied. Common oscillations in the analyzed time series are dominated by the annual oscillation with amplitude less than 5 mm. 相似文献
12.
Determination of a shallow velocity–depth model from seismic refraction data by coherence inversion1
Seismic refractions have different applications in seismic prospecting. The travel- times of refracted waves can be observed as first breaks on shot records and used for field static calculation. A new method for constructing a near-surface model from refraction events is described. It does not require event picking on prestack records and is not based on any approximation of arrival times. It consists of the maximization of the semblance coherence measure computed using shot gathers in a time window along refraction traveltimes. Time curves are generated by ray tracing through the model. The initial model for the inversion was constructed by the intercept-time method. Apparent velocities and intercept times were taken from a refraction stacked section. Such a section can be obtained by appling linea moveout corrections to common-shot records. The technique is tested successfully on synthetic and real data. An important application of the proposed method for solving the statics problem is demonstrated. 相似文献
13.
Receiver function estimated by maximum entropy deconvolution 总被引：2，自引：0，他引：2
Maximum entropy deconvolution is presented to estimate receiver function, with the maximum entropy as the rule to determine auto-correlation and cross-correlation functions. The Toeplitz equation and Levinson algorithm are used to calculate the iterative formula of error-predicting filter, and receiver function is then estimated. During extrapolation, reflective coefficient is always less than I, which keeps maximum entropy deconvolution stable. The maximum entropy of the data outside window increases the resolution of receiver function. Both synthetic and real seismograms show that maximum entropy deconvolution is an effective method to measure receiver function in time-domain. 相似文献
14.
It has been found that the Wiener-Hopf least-squares method is a very successful tool for the determination of resistivity sounding filters. The values of the individual filter coefficients differ quite appreciably from those obtained by the Ghosh procedure. These differences in the filter coefficients, however, have only a negligible effect on the output of the filter. It seems that these differences in the coefficients correspond to a filter function of a rather narrow frequency band around the Nyquist frequency, which is only very weakly present in the input and output functions. 相似文献
15.
Consider the mathematical model of a horizontally layered system subject to an initial downgoing source pulse in the upper layer and to the condition that no upgoing waveforms enter the layered system from below the deepest interface. The downgoing waveform (as measured from its first arrival) in each layer is necessarily minimum-phase. The net downgoing energy in any layer, defined as the difference of the energy spectrum of the downgoing wave minus the energy spectrum of the upgoing wave, is itself in the form of an energy spectrum, that is, it is non-negative for all frequencies. The z-transform of the autocorrelation function corresponding to the net downgoing energy spectrum is called the net downgoing spectral function for the layer in question. The net downgoing spectral functions of any two layers A and B are related as follows: the product of the net downgoing spectral function of layer A times the overall transmission coefficient from A to B equals the product of the net downgoing spectral function of layer B times the overall transmission coefficient from B to A. The net downgoing spectral function for the upper layer is called simply the spectral function of the system. In the case of a marine seismogram, the autocorrelation function corresponding to the spectral function can be used to recursively generate prediction error operators of successively increasing lengths, and at the same time the reflection coefficients at successively increasing depths. This recursive method is mathematically equivalent to that used in solving the normal equations in the case of Toeplitz forms. The upgoing wave-form in any given layer multiplied by the direct transmission coefficient from that layer to the surface is equal to the convolution of the corresponding prediction error operator with the surface seismogram. The downgoing waveform in this given layer multiplied by the direct transmission coefficient from that layer to the surface is equal to the convolution of the corresponding hindsight error operator (i.e., the time reverse of the prediction error operator) with the surface seismogram. 相似文献
16.
Moshe Reshef 《Geophysical Prospecting》2014,62(6):1453-1467
We present an innovative approach for seismic image enhancement using multi‐parameter angle‐domain characterization of common image gathers. A special subsurface angle‐domain imaging system is used to generate the multi‐parameter common image gathers in a summation‐free image space. The imaged data associated with each common image gathers depth point contain direction‐dependent opening‐angle image contributions from all the available incident and scattered wave‐pairs at this point. Each direction‐dependent opening‐angle data can be differently weighted according to its coherency measure. Once the optimal migration velocity is used, it is assumed that in the actual specular direction, the coherency measure (semblance) along reflection events, from all available opening angles and opening azimuths, is larger than that along non‐specular directions. The computed direction‐dependent semblance attribute is designed to operate as an imaging filter which enhances specular migration contributions and suppresses all others in the final migration image. The ability to analyse the structural properties of the image points by the multi‐parameter common image gather allows us to better handle cases of complicated wave propagation and to improve the image quality at poorly illuminated regions or near complex structures. The proposed method and some of its practical benefits are demonstrated through detailed analysis of synthetic and real data examples. 相似文献
17.
Velocity analysis using AB semblance 总被引：1，自引：0，他引：1
S. Fomel 《Geophysical Prospecting》2009,57(3):311-321
I derive and analyse an explicit formula for a generalized semblance attribute, which is suitable for the velocity analysis of prestack seismic gathers with distinct amplitude trends. While the conventional semblance can be interpreted as a squared correlation with a constant, the AB semblance is defined as a correlation with a trend. This measure is particularly attractive for analysing class II AVO anomalies and converted waves. Analytical derivations and numerical experiments show that the resolution of the AB semblance is approximately twice as low as that of the conventional semblance. However, this does not prevent it from being an effective attribute. I use synthetic and field data examples to demonstrate the improvements in velocity analysis from AB semblance. 相似文献
18.
Least-squares reverse time migration is often formulated as an iterative updating process, where estimating the gradient of the misfit function is necessary. Traditional time domain shot-profile least-squares reverse time migration is computationally expensive because computing the gradient involves solving the two-way wave equation several times in every iteration. To reduce the computational cost of least-squares reverse time migration, we propose a double-plane-wave least-squares reverse time migration method based on a misfit function for frequency-domain double-plane-wave data. In double-plane-wave least-squares reverse time migration, the gradient is computed by multiplying frequency-domain plane-wave Green's functions with the corresponding double-plane-wave data residual. Because the number of plane-wave Green's functions used for migration is relatively small, they can be pre-computed and stored in a computer's discs or memory. We can use the pre-computed plane-wave Green's functions to obtain the gradient without solving the two-way wave equation in each iteration. Therefore, the migration efficiency is significantly improved. In addition, we study the effects of using sparse frequency sampling and sparse plane-wave sampling on the proposed method. We can achieve images with correct reflector amplitudes and reasonable resolution using relatively sparse frequency sampling and plane-wave sampling, which are larger than that determined by the Nyquist theorem. The well-known wrap-around artefacts and linear artefacts generated due to under-sampling frequency and plane wave can be suppressed during iterations in cases where the sampling rates are not excessively large. Moreover, implementing the proposed method with sparse frequency sampling and sparse plane-wave sampling further improves the computational efficiency. We test the proposed double-plane-wave least-squares reverse time migration on synthetic models to show the practicality of the method. 相似文献
19.
A technique for automatic cross-well tomography based on semblance and differential semblance optimization is presented. Given a background velocity, the recorded seismic data traces are back-propagated towards the source, i.e. shifted towards time zero using the modelled traveltime between the source and the receiver and corrected for the geometrical spreading. Therefore each back-propagated trace should be a pulse, close to time zero. The mismatches between the back-propagated traces indicate an error in the velocity model. This error can be measured by stacking the back-propagated traces (semblance optimization) or by computing the norm of the difference between adjacent traces (differential semblance optimization).
It is known from surface seismic reflection tomography that both the semblance and differential semblance functional have good convexity properties, although the differential semblance functional is believed to have a larger basin of attraction (region of convergence) around the true velocity model. In the case of the cross-well transmission tomography described in this paper, similar properties are found for these functionals.
The implementation of this automatic method for cross-well tomography is based on the high-frequency approximation to wave propagation. The wavefronts are constructed using a ray-tracing algorithm. The gradient of the cost function is computed by the adjoint-state technique, which has the same complexity as the computation of the functional. This provides an efficient algorithm to invert cross-well data. The method is applied to a synthetic data set to demonstrate its efficacy. 相似文献
It is known from surface seismic reflection tomography that both the semblance and differential semblance functional have good convexity properties, although the differential semblance functional is believed to have a larger basin of attraction (region of convergence) around the true velocity model. In the case of the cross-well transmission tomography described in this paper, similar properties are found for these functionals.
The implementation of this automatic method for cross-well tomography is based on the high-frequency approximation to wave propagation. The wavefronts are constructed using a ray-tracing algorithm. The gradient of the cost function is computed by the adjoint-state technique, which has the same complexity as the computation of the functional. This provides an efficient algorithm to invert cross-well data. The method is applied to a synthetic data set to demonstrate its efficacy. 相似文献
20.
The magnetic anomaly due to a buried dike consists of the sum of two easily separated elementary functions. These functions, which have simple symmetry, are called even and odd functions. The correlation factors (r
0,1 for the even andr
0,2 for the odd function) between least-squares residual anomalies from even and odd functions are computed. Correlation values are used to determine the depth to the top and the half-width of the dike. The method also includes the determination of the index parameter and the amplitude coefficient. The validity of the method is tested against a theoretical and a field example where the parameters of the latter were determined by other investigators in comparing the results. 相似文献