摘要:

AbstractIn 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 demon

ISSN:0016-8025    

DOI:10.1111/j.1365-2478.1979.tb00955.x

出版商:Blackwell Publishing Ltd    

年代:1979

数据来源: WILEY

摘要:

AbstractAn algorithm for separation of signals according to their coherency is proposed. The algorithm, called Superstack, is used on common depth point data after normal moveout corrections have been applied. The algorithm can be regarded as an iterative stacking procedure. After each stack, input values are changed depending on the consistency of the output of the previous stack.The Superstack algorithm is able to provide better separation of signals showing a different degree of horizontal consistency (coherency) than the normal horizontal stack.All noise signals in a CDP‐gather may be assumed to show less horizontal consistency than the primary reflections. On this basis the algorithm will give an improved primary/multiple and an improved primary/noise ratio.The Superstack is very general, should not be especially expensive in terms of computer time, and can easily be implemented in routine processin

ISSN:0016-8025    

DOI:10.1111/j.1365-2478.1979.tb00956.x

出版商:Blackwell Publishing Ltd    

年代:1979

数据来源: WILEY

摘要:

AbstractLong leg multiples can be suppressed by a method which provides an alternative to weighted common‐depth‐point stacking and multichannel stacking filtering. The suppression is achieved by coherency weighting whereby the time‐dependent weighting factor decreases as the semblance of the multiple reflections increases.The algorithm of the method is described. Its efficiency is discussed in relation to the input data and results of its application to marine seismic data are presented.For practical application, the stacking velocity of the multiples has to be known. As the process is based on stacking velocities, different types of multiples can be handled, for instance water‐bottom multiples or internal multiples. The parameter analysis shows that the degree of multiple suppression can easily be controlled by adapting the parameters of the procedure to the field conditions.During the suppression of multiples, the primaries are saved according to the moveout differences between the two. The non‐linear behaviour of the process causes signal suppression and distortion effects, which have to be corrected by AGC normalization and low‐pass filtering.Among the various applications available, only the suppression of long leg water‐bottom multiples is treated here. The results show that their suppression on the basis of moveout differences is efficient even when standard length streamers are used in regions with water depth of up to 1500 m and more, if the stacking velocity of the primaries is about 10 to 20% higher than that of the multiples. Even if those parts of the primaries which are masked by the multiples are suppressed in the individual common‐depth‐point gathers by the procedure, the remaining primaries in the AGV stacked section are largely uncovered by the mul

ISSN:0016-8025    

DOI:10.1111/j.1365-2478.1979.tb00957.x

出版商:Blackwell Publishing Ltd    

年代:1979

数据来源: WILEY

摘要:

AbstractIn contrast to the conventional deconvolution technique (Wiener‐Levinson), the spike‐, predictive‐, and gap‐deconvolution is realized with the help of an adaptive updating technique of the prediction operator. As the prediction operator will be updated from sample to sample, this procedure can be used for time variant deconvolution. Updating formulae discussed are the adaptive updating formula and the sequential algorithm for the sequential estimation technique. This updating technique is illustrated using both synthetic and real seism

ISSN:0016-8025    

DOI:10.1111/j.1365-2478.1979.tb00958.x

出版商:Blackwell Publishing Ltd    

年代:1979

数据来源: WILEY

摘要:

AbstractThe first part of this paper examines a special case of acoustical imaging in which the source and the receiver coincide. The benefits of weighting and muting are studied in detail by means of computer modeling. The test model consists of a single planar interfacez=z1, abruptly terminated atx= o. The amplitude and phase responses are computed in the planez=z0= o for two separations of neighboring stations, Δx=λ/10 and Δx=λ/2. Six different weighting factors are used in the test. However, in this source‐receiver coincident case, three of the weighting factors produce identical responses, so that all six test factors may be represented by only four curves. It is found that when the spatial sampling at the aperture approaches the condition of critical sampling, i.e. Δx=λ/2, only the weighting factor which implicitly takes into account beam steering along the specular reflection path is acceptable. This factor alone keeps the amplitude and the phase curves undistorted until the difference 2 ·ΔRbetween two neighboring paths reaches approximately λ/2. If we set 2 ·ΔR=λ/2, we may construct a set of curves which we may call quite appropriately muting curves. These curves are physically interpretable only for station separation Δx>λ/4. The muting curves are symmetrical about the linex= 0 and their angular opening depends on spatial separation Δx, depthz, and wavelength λ (which may vary with depth).The second part of this paper suggests how the weighting factor with implicit beam steering can be applied to reconstruction of two and three‐dimensional wavefields. Seismic migration of common depth point (CDP) stacked line data is also discussed. This is a hybrid case which presents certain theoretical difficulties. We shall also mention the velocity problem which is inherent to migration of CDP stacked data.The third and final part concerns implementation of the migration of CDP stacked data. When the spatial sampling is between λ/4 and λ/2, the migration process will benefit from beam steering and from muting. The benefits are more subtle when the separation of the traces is less than λ/4. However, in that case the cost of data collection is considerable and often prohibitive. In either case the migration of seismic data can be expedited by use of precalculated tables of migration velocities, ray path distances, and weig

ISSN:0016-8025    

DOI:10.1111/j.1365-2478.1979.tb00959.x

出版商:Blackwell Publishing Ltd    

年代:1979

数据来源: WILEY

摘要:

AbstractNonlinear sweeps have often successfully been employed in the 1960s. However, this area of sweep technology has been neglected since the introduction of digital recording techniques in the Vibroseis system. Now the advent of computerized recording instruments yields a new economical possibility of forming approximately nonlinear sweeps by combining several linear sweeps with or without time gaps to a “Combisweep”. The total duration of a Combisweep may be as long as the maximum available recording time, for example 32 s.Beside the attenuation of correlation noise, the new method has further merits, such as the weighting of predetermined frequency ranges, in order to effect a certain kind of optimum filtering on the emitter side, or in order to compensate to some degree for frequency dependent absorption.In all these applications the Combisweep is considered as one signal in the correlation process. But by correlating with the individual sweeps or a partial combination of them and by applying automatic switching at predetermined times within the gaps between the individual sweeps additional possibilities arise, such as obtaining in one run with a twenty‐four channel recording unit twenty‐four traces with small distances between vibrators and geophones for shallow reflections and another twenty‐four traces with larger distances for deeper reflections. Various Combisweeps and their applications are

ISSN:0016-8025    

DOI:10.1111/j.1365-2478.1979.tb00960.x

出版商:Blackwell Publishing Ltd    

年代:1979

数据来源: WILEY

摘要:

AbstractA numerical technique is developed to solve the three‐dimensional potential distribution about a point source of current located in or on the surface of a half‐space containing arbitrary two‐dimensional conductivity distribution. Finite difference equations are obtained for Poisson's equations by using point‐ as well as area‐discretization of the subsurface. Potential distributions at all points in the set defining the half‐space are simultaneously obtained for multiple point sources of current injection. The solution is obtained with direct explicit matrix inversion techniques. An empirical mixed boundary condition is used at the “infinitely distant” edges of the lower half‐space. Accurate solutions using area‐discretization method are obtained with significantly less attendant computational costs than with the relaxation, finite‐element, or network solution techniques for models of

ISSN:0016-8025    

DOI:10.1111/j.1365-2478.1979.tb00961.x

出版商:Blackwell Publishing Ltd    

年代:1979

数据来源: WILEY

摘要:

AbstractComputations of the time‐domain electromagnetic response of a multi‐layered earth have been carried out for different source‐receiver coil systems. The primary excitation is a train of half‐sinusoidal waveforms of alternating polarity. The conversion into the time‐domain involves Fourier series summation of the matched complex mutual coupling ratios of the layered earth models computed by a digital linear filter method. As an example, the response of a perpendicular coil system on the ground surface for two source‐receiver separations has been presented for a five‐layer earth model. This has been compared with the responses of homogeneous, two‐layer, three‐layer, and four‐layer models.Next, the investigations have been extended to study the problems of equivalence of three‐layer models, the intermediate layer of which is either conductive or resistive. For an intermediate conductive layer (H‐type), the studies show that in the early portion of the signal the interpretation of a true three‐layer earth is possible to some extent, whereas the ambiguity due to equivalence persists in the late samples. On the other hand, for an intermediate resistive layer (K‐type), the three‐layer earth and its equivalent model cannot be distinguished from each other over the entire sampling period.On the basis of a computational approach, equivalence has been empirically established as √h/ρ=constantfor H‐type earth‐sections, and ash2ρ=constantfor K‐type earth sections, wherehand ρ are respectively the thickness a

ISSN:0016-8025    

DOI:10.1111/j.1365-2478.1979.tb00962.x

出版商:Blackwell Publishing Ltd    

年代:1979

数据来源: WILEY

摘要:

AbstractThe Wiener filtering scheme is obtained for a multichannel complex system utilizing the “block‐Toeplitz” property of autocorrelation matrix. A numerical example is given to elucidate the application of the filter design. The study also outlines Burg's maximum entropy method to include the multi‐channel comple

ISSN:0016-8025    

DOI:10.1111/j.1365-2478.1979.tb00963.x

出版商:Blackwell Publishing Ltd    

年代:1979

数据来源: WILEY

摘要:

AbstractThe impulse response of models of subsurface formations are statistically analyzed for abstracting seismic parameters which could be characteristic of the stratigraphy and lithology of the formations. Two types of formations have been considered, consisting either of sand‐shale sequences or of coal‐shale sequences. Models of the formations are generated using the Monte Carlo method. It is found that three features in the power spectrum of the impulse response, namely the frequencyfeat which the spectrum can be divided into a zone of high energy from a zone of low energy, the lowest frequencyfpwhere there is a significant energy peak, and the frequencyfmat which there is a maximum energy, can be used statistically to distinguish between the formations consisting of sand‐shale sequences and the formations made up of coal‐shale sequences. Three additional parametersA2/A1,A2/A0, andA1/A0, whereAdenotes the autocorrelation function of the impulse response and the subscripts denote the lags, are also statistically significant discriminators between the sand‐shale formations and the coal‐shale formations. The discrimination between the two subgroups of each model consisting of more (or less) than fifty percent of one lithology is also feasible, although there are fewer discriminant

ISSN:0016-8025    

DOI:10.1111/j.1365-2478.1979.tb00964.x

出版商:Blackwell Publishing Ltd    

年代:1979

数据来源: WILEY