INVERSION OF REFLECTION DATA *

An iterative inversion method which also takes into account wave energy absorption is described. This method allows estimates of the acoustic impedance in sedimentary layers with nearly plane and parallel stratification. A set of reflection data has been inverted and an impedance model was obtained which correlates well with the essential features of the borehole velocity log.     

LINEARIZED INVERSION OF SEISMIC REFLECTION DATA*

This is the first of a series of papers giving the solution of the inverse problem in seismic exploration. The acoustic approximation is used together with the assumption that the velocity field has the form . The forward problem is then linearized (thus neglecting multiple reflected waves) and the inverse problem of estimating δ is set up. Its rigorous solution can be obtained using an iterative algorithm, each step consisting of a classical Kirchhoff migration (hyperbola summation) plus a classical forward modeling step (circle summation).     

一种反演不均匀介质大地电磁测深资料的方法

通过反演受近地表不均匀介质影响的大地电磁测深资料的新方法,可获得较准确的一维地电断面参数、不均匀体埋藏深度及其电性特征。本方法计算速度快,单测ρxy,ρyx可独立反演并相互验证结果的准确性     

A NEW APPROACH TO THE INVERSION OF SEISMIC DATA*

A new inversion method for seismic reflection data is based on impedance concepts and uses transformations to reduce the essentially non-linear problem to a linear eigenvalue formulation without approximation. A set of reflection data has been inverted using this method. The characteristic impedances of the layers so determined are compared with log data from a reference borehole.     

INVERSION OF FIRST-BREAK TRAVELTIME DATA OF DEEP SEISMIC REFLECTION PROFILES1

First breaks of 2D deep reflection data were used to construct velocity-depth models for improved static corrections to a deeper datum level and for geological interpretations. The highly redundant traveltime data were automatically picked and transformed directly into a velocity-depth model by maximum depth methods such as the Giese- and the Slichter-method. Comparisons with the results of synthetic calculations and a tomographic approach using iterative inversion methods (ART, SIRT) showed that maximum depth methods provide reliable velocity models as a basis for the computation of static corrections. These methods can economically be applied during data acquisition in the field. They provide particularly long-period static anomalies, which are of the order of 20–40 ms (0.5-1 wavelength) within CMP gathers of an example of a deep reflection profile in SW-Germany sited on crystalline basement. Reprocessing of this profile, which was aimed at the comparison between the effects of the originally used and the new statics, did not result in dramatically improved stacking quality but showed a subtle influence on the detailed appearance of deep crustal events.     

AN INVESTIGATION OF THE SPECTRAL PROPERTIES OF PRIMARY REFLECTION COEFFICIENTS*

This paper investigates the form of the nonwhiteness found in the reflection coefficients from a wide variety of rock sequences around the world. In all but one case densities are taken as constant due to the paucity of suitable density data. The reflection sequences are pseudo-white only above a corner frequency, below which their power spectrum falls away according to a power law f^β, where β is between 0.5 and 1.5. This spectrum can be adequately modelled in practice very simply with an ARMA (1, 1) process which acts on a white innovation sequence. The corollary of this is that before wavelet estimation methods are applied (all of which-except those based on synthetic seismograms—presuppose white reflection sequences) or deconvolution filters estimated, seismic traces should be filtered with the inverse of this process. Interestingly, the estimated ARMA processes group themselves into two clearly differentiated categories, having very different indices of predictability (or, strictly, indices of linear determinism). The two categories apparently correlate precisely with two kinds of sedimentation: one which consists largely of sequences of rocks with repeating properties, called “repetitive” in this paper but perhaps loosely describable as “cyclic”, and the other which is randomly bedded with no apparent pattern of components. The former has indices of predictability which are two to four times as great as those of the latter. Another, probably related, property is that β for the repetitive sequences tends to be greater than that for non-repetitive rock columns. The observed power spectra are shown to be consistent with a simple model for the logarithm of acoustic impedance consisting of a mixture of processes where the distribution of (time) scale parameters is reciprocal. Detailed effects of block-averaging and sampling the logs are shown to depend on the type of sequence under examination.     

COMPLETE INVERSION OF ZERO-OFFSET SEISMIC DATA*

The one-dimensional seismic inverse problem consists of recovering the acoustic impedance (or reflectivity function) as a function of traveltime from the reflection response of a horizontally layered medium excited by a plane-wave impulsive source. Most seismic sources behave like point sources, and the data must be corrected for geometrical spreading before the inversion procedure is applied. This correction is usually not exact because the geometrical spreading is different for primary and multiple reflections. An improved algorithm is proposed which takes the geometrical spreading from a point source into account. The zero-offset reflection response from a stack of homogeneous layers of variable thickness is used to compute the thickness, velocity and density of each layer. This is possible because the geometrical spreading contains additional information about the velocities.     

CONSTRAINED INVERSION OF POTENTIAL FIELD DATA*

For constrained inversion of potential field data within the framework of generalized inversion an analysis of data error variances leads to confidence limits for the model parameters. For that purpose Pseudo-hyper-ellipsoids can be used to describe the nonlinear behaviour of the given inverse problem, and upper and lower bounds can be added to those parameters of which some independent knowledge is available. A gravity example is treated to show the application of the method.     

INVERSION METHOD IN THE SLANT STACK DOMAIN USING AMPLITUDES OF REFLECTION ARRIVALS*

Almost all ray-tracing methods ignore the analysis of the amplitudes of seismic arrivals and therefore utilize only half of the available information. We propose a method which is a combination of ray-tracing imaging and transformation of the amplitudes of wide-aperture data. Seismic data in the conventional X-T domain are first transformed to the domain of intercept time τ and ray parameter p to recover the plane wave response. The next step is the derivation of a series of plane wave reflection coefficients, which are mapped as a function of τ and p. The reflection coefficients R(τ, p) for two arbitrarily chosen traces can then be used in our inversion method to derive a slowness-depth and a density-depth profile. It is shown that the inclusion of amplitudes of seismic arrivals (in this method, we consider the acoustic case) makes the inverse method highly stable and accurate. In a horizontally stratified medium one can recover separate profiles of velocity and density. Since this method utilizes large-offset data, it can be used for separate recovery of velocity and density to a greater depth.     

A NONITERATIVE PROCEDURE FOR INVERTING PLANE-WAVE REFLECTION DATA AT SEVERAL ANGLES OF INCIDENCE USING THE RICCATI EQUATION*

Various exact methods of inverting the complete waveform of vertical seismic reflection data to produce acoustic impedance profiles have been suggested. These inverse methods generally remain valid for nonvertical, plane-wave data, provided total reflection does not occur. Thus, in principle, the “seismogram” at each ray parameter in a slant stack can be interpreted separately. Rather than invert each plane-wave seismogram separately, they can all be interpreted simultaneously and an “average” model thus obtained. Inversion for both the velocity and the density also becomes possible when two or more plane-wave seismograms are simultaneously inverted. The theory for a noniterative inversion method, based on the time-domain Riccati equation, is discussed. Numerical examples of inversions using this technique on synthetic data demonstrate its numerical stability and the advantage of simultaneous inversion of several seismograms to reduce the effect of noise in the data and increase the stability of the inversion process.     

TUTORIAL THE PROGRESSIVE ATTENUATION OF HIGH-FREQUENCY ENERGY IN SEISMIC REFLECTION DATA*

Seismic reflection data always exhibit a progressive loss of high-frequency energy with time. This effect is partly attributable to irreversible processes such as the conversion of elastic energy into heat (commonly known as absorption), and partly to reversible processes associated with interference between reflected waves arriving at different times. This paper looks only at reversible linear elastic effects at normal incidence and asks the following question: if there were no such absorption, would there still be a progressive loss of high-frequency energy? Using normal incidence and a layered elastic earth model we prove the following results. 1. The normal incidence response of a sequence of plane parallel elastic layers is non-white. 2. The pressure wave reflected by a layer that is thin compared with a wavelength is differentiated with respect to the incident wave. 3. The transmission response of a thin layer is consequently low-pass and the transmission response of a sequence containing many thin layers is very low-pass. 4. The well-known effect of the transport of acoustic energy by peg-leg multiples within thin layers is identical with this low-pass transmission response. 5. It follows that the high frequency energy is reflected back early in the seismogram. 6. By comparison, very low-frequencies are transmitted through the layered sequence easily and are reflected with difficulty. There is probably a lack of low-frequency energy in the reflection seismogram, by comparison with the spectrum of the incident plane wave. It follows that any meaningful evaluation of frequency-dependent absorption in seismic data cannot take place unless the frequency-dependent linear elastic effects are taken into account first.     

地震危险性估计的一种尝试

本文根据三角网统一平差和跨断层测量资料，利用位错理论的反演方法，计算了唐山和北京，怀来地区几条主要断层滑动速率和滑动方向，其结果与我们用有限元方法计算的断层应力场配套。并获得三点结果：（１）断层滑动速率大，则断层上庆力高，反之亦然；（２）断层滑动方向与断层应力场方向配套；（３）当跨断层短线大度年变化持续出现线笥关系时，断层浅部与深部滑动一致，而且断层浅部滑速率大，此却表示有发生地震的危险性。     

AN OPTIMIZED TECHNIQUE FOR DETERMINING STACKING VELOCITY FROM SEISMIC REFLECTION DATA*

A new method of estimating seismic stacking velocity from reflection seismograms is based on Fibonacci search technique and provides the highest rate of reduction of the interval of uncertainty of the stacking velocity. A review of the Fibonacci search strategy is presented, the application of the method is illustrated with synthetic and field examples.     

NON-LINEAR ESTIMATION OF REFLECTION COEFFICIENTS FROM SEISMIC DATA*

For years, reflection coefficients have been the main aim of traditional deconvolution methods for their significant informational content. A method to estimate seismic reflection coefficients has been derived by searching for their amplitude and their time positions without any other limitating assumption. The input data have to satisfy certain quality constraints like amplitude and almost zero phase noise—ghosts, reverberations, long period multiples, and diffracted waves should be rejected by traditional processing. The proposed algorithm minimizes a functional of the difference between the spectra of trace and reflectivity in the frequency domain. The estimation of reflection coefficients together with the consistent “wavelet’ is reached iteratively with a multidimensional Newton-Raphson technique. The residual error trace shows the behavior of the process. Several advantages are then obtainable from these reflection coefficients, like conversion to interval velocities with an optimum calibration either to the well logs or to the velocity analysis curves. The procedure can be applied for detailed stratigraphic interpretations or to improve the resolution of a conventional velocity analysis.     

大地电磁测深资料的联合反演研究

本文从大地电磁扬的色散关系出发,阐述了进行大地电磁资料一维联合反演的物理意义。论证了对于以色散关系相联系的一对大地电磁响应函数,特别是阻抗实部和虚部视电阻率进行联合反演的必要性和可能的应用前景。对比研究了大地电磁阻抗各单参量及其联合反演的效果。结果表明,在加快反演迭代速度,限定反演解的非唯一性、保证反演迭代的稳定进行等方面,联合反演比单参量反演具有明显的优越性;在大多数情况下,阻抗实部视电阻率和阻抗虚部视电阻率联合反演的效果要比通常所采用的常规视电阻率和阻抗相位的联合反演效果好。实际大地电磁资料的试验表明,各种不同平均阻抗的利用和综合反演解释将有助于获得更为可靠的结果。     

DETERMINATION OF LATERAL INHOMOGENEITIES IN REFLECTION SEISMICS BY INVERSION OF TRAVELTIME RESIDUALS*

Lateral inhomogeneities generate fluctuations in the traveltime of seismic waves. By evaluation of these traveltime fluctuations from different source and receiver positions, lateral inhomogeneities can be located using a pseudo inverse matrix method (Aki, Christoffersson and Husebye 1977). The formulation of the problem is possible for transmitted waves as well as for reflected and refracted waves. In reflection seismics this method is of importance, if no reflections from the inhomogeneities themselves, but only reflections from lower boundaries can be observed. The basic assumptions for the mathematical formulation are (1) the average velocities and depths of the reflecting horizons are known already from standard processing methods, and (2) the traveltime residuals are due to lateral velocity changes between different reflectors or between reflectors and the surface. The area of the earth to be considered is divided into layers and the layers into rectangular blocks. The parallel displacement of a ray after passing a disturbed block is neglected, only the traveltime residual is taken into account. In this paper the method and its application to data obtained with two-dimensional models are described.     

SOME REMARKS ON NOISE STABILITY IN DYNAMIC INVERSION OF REFLECTION SEISMIC DATA1

The dynamic inversion of reflection seismic data is investigated with reference to the influence of noise on pseudo-impedance logs. Model traces are calculated with 0, 5, 15 and 50% noise, respectively. In solving the inversion problem, the algorithm of Marquardt and Levenberg is used in connection with singular value decomposition (SVD). The results are within a 1% error range so that there was no visible change in the logs. Further signal analysis show that there is no dependence on the phase content of the wavelet used if all other parameters of the model are known.     

FULL WAVE EQUATION DOWNWARD CONTINUATION OF SEISMIC REFLECTION DATA*

A new method for suppressing multiple reflections in seismograms is developed. It is based on a downward continuation procedure which uses the full acoustic wave equation (hyperbolic form) as a downward continuation operator. We demonstrate that the downward continuation of the recorded wave field maps a reflectivity function without multiply reflected events. The method is applied successfully to individual traces of plane-wave decomposed (slant-stacked) synthetic and field data.     

利用联合反演技术进行反射地震的波速成象

本文介绍了根据反射地震数据进行波速成象的一种方法,其基础为多种反演技术的综合。由于要求的波速图象C（x,z）具有间断性,除利用走时数据T（x,t）外,在地层比较水平的情况下,还利用了均方根速度V（x,t）和统计子波W（t）的数据来成象。计算机层析成象过程分为三步:首先重做速度分析,取得与初次反射走时一致的均方根速度数据;然后用反射走时与均方根速度联合反演对应分析道的层速度和界面深度;最后由联合反演结果和反射面走时求波速图象函数的数字化版。文中还给出了波速成象方法在我国西北某沉积盆地上的应用及验证结果。     

INVERSION FROM FINITE OFFSET DATA AND THE SIMULTANEOUS RECONSTRUCTION OF THE VELOCITY AND DENSITY PROFILES*

Recursive inversion algorithms are described which facilitate (a) a direct inversion of a one-dimensional velocity distribution from finite offset data and (b) the related simultaneous reconstruction of a two-parameter, say velocity-density, medium. The suggested procedures are based on an extended format of the WKBJ-Bremmer scattering model. The attained accuracy levels and the limitations are highlighted by computer simulations against synthetic data.