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- Volume 36, Issue 8, 1988
Geophysical Prospecting - Volume 36, Issue 8, 1988
Volume 36, Issue 8, 1988
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CHOOSING THE AVERAGING INTERVAL WHEN CALCULATING PRIMARY REFLECTION COEFFICIENTS FROM WELL LOGS1
Authors A. T. WALDEN and J. W. J. HOSKENAbstractMost seismic data is processed using a sample interval of 4 ms two‐way time (twt). The study of the statistical properties of primary reflection coefficients showed that the power spectrum of primaries can change noticeably when the logs are averaged over blocks of 0.5, 1 and 2 ms twt (block‐averaging). What is a suitable block‐averaging interval for producing broadband synthetics, and in particular how should the power spectrum of primaries be constructed when it is to be used to correct 4 ms sampled deconvolved seismic data for the effects of coloured primary reflectivity?
In this paper we show that for a typical sonic log, a block‐averaging interval of 1 ms twt should satisfy some important requirements. Firstly, it is demonstrated that if the reflection coefficients in an interval are not too large the effect of all the reflection impulses can be represented by another much sparser set at intervals of Δt twt, The coefficient amplitudes are given by the differences in the logarithmic acoustic impedances, thus justifying block‐averaging. However, a condition for this to hold up to the aliasing (Nyquist) frequency is that Δt takes a maximum value of about 1 ms twt. Secondly, an event on a log should be represented in the seismic data. For this the acoustic impedance contrast must have sufficient lateral extent or continuity. By making some tentative suggestions on the relation between continuity and bed‐thickness, a bed‐thickness requirement of 0.15 m or more is obtained. Combining this requirement with the maximum number of beds allowable in an interval in order that multiple reflections do not contribute significantly to the reflections in the interval, again suggests a value of about 1 ms for the block‐averaging interval.
With this in mind an experiment was performed on three sonic logs. The logs were block‐averaged at 1 ms, and primary reflection coefficients calculated. These primaries were then anti‐alias filtered and resampled to get a series of primaries at 4 ms, followed by ARMA spectrum fitting. The same logs were also block‐averaged at 4 ms directly and primaries computed, followed by ARMA spectrum fitting. In all three cases the first approach gave the ARM A model spectrum with greatest dynamic range, which strongly suggests that direct 4 ms block‐averaging introduces significant aliased energy into low frequencies of the primaries spectrum.
The conclusion is that routine computation of broadband synthetics (primaries only or primaries plus multiples) should be carried out using a block‐averaging interval of 1 ms twt, followed by anti‐alias filtering and thinning to the desired final sample interval. In theory it would be advantageous to go to even finer intervals‐say 0.5 ms‐but in practice at this level the averaging of slowness imposed by the somic logging tool appears to attenuate high‐wave number fluctuations, i.e. it interferes with the‘real’data. The 1ms choice is thus a reasonable compromise which will help minimize non‐trivial aliasing effects and should give better matches to the seismic data.
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MIGRATION OF MIXED‐MODE VSP WAVEFIELDS1
Authors P. B. DILLON, H. AHMED and T. ROBERTSABSTRACTTwo‐dimensional VSP surveys are often conducted to provide structural illumination of the subsurface away from the borehole. The illumination is achieved through offsetting the source with respect to the downhole geophone. This inevitably gives rise to mode‐conversions in both downgoing and upgoing wavefields.
Migration of mixed‐mode wavefields is complex because the velocity profile used for wavefield extrapolation is valid only for a particular propagation mode; the other mode always propagates at a different velocity. It is therefore advisable to separate the wave‐types (P‐wave and SV‐wave) prior to migration. This may be achieved through wavemode filtering, a multichannel process which exploits the relation between propagation velocity, slowness of events at the recording array and particle motion. The necessary information about particle motion is available only if the VSP data are acquired with a three‐component downhole geophone assembly.
The wavemode filter partitions wave‐types at the recording array; it provides no information about the various changes of propagation mode experienced by the energy as it travels from source to geophone. For the purpose of migration, the intermediate modes of propagation must be deduced.
Much of the energy arriving at the receivers is P‐wave which has followed the P‐wave velocity profile from the source. It can therefore be imaged by conventional (Kirchhoff) migration. As an example of SV‐wave imaging, a common mode‐code is P‐wave from source to reflector and SV‐wave from reflector to geophone. Migration of such data calls for back‐propagation of the geophone array wavefield, at SV‐wave velocity, to the point in the subsurface where it is time‐coincident with the forward propagated downwave, at P‐wave velocity.
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APPLICATION OF PETROPHYSICAL MEASUREMENTS TO THE PREDICTION OF SEISMIC RESPONSES OF DIFFERING LITHOLOGYOR PORE FLUIDS1
More LessABSTRACTDetermination of petrography and pore fluid content is an ultimate goal of an integrated seismic‐petrophysical study. For lack of a general inversion technique, forward modelling is useful in studying the relations between lithology, stratigraphy, pore fluid content and the seismic response. This report describes a study of two clastic sequences in Utah, from which 32 rock samples were analysed. A detailed petrographic study was done. Laboratory measurements were made of ultrasonic compressional‐ and shear‐wave velocity as a function of pressure. We computed the velocities at seismic frequencies for the samples when dry, over‐pressured, brine saturated, and oil saturated. The velocities were sensitive to the porosity, carbonate cementation and the depositional facies. We generated velocity profiles for hypothetical reservoirs for a range of saturation states. The velocity profiles were used to generate synthetic seismic shot gathers to study the seismic response of these clastic reservoirs. The fluid‐saturation strongly affects the seismic respone, as does the presence of a coal seam. An amplitude change with offset is often observed. However, stratigraphy appears to have a stronger effect on the seismic response.
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TIME‐DOMAIN COMPUTATION OF NON‐NORMAL INCIDENCE WAVEFIELDS IN PLANE LAYERED MEDIA1
By R.‐G. FERBERABSTRACTA new time‐domain method is introduced for the calculation of theoretical seismograms which include frequency dependent effects like absorption. To incorporate these effects the reflection and transmission coefficients become convolutionary operators. The method is based on the communication theory approach and is applicable to non‐normal incidence plane waves in flat layered elastic media. Wave propagation is simulated by tracking the wave amplitudes through a storage vector inside the computer memory representing a Goupillaud earth model discretized by equal vertical transit times. Arbitrary numbers of sources and receivers can be placed at arbitrary depth positions, while the computational effort is independent of that number. Therefore, the computation of a whole plane‐wave vertical seismic profile is possible with no extra effort compared to the computation of the surface seismogram. The new method can be used as an aid to the interpretation of plane‐wave decomposed reflection data where the whole synthetic vertical seismic profile readily gives the interpreter the correct depth position of reflection events.
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BAYESIAN ESTIMATION IN SEISMIC INVERSION. PART I: PRINCIPLES1
More LessABSTRACTThis paper gives a review of Bayesian parameter estimation. The Bayesian approach is fundamental and applicable to all kinds of inverse problems. Its basic formulation is probabilistic. Information from data is combined with a priori information on model parameters. The result is called the a posteriori probability density function and it is the solution to the inverse problem. In practice an estimate of the parameters is obtained by taking its maximum. Well‐known estimation procedures like least‐squares inversion or l1 norm inversion result, depending on the type of noise and a priori information given. Due to the a priori information the maximum will be unique and the estimation procedures will be stable except (in theory) for the most pathological problems which are very unlikely to occur in practice. The approach of Tarantola and Valette can be derived within classical probability theory.
The Bayesian approach allows a full resolution and uncertainty analysis which is discussed in Part II of the paper.
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BAYESIAN ESTIMATION IN SEISMIC INVERSION. PART II: UNCERTAINTY ANALYSIS1
More LessABSTRACTA parameter estimation or inversion procedure is incomplete without an analysis of uncertainties in the results. In the fundamental approach of Bayesian parameter estimation, discussed in Part I of this paper, the a posteriori probability density function (pdf) is the solution to the inverse problem. It is the product of the a priori pdf, containing a priori information on the parameters, and the likelihood function, which represents the information from the data. The maximum of the a posteriori pdf is usually taken as a point estimate of the parameters. The shape of this pdf, however, gives the full picture of uncertainty in the parameters. Uncertainty analysis is strictly a problem of information reduction. This can be achieved in several stages. Standard deviations can be computed as overall uncertainty measures of the parameters, when the shape of the a posteriori pdf is not too far from Gaussian. Covariance and related matrices give more detailed information. An eigenvalue or principle component analysis allows the inspection of essential linear combinations of the parameters.
The relative contributions of a priori information and data to the solution can be elegantly studied. Results in this paper are especially worked out for the non‐linear Gaussian case. Comparisons with other approaches are given. The procedures are illustrated with a simple two‐parameter inverse problem.
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THE DETECTION OF BURIED PLACER DEPOSITS BY GROUND MAGNETIC SURVEY1
Authors E. J. SCHWARZ and N. WRIGHTABSTRACTA method is proposed to detect buried magnetite concentrations within river sediments. Model studies show that relatively small (thickness 1 m, width 10 m) plate‐shaped volumes with magnetite contents of 0.5% within a non‐magnetic matrix can be detected by a detailed ground magnetic survey using a sensitive (0.1 nT) magnetometer. Tests along lines perpendicular to the river but at a different angle to the bedrock trend (or the aeromagnetic anomaly trend) reveal that essentially all total field and vertical’gradient’anomalies detected in the profiles are elongated in the river and/or valley direction. This shows that the anomaly sources are (buried) volumes of higher magnetite content within the river sediments. Further evidence for this is (1) that higher intensity total field and vertical’gradient’anomalies occur in an area where the river cuts through strongly magnetic serpentinites, (2) the absence of high frequency anomalies over unsorted glacial till, and (3) some features on power spectra. Relatively large volumes of high magnetite concentrations within the river sediments may well contain the highest concentration of heavy economic minerals such as gold. Consequently, the areas of greatest interest in the exploitation of buried placers may be selected from maps obtained by detailed magnetic surveys either on the ground or at low altitude by helicopter.
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A GYRO‐ORIENTED 3‐COMPONENT BOREHOLE MAGNETOMETER FOR MINERAL PROSPECTING, WITH EXAMPLES OF ITS APPLICATION1
Authors W. BOSUM, D. EBERLE and H.‐J. REHLIABSTRACTA triple axis borehole magnetometer is described that consists of a Förster‐probe (fluxgate) triplet (sensitivity 1 n T), a Förster‐probe gradiometer (sensitivity 2 nT/40 cm), a gyro unit (mean angular drift approx. 0.5°/h) which is equipped with accelerometers (sensitivity 1/100°), and a data transmission unit (with multiplexer and 16‐bit AD converter). The sensitive fluxgate‐magnetometer can detect weakly magnetic or small source bodies. Data from the gyro and the accelerometers allow the 3‐component magnetic field values to be transformed to north, east and vertical components. Since they do not rely on magnetically‐determined directional data, the results are not disturbed by local anomalies of the magnetic declination. Furthermore, the magnetometer can also be used in vertical boreholes. 3‐component measurements are carried out at discrete points in the neighbourhood of a source body to locate its position, and within the source body to determine the direction of magnetization. The strength of magnetization and information on magnetic classification are obtained by continuous measurement of one or more components within the source body. Calculation algorithms and computer programs are available to simplify data processing and interpretation. Survey examples are discussed.
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INTERPRETATION OF RESISTIVITY MEASUREMENTS OVER 2D STRUCTURES1
More LessABSTRACTResistivity measurements were carried out in a survey area in the south of Germany. This area is characterized by complicated subsurface geology. Schlumberger full‐arrays and their respective half‐arrays were recorded simultaneously. The results obtained by the one‐dimensional (1D) interpretation of the full‐array measurements were incorrect because of a resistivity discontinuity. This discontinuity, under a relatively thick overburden, could only be located by the half‐array soundings. Its exact location and the resistivity distribution in the subsurface were ascertained by comparing the sounding curves with 2D model curves, which are calculated by a finite‐difference method.
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TRANSIENT EM ANALOGUE MODELLING FOR KOREAN TREASURE HUNTING WITH THE SIROTEM SYSTEM1
Authors SANG KYU LEE and G. BUSELLIABSTRACTThe inductive transient electromagnetic method (TEM) shows good potential for the detection of metallic relics of historical interest, such as buried antique bells, Buddhist idols, or precious metal nuggets. The effectiveness of the method was investigated with analogue models, using transmitter‐receiver loop configurations with sizes or receiver spacings slightly different from those usually applied in earth resources exploration with the Sirotem system.
The analogue modelling results show that the location and depth of the buried treasure may be obtained from the Sirotem data. A solid metallic object such as an antique bell could be detected to a depth about 12 times greater than its size, and treasure consisting of separate metallic objects, such as gold nuggets, could be detected to a depth 5 times its linear dimensions with a transmitter current of ˜ 20 A.
In scaling down the dimensions of a target, its conductivity should be increased in order to preserve the same TEM conditions found in the field. However, since the buried treasure consists of gold or copper objects, it is not possible to properly scale the conductivity. Hence, in the field, the depth detection limit is expected to be greater than that derived from analogue modelling.
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