PART I: THE SECTIONAL AUTO-CORRELOGRAM

The auto-correlation function of a seismic trace contains information on all the multiple reflection activity present in the trace. The interpretation of this information is facilitated by the arrangement of autocorrelation functions in cross-sectional form, in the manner of a normal record section. This is the concept of the Sectional Auto-Correlogram. Specifically, the Sectional Auto-Correlogram will… Show if the record section does not include significant multiples, thus allowing confident picking of the primary reflections. Show if the record section does include significant multiples, giving their travel times and inclinations (and, under certain circumstances, their reflection coefficients). Indicate by what process the multiples should be treated. Yield an authoritative measure of the success of a multiple-attenuating treatment. Delineate shallow horizons, even those whose primary reflections are too early to be recorded satisfactorily. Give the true travel time of a primary reflector, and the sign of its reflection coefficient. The Sectional Auto-Correlogram allows the study of primary reflectors by consideration of the multiples generated by them, and in this sense may be said to turn multiple reflections to advantage. Thus a primary reflection at a certain time is defined if we find that every reflection on the record is followed by a multiple after this certain time. Alternatively, a primary reflection at a certain time is defined if, after that certain time, we can find a repetition of the entire record. The Sectional Auto-Correlogram also has secondary uses in fault identification, crustal studies and weathering problems.     

CATCHMENT-WIDE, SECTIONAL AND LOCAL ASPECTS IN SEDIMENT TRANSPORT MODELLING AND MONITORING

1.INTRODUCTIONOVerthelastdecadesmuchprogresshasbeenmadeconcerningsedimenttransPOrtmodellingandmonitoring.Thedifferelltiationincatchmeflt-tvide,sectionalandlocalaspectsreflectsthefactthatmanysedimenttransportandpredictionmodelsaredealingwithspecialpartsofriverSystems,mainlydifferinginscale.Overthepastyears,scaleissuesinhydrologyhaverapidlyincreasedinimportance(BLoSCHL,1996).Onalargescaletheapplicationoffractals,self-similarityanalysistolandscapeorganizationandoptimalchannelnetlvorks(O…     

ON THE ORIGIN AND INTERPRETATION OF SELF-POTENTIAL ANOMALIES*

The renewed interest in the self-potential method of exploration for mineral deposits gives an understanding of the self-potential mechanism new importance. The cause of SP anomalies in general lies in the interference between simultaneously occurring nonequilibrium phenomena. However, theories of the mechanism of mineral SP anomalies generally relate the SP anomaly to the equilibrium potential of the chemical reaction supposed to occur on the ore body surface. In this paper, I reformulate these equilibrium mechanisms in terms of nonequilibrium thermodynamics. The result is that the SP anomaly depends not on the equilibrium potential alone, but also on the potential resulting from current transferred across the ore body—electrolyte interface. It is not possible to calculate the overpotential theoretically because of the number of complicating factors, and experimental data are not available. This does not imply that SP data are uninterpretable quantitatively. SP data may be interpreted similarly to other potential field data.     

VERTICAL HETEROGENEITY AND MOVEOUT IN THE ONE-DIMENSIONAL MEDIUM*

Since the important contributions of Dürbaum and Dix, 30 years ago, velocity profile estimation procedures on horizontally layered and vertically heterogeneous media from seismic probing data have been based largely on hyperbolic moveout models and RMS and stacking velocity concepts. Re-examination of the fundamentals reveals that quantitative velocity heterogeneity and canonical valocity profiles have been implicit factors for moveout modelling and for profile inversion in the use of the Dix procedure. Heterogeneity h is the ratio (and v_RMS the geometric or harmonic mean) of the path-average and time-average velocities for a raypath or, in a more restricted sense, for the normal ray belonging to a velocity profile. The canonical profile for a given velocity profile or profile segment is a moveout-equivalent monotonically increasing ramp-like profile. The ramp or constant gradient in depth is the simplest velocity profile approximator which can explicitly accommodate velocity heterogeneity. A ramp model structure is detailed which facilitates moveout simulation and model parameter estimation, and the parametric effects are explored. The horizontal offset range is quantified for which this model can give good moveout approximations.     

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.     

FIELD CONTINUATION AND THE STEP MODEL IN AEROMAGNETIC INTERPRETATION*

Downward continuation of the field in the neighborhood of a singularity of a magnetic anomaly is used to render the anomaly more two-dimensional, to make the bottom of the causal body more remote, and to obtain an auxiliary function, φ (O.z), by means of which the anomaly may be interpreted in terms of an equivalent vertical contact or step model. The concept of “apparent depth” is introduced and used in studying depth extent and susceptibility. The methods are illustrated with theoretical and practical examples.     

COMPUTER TECHNIQUES FOR THE ZONING AND CORRELATION OF WELL-LOGS*

This paper reviews computer techniques used in the automatic zoning and correlation of well-logs. Prior to correlating, well-logs are to be segmented–or ‘zoned’–so as to delineate sections that have similar properties. Techniques discussed include statistical methods such as variance tests and Student's t-test, linguistic analysis, the use of Walsh functions and spectral analysis. Well-log correlation, which may be between traces from different wells or between traces from the same hole (as in dip logs), is used in basin studies and the determination of structural dip. A variety of methods are reviewed including conventional time and frequency correlation, sequence slotting, pattern recognition and frequency analysis. Future directions for investigation are proposed.     

FIELD CONTINUATION AND THE STEP MODEL IN AEROMAGNETIC INTERPRETATION*

Downward continuation of the field in the neighborhood of a singularity of a magnetic anomaly is used to render the anomaly more two-dimensional, to make the bottom of the causal body more remote, and to obtain an auxiliary function, φ (O, z), by means of which the anomaly may be interpreted in terms of an equivalent vertical contact or step model. The concept of “apparent depth” is introduced and used in studying depth extent and susceptibility. The methods are illustrated with theoretical and practical examples.     

CONTINUOUS ANALYSIS OF THE VELOCITY FUNCTION AND OF THE MOVE OUT CORRECTIONS*

Several papers presented at the last SEG Convention in Houston by Schneider, Backus et al have shown how important and fruitful it was to obtain a continuous knowledge of the velocity functions and they have solved their problem by a Dynamic Correlation Analysis. Our purpose is to introduce here a method based on the best summation of a set of traces instead of the best correlation. Practically, this approach has several advantages: 1) Two traces only can be correlated at each step whereas the summation can bear on any number of them; 2) Optimizing the summation is actually what we are looking for since, at the long end, the success of the improvement is evaluated from the compositing of several traces either weighted or not. On the other hand, an advantage of correlation is the possibility of adding correlations obtained at several places in a same neighbourhood in order to improve the results. With the summation method this is feasible only when dips are inexistent: we shall see that the difficulty due to the dip effect can be turned around. The basic principle of the method can be summed up as follows: traces relating to a same reflection point are considered; several composites are made, each after applying different move out corrections ranging widely around an estimated adequate velocity function. At each time coordinate, the best adapted velocity function, i.e. the one that yields the best phase relation between reflected events, corresponds to the composite trace the average amplitude of which is the largest. This way, the velocity function corresponding to primary reflections as well as those corresponding to multiple reflections can be established accurately. Some examples are shown.     

TESTING THE TRANSIEL METHOD IN MINERAL AND GEOTHERMAL EXPLORATION*

Transiel is the name given to a qualitative, time domain induced polarization (IP) method. The aim of the method is twofold: to locate and to distinguish between deep and shallow polarizable media. This discrimination is based on the data analysis, which distinguishes Transiel from the conventional IP methods. Two case histories are presented: one related to mineral prospecting and the other to geothermal exploration. The information supplied by Transiel on the deep polarizable layers is checked at each test site by an independent inversion of the recorded transients. At the mineral test site, the method correctly predicts the target location. In this particular survey, the maximum penetration depth of the method is 700 m. At the geothermal test site, a fair correlation is found between IP anomalies and the productive wells. Since the method's penetration depth does not exceed 500 m, we believe that the observed IP anomalies are related to reduction phenomena occurring in the overburden and leading to pyrite formation. We suppose that these phenomena are caused by thermochemical exchanges between the reservoir and the overburden above zones of high reservoir permeability.     

THE AMPLITUDE AND PHASE RESPONSE OF A SEISMIC VIBRATOR*

The amplitude and phase response of a simple model is compared with the performance of a real vibrator working in the field. The field results show a characteristic phase response which confirms that the real drive force applied to the baseplate and its load impedance is faithfully represented by the acceleration of the reaction mass. It follows that all the parameters necessary to calculate the load impedance and the true power dissipated in the earth can be measured at the output of the vibrator. It also follows that the current method of baseplate phase compensation should be reconsidered.     

THEORETICAL AND EXPERIMENTAL APPROACHES TO THE GEOPHONE SPURIOUS FREQUENCY*

The geophone spurious frequency is modeled as the resonance of the planar motion of a spider spring carrying a moving mass. An analytic solution is found using the Castigliano method by assuming that the spring arm is a single-mode vibrating cantilever beam. The spring shape is found from this analysis. When the typical spring has a circumferentially varying cross-section, the Castigliano method is no longer applicable. A dimensional analysis is used as an approximate method for general design. Based on the theoretical result, a rotational fixture and a translational fixture were designed for experimental purposes. A low-noise fixture and a phase-averaging technique provide the amplitude and spurious resonance in the frequency domain. Finally, a test is run by using a rotational fixture to compare with the approximate method of spurious frequency prediction. Very good agreement between prediction and experiment is found.     

A METHOD TO DETERMINE THE VELOCITIES OF THE SEAFLOOR AND NEAR-SURFACE SEDIMENTS*

Shotpoint gathers from conventional reflection seismic surveys contain both reflected and refracted waves. In this study shot records were processed and analyzed, and the data were modeled with reflected, refracted, and reflected-refracted waves to fit the recorded data. The result is a detailed velocity model. The inverse problem for refracted waves was solved by using the Wiechert-Herglotz inversion. A 500-km-long 26-fold reflection seismic line from the Barents Sea, north of Norway, has been investigated. The data show high velocities, multiple reflections, and various types of noise. To test the method a total of 34 shot gathers were analyzed along this line. The aim of the interpretation was to determine the velocity in the seafloor and the near-surface sediments. It is possible to map the vertical as well as the lateral velocity distribution in detail. Depending on the length of the streamer and the velocity gradient in the sediments, the calculated depth varies between 300 and 500 m below the seafloor. These velocities were also compared to the stacking velocities obtained from the reflection seismic data to see how the velocities determined by different methods were related. The velocity distribution in the sediments is one of the key factors in seismic interpretation. The technique discussed in this paper can contribute to velocity information both in the processing and interpretation of seismic data.     

THE GRAVITY AND MAGNETIC FIELDS FROM ELLIPSOIDAL BODIES IN THE WAVENUMBER DOMAIN*

Wavenumber domain expressions for bodies with elliptical cross-section and of ellipsoidal shape have been developed both for homogeneous bodies and for certain bodies of density/magnetization varying linearly with depth or, more generally, according to a polynomial with depth. The simple expressions thus obtained lend themselves to an easy analysis, especially for long and short wavelengths. At the long-wavelength end of the spectra their decay is governed by an exponential with a decay “depth” equal to the depth to the center of mass. At the short-wavelength end this depth is replaced by the depth to the upper focus of the ellipsoid (or the elliptic cross-section). For vertically inhomogeneous ellipsoids the decay rate is also dependent on the product of the vertical gradient of density/magnetization and their semi-axes.     

SOME RELATIONS BETWEEN POTENTIAL FIELDS AND THE STRENGTH AND CENTER OF THEIR SOURCES*

From gravity it is well known how to determine the excess mass and the horizontal center of mass of the disturbing body. We show that a magnetic body—under rather weak assumptions—possesses excess magnetization and centers of magnetization (both horizontal and vertical), which can be uniquely determined from measurements. It also follows that the vertical center of mass can be uniquely determined from the vertical derivative of the gravity field.     

THE SPECTRAL FUNCTION OF A LAYERED SYSTEM AND THE DETERMINATION OF THE WAVEFORMS AT DEPTH*

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.