Datum Plane Research Articles

Trend-surface analysis as an aid in exploration for Mississippi valley-type ore deposits

An examination of the characteristics of Mississippi Valley-type ore deposits shows that these deposits have many similarities which appear to be structurally controlled. To define the relationship between the ore deposits and these structural conditions, trend-surface analysis using the Precambrian surface as the datum plane was performed within the general Missouri area. Examination of the residual maps prepared from this analysis shows that all the ore deposits have the same spatial relationship to areas of strong residual highs. A more detailed study was conducted in the area of the Viburnum Trend using a datum plane just below the ore horizon. The spatial relationship shown on the Precambrian residual map was even better defined in this study. From this study, it appears that the optimum structural conditions necessary for the deposition of Mississippi Valley-type ore deposits exist in regions located next to and slightly downgradient from areas which exceed one positive standard deviation from the trend surface. The methods described in this paper could comprise an extremely useful tool in exploration programs as they can define high probability locations in which to concentrate further exploration efforts.

PATTERNS FROM LAND ALIENATION MAPS∗

Land entry and land patent data available in the original Land Office Tract Books and in the Numerical Index provide a seldom used datum plane for geographical investigation which is useful in developing the historical settlement geography of a region. Patterns of entries and patents in the Nebraska Sand Hills reflect restrictions imposed on man by the environment, the process of sequential settlement, abandoned geographical features, and other patterns which establish a conceptual base for further research. The maps provide insights that may be used to explain some aspect of the settlement process.

GRAVITY COMPUTATIONS BY FLUX DENSITY SUMMATIONS*

AbstractGravity profiles can be computed by summing flux lines uniformly radiating from source elements within a density distribution. Digital computations are performed efficiently, irregular density distributions modeled, and alterations easily made to the model to alter the profile by recomputation of only the altered elements. The concept applies to both two‐ and three‐dimensional models and the corresponding datum plane contours. Two‐dimensional computations are described and illustrated.

Palaeomagnetism and the Globorotalia truncatulinoides Datum in the Tasman Sea and Southern Ocean: Reply

DR THEYER replies: Watkins, Kennett and Vella's critique1 requires further discussion on a baffling stratigraphic problem occurring in the far South-east Indian Ocean. In that area, Globorotalia truncatulinoides overlaps with distinctive late Miocene-Pliocene foraminifers and radiolarians in at least twelve widely separated piston cores2,3. To explain an overlap of such magnitude and stratigraphic consistency by invoking simple reworking seemed unreasonable to me and I therefore proposed a mid-Pliocene (Gauss) G. truncatulinoides datum plane for this area2. There are, of course, alternative interpretations. One can assume, for example, that the region is affected by an extensive Brunhes-Gauss disconformity (representing a removal of mostly Matuyama sediments) and that some mixing of Brunhes and Gauss sediments has occurred above and below the hiatus. This explanation is compatible with a Quaternary range of G. truncatulinoides, which now seems established (J. P. Kennett, personal communication) for at least parts of the present area and would agree with the early Pliocene evolutionary sequence of the radiolarian Lamprocyclas heteroporos4 which occurs in the Gilbert sections of cores E39-40, E39-48 and E39-56 (ref. 3). It would also be in keeping with the 230Th dates in E39-40 (ref. 3) and the internal consistency of all important radiolarian and foraminiferal ranges in the cores. Finally, it would agree with previous work in this area which describes an erosional disconformity of predominantly Gauss age3,5. This alternative explanation is now being tested with additional palaeomagnetic work, 230Th analyses and study of nannofossils. I recognize that my original interpretation, which at the time of its composition seemed adequately substantiated by my findings2,3, is only one of other possible explanations and may even be wrong. Watkins, Kennett and Vella1, however, do not really question my interpretation as such, but attempt to invalidate it by discrediting my palaeomagnetic measurements and faunal identifications.

Radiolarian Definition and Paleoecology of Late Miocene to Early Pliocene in Southern California: ABSTRACT

The late Miocene to early Pliocene appears to be well represented by radiolarian faunas in formations in southern California. From radiolarian biostratigraphic studies in southern California the writers suggest that the base of the Mohnian (as represented by the section at Newport Bay) is equivalent to the base of the Ommatartus antepenultimus Zone of Riedel and Sanfilippo, and the top of Delmontian (as represented by the Malaga Mudstone at Malaga Cove) is within the Pterocanium prismatium Zone of these same writers. The uppermost occurrences of Prunopyle titan, Lychnocanium grande and Theocyrtis redondoensis and the lowermost occurrence of Lamprocyclas heteroporos occur relatively close together and represent the Miocene-Pliocene transition in the Malaga Cove section. Th most reliable datum plane for the Miocene-Pliocene boundary in southern California might be the lowermost occurrence of Lamprocyclas heteroporos, for this appears to be an evolutionary event. From radiolarian paleoecologic studies in southern California we suggest that the late Miocene to early Pliocene was a period of paleotemperature fluctuation with sea surface temperatures fluctuating as much as 10°C. The radiolarian diversities also fluctuated during this same period with a general trend toward a diversity decrease upsection. There were differential (selective) radiolarian extinctions during this same period in that shallow water (epipelagic) forms appear to be more severely affected than deep or tropical submergent forms. End_of_Article - Last_Page 431------------

A technique for measuring the flatness errors of machined surfaces

Geometrical features of a simple tilting platform for datum-plane adjustment are described. A method is suggested whereby this platform can be used in conjunction with a rotary table to establish a datum plane for the upper surface of an object placed on the platform. With the aid of a standard Talylin true flatness deviations can be measured simply and directly. The accuracy of the technique is verified using an optical flat.

On: “Reduction of Unevenly Spaced Potential Field Data to a Horizontal Plane by Means of Finite Harmonic Series” by Roland G. Henderson and Lindrith Cordell (GEOPHYSICS, October 1971, p. 856–866)

The authors recommend on page 864, that their technique for correcting for anomalous vertical gradients in the gravity field be applied only in “cases where high topographic relief produces large corrections to the station Bouguer anomaly.” The correction applied by the authors amounts to the continuation of the observed gravity field onto a single‐elevation plane from the varying elevations of the observation points. The authors should therefore caution the reader against choosing the datum plane such that the gravity field is continued through sources of interest lying above the datum plane—an easily made mistake in areas of high topographic relief.

Time-Transgressive Aspects of Some Critical Planktonic Species: ABSTRACT

The origin of Globigerina bulloides in temperate areas occurs in the middle Miocene in Neogene zones 9 or 10, whereas in tropical sections it appears in the upper Miocene in Neogene zones 16 or 17, a cool-water cycle. In both cases it could be represented as being derived from Globigerina praebulloides. The origin of the temperate Globorotalia (Turborotalia) pachyderma, dextrally coiled, occurs in Neogene zone 13 or just below in temperate areas, whereas it invaded subtropical areas only during the principal cold cycles subsequent to deposition of zone 13. Forms of Neogloboquadrina lacking umbilical toothlike structures such as N. dutertrei subcretacea appeared in tropical and warm temperate areas in the late Miocene. Neogloboquadrina dutertrei dutertrei with umbilical toothlike structures appeared near the end of Pliocene or at the beginning of Pleistocene time in Neogene zone 22 in tropical areas, whereas the primitive forms continued into the Holocene in temperate areas. Thus, there is an apparent extinction datum plane of the primitive form near the end of Neogene zone 21 deposition in tropical areas but not in temperate areas. Coiling characteristics and form ratios distinguish this group from Globorotalia (Turborotalia) pachyderma. Praeorbulina spp. appear initially in the lower Miocene Neogene zone 8 in tropical areas; isomorphs of this genus appear initially in temperate areas in Neogene zones 11 or 12. The earlier forms originated from species of Globigerinoides whereas those in temperate areas appear to have originated from Globigerina. Ecologic-evolutionary relations are responsible for these and many other kinds of time-transgressive aspects of planktonic datum planes. End_of_Article - Last_Page 330------------

EFFECT OF LONG PERIOD WAVES ON HYDROGRAPHIC SURVEYS

In conjunction with routine hydrographic surveys at Santa Cruz Harbor, California, bottom elevation discrepancies were observed which were not associated with positional errors It was suspected that these errors were associated with long period wave activity, common at this particular location on the Pacific Coast The existing practice for obtaining hydrographic soundings is by use of floating craft using either echo sounding techniques or a "lead line " Both of the above techniques utilize the instantaneous water surface at the survey boat as a datum reference Normally the water surface elevation is determined by use of a water level recorder Based on the analysis of 50 repetitions of a well monumented cross section in Santa Cruz Harbor, it was concluded that long period waves affect the results of hydrographic surveys by slowly varying the datum plane In the case of Santa Cruz Harbor, the maximum error due to this effect would be about +15 feet.

Photogrammetric measurements of dynamic displacements

The feasibility of the determination of the patterns of vibrations of a plate by means of stereophotogrammetric methods was established. A square plate, free on all edges, was vibrated in resonance at the first three observable modes and simultaneously photographed by a pair of cameras by means of a rapid-flash tube. Chladni figures were used to establish a datum plane, and measurements on the pair of photographs were used to compute displacements on a set of grid intersections scribed on the plate.

A GENERALIZED FORM OF NETTLETON'S DENSITY DETERMINATION*

ABSTRACTThe formula for the Bouguer anomaly contains the density of the masses above the datum plane. If we use a wrong value for the density we obtain on the Bouguer map additional anomalies which coincide with the topographic features.If we do not know the Bouguer density we can compute several Bouguer maps based on different arbitrary densities. Then we select that map which shows the least correlation with the topography and obtain in this way a reasonable value for the density. This method has been found by Nettleton.Several authors have formulated this process mathematically and have elaborated numerical methods. This paper will present such a method. It differs from the former methods by the following: A general formula for the Bouguer density is presented, using a non‐specified linear operator. By choosing special definition for this operator, we can obtain the formulae of several of the known methods. It is shown that the determination of the density by “Nettleton Profiles” gives less reliable results than the statistical investigation of the whole area covered by the gravity survey. The known methods do not consider the variations of the vertical gradient. It is shown that in areas with a regional gravity anomaly or an extended topographic feature the known methods yield poor results. It is shown that the vertical gradient of gravity used as operator gives a most exact and simple formula. It is shown how the electronic computer—after reading the Bouguer values based on an arbitrary initial density—can compute the residuals, derivatives etc., which are based on the corrected Bouguer density.

SUR LA DEFINITION DE L'ANOMALIE DE BOUGUER ET SES CONSEQUENCES PRATIQUES*

ABSTRACTWhen interpreting Bouguer Anomalies, it is important that the location of the point to which the corrected measurement is related, is correctly defined: the station itself or its projection on the datum plane. The consequences of this choice are not negligeable when the topography is rough.

Contour Map of the Waves

We have decided to draw a contour map of the waves on the other from National Disaster Prevention Scientific and Technical Center. We photographed the waves in following two ways from planes simultaneously, with the cameras equipped with synchronous shutter mechanism.1. Successive stereophotographs are taken, so that the sea shore and oil towers in the sea can be imaged in a stereomodel and some reference points can be furnished for the facilities of the absolute orientations and the plotting works.2. Under a basis of stereoscopic Observation, successive stereophotographs are taken so that a datum plane of 0m can be found by the numerical method and then the wave map can be plotted.

Loess in the Manawatu district, New Zealand

Abstract Loess covers most of the terrace and rolling lands of the Manawatu district. A volcanic ash, the Aokautere Ash, interbedded in the loess provides a datum plane that allows measurement of thickness of the loess that accumulated after the ash was erupted. This increases from about 2 ft at a distance from the two main rivers to about 10 ft on their south-eastern banks. The loess coarsens with increasing thickness and most of it is thought to have been blown from the river beds by the prevailing north-westerly winds. It was probably accumulating rapidly when the ash was erupted, and continued accumulating until shortly after the formation of the Ohakea Terrace. The width of bare river beds would have been at a maximum during the aggradational phase that culminated in the formation of the Ohakea Terrace, and the bulk of the loess probably accumulated then. This phase started about 20,000 years ago and ended about 10,000 years ago. The differences in soils on the loess in areas of similar climate are attributed to differences in grain size of the loess and to soil development that took place while the loess was accumulating; this would be more effective where the loess accumulated slowly than where it accumulated rapidly. To the north of the Manawatu district, differences in the soils are due to an increasing proportion of fine volcanic ash in the loess as well as to an increase in rainfall.

SEISMIC DATUM CONSTRUCTION IN AREAS OF RUGGED TOPOGRAPHY

One of the steps in the reduction of seismic data is the correction for variations in surface elevation. This requires the adoption of a common reference surface, usually known as the seismic datum, but also referred to as the floating datum, the undulated or warped datum, or the datum plane. Ideally, the seismic datum should parallel the velocity layers, and in that sense it is an isovelocity surface; in practice, the datum is more often a surface of convenience. In its simplest form, the datum is a horizontal plane, but commonly it is undulated to conform to the generalized topography. While the warping of a datum surface serves to simplify and minimize the elevation corrections, it is usually done in the knowledge that the isovelocity surfaces are often similarly undulated. Such undulations of the velocity layers are generally attributed to the variations in loading caused by the irregularity of the ground surface. In an attempt to develop an objective means of constructing a satisfactory universal seismic datum, a zone chart was designed, similar to the terrain‐correction zone chart employed in gravity reductions. The compartmented transparent disk, superimposed on a topographic map and centered over the shotpoint, permits the calculation of a properly weighted, or “normalized,” elevation which serves as the basis for the undulated seismic datum. Tests of the resulting datum indicate that it will normally compensate adequately for velocity variations due to topographic loading and, consequently, insure a more accurate interpretation of the seismic data.

Diffused light interferometry for measurement of isopachics

A simplified optical method, based on interference phenomena of diffused light, is described for the determination of isopachic patterns. The procedure consists in using a monochromatic diffused light beam to illuminate the model surface. If an optically flat glass plate, used as datum plane, is brought in contact with the model front surface an interference pattern is produced related to the thickness of the air-film between the datum plane and the surface of the model. Interference patterns before and after loading of the specimen allow the determination of isopachics. Curves of variation of interference fringes throughout the surface of the specimen, before their use for the determination of thickness variation, must be readjusted in convenient scale as well as for the elimination of superimposed simple interference patterns due to arbitrary inclination of the datum optical plane before and after loading. The method does not necessitate a complicated equipment. It is straightforward and very sensitive. It can be applied to transparent as well as to opaque models made of metal sheets. It can also be used as a supplementary means to measure thickness-strains in the birefringent coating method. The surface of the model though polished could not be obligatorily optically flat. The method was applied to several illustrative examples with transparent and opaque models. The results obtained are in good agreement with those yielded by theoretical or other experi- mental solutions.

WELL SURVEYS AND THE CALIBRATION OF VELOCITY LOGS*

AbstractIn the last two years several double‐receiver Velocity Logs (V‐Logs) have come into service. Theoretically, in this type of log the effect of the travel time in the mud and in the invaded or altered formations, responsible for the “Lag” (or delay times) in single receiver V‐Logs, could be eliminated. Thus the integration of the interval times would give the “real” vertical time as a function of depth. In practice, several authors have already noted that even for V‐logs with two receivers the integrated times differ from the results of the conventional well surveys.We consider here some of the geometrical, geological and instrumental factors that affect the time measurement of double receiver Velocity Logs, as well as the possibility that the discrepancy between the V‐logs and the conventional well survey could in some cases be due to faults, dip, folding, or the intrusion of high velocity layers near the well. Some examples are given, and the question of the polarity of first arrivals in well surveys is discussed.At present the discrepancies between the integrated times of even double receiver V‐Logs and the results of the well surveys remain too great to permit us the economy of eliminating the well survey. Furthermore, for the study of these discrepancies we must continue to shoot a considerable number of calibration points. We have, however, succeeded in reducing greatly the cost of the conventional survey by reorganising our well shooting methods. These methods, as well as the problems of surface corrections and the choice of datum plane they entail, are discussed.

PRINZIPIELLE BEMERKUNGEN ZU THEORIE UND PRAXIS DER METHODE DER ZWEITEN ABLEITUNG BEI DER INTERPRETATION GRAVIMETRISCHER MESSERGEBNISSE

ABSTRACTThe first part of the paper deals with theoretical considerations concerning the arithmetic mean of gravity values and its use with regard to the derivation of approximation formulae for the second derivative. In order to calculate the second derivative in practice the arithmetic mean. ḡ(r) of a continuum of gravity values on a circle of radius r is approximated by a Taylor polynomial and then replaced by the arithmetic mean gn(r) of n discrete gravity values. Because of the invariance of ġ(r) with regard to rotations of the coordinate system in the horizontal datum plane there exists a lower limit for the number n; this lower limit depends on the degree of the Taylor polynomial used in the formula for gzz.The general results of the first part yield routine formulae for the special case of a regular hexagonal grid; these formulae are given and discussed in the second part of the paper. Three formulae are applied to the gravity data of the Los Angeles Basin. Some remarks concerning the comparability of different approximation formulae and some hints with regard to routine calculations conclude the paper.

A NEW METHOD FOR INTERPRETATION OF AEROMAGNETIC MAPS: PSEUDO‐GRAVIMETRIC ANOMALIES

The purpose of this paper is to describe a method of interpretation based on a transformation of the total magnetic intensity anomalies into simpler anomalies. The result of this transformation is the elimination of the distortion due to the obliquity of the normal magnetic field, so that the resulting anomalies will be located on the vertical of the disturbing magnetized bodies. The starting point of the theory is the well known relation between magnetic potential V and Newtonian potential U—relation which can be written: [Formula: see text] with: [Formula: see text] = magnetization, f = 66.7×10−9 u ⋅CGS, σ = assumed density of magnetized bodies. This relation may be considered as a partial differential equation. The boundary condition consists in the measured values of the total field T(P ) known at each point P at the datum plane. As T(P) is the derivative of a harmonic function V, we can determine this function everywhere above the datum plane. Solving then the partial differential equation, we find the Newtonian potential U and its vertical derivatives g, g′, g″⋯. Finally, we obtain these quantities as functionals of the measured magnetic anomaly T(P). For instance, one of the formula is [Formula: see text] where H(M, P) is the kernel of the transformation allowing the direct computation of g(M)—an anomalous field which will be called “pseudo‐gravimetric anomaly.” Of course, the pseudo‐gravimetric anomaly has all the usual properties of a gravimetric anomaly. The field of g(M) presents no distortion and the interpretation becomes as easy as that of a Bouguer anomaly map. To perform the actual routine calculations of this transformation, we start with the values of T taken on a rectangular or trigonal grid, as for the usual computation of the vertical derivatives. The use of punched‐card equipment speeds up considerably these calculations.

Modern Aircraft Geometry

THE determination of the shape and position of the various constructional elements in an aircraft must be based on principles different from those used in the case of an ordinary machine such as, for example, a lathe. In the latter case, the position of the parts in relation to each other can be given by measurements to existing plane base surfaces and centre lines. In aircraft work, on the other hand, where such base surfaces and centre lines are lacking, an attempt was made from the beginning to work with certain imaginary base planes named according to their position in the aircraft, such as datum plane, plane of symmetry, wing datum plane, and so on. This was unsatisfactory, however, and now the conception of co‐ordinates forms the basis for dimensioning.