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Semiquantitative interpretation of data from airborne radioactivity surveying requires detailed knowledge of scattered gamma-ray intensity at considerable air distances from natural thick uranium sources. Based on the concept of an elementary source of infinite thickness rather than a conventional point source, empirical expressions, which are of the form dictated by theory, are developed for measured gamma-ray intensities from two extreme types of natural uranium sources, the elementary and the broad source. Computation, based on published solutions of the Boltzmann equation for gamma-ray transport in one medium, is in agreement with experimental measurements. The calculated value for primary, scattered, and total intensities from thick uranium sources show that at considerable air distances the scattered intensities are more than half of the total intensity for energies above 0.4 Mev and become much more than half as the lower limit of detector energy response is decreased below 0.4 Mev. From the expression for the gamma-ray intensity of elementary source, gammaray intensities from idealized sources, selected to approximate most nearly naturally occurring sources, have been computed. All computations are based on the assumptions of quarter-mile flight line spacing, and flight path at 500 feet above ground at atmospheric pressure. The computed data are strictly valid only for these conditions of airborne radioactivity surveying and for scintillation detectors of essentially identical spectral energy response. The intensities and areas under the curve that would be recorded by a countingrate meter have been computed for selected source types, the elementary, the finite, the slab, the line, and the broad source. The peak intensity and the area under the curve are the two interrelated observable quantities most useful for interpretation. The shape of recorded anomalies as shown by analysis of experimental and computed data cannot be used for interpreting grade-area and (or) grade of natural sources although shape is useful in determining source type. In interpreting anomalies, 4 of the 5 source types can be distinguished by the appearance of an anomaly, either on one or on two or more adjacent flight lines; one type, the broad source, can be readily distinguished by flattening of the anomaly on adjacent flight lines. With source type identified, the grade-area and (or) grade of a natural source can be determined from tabulated data for the two observable quantities, the peak intensity and the area under the curve. The accuracy of interpretation of grade of broad and slab sources has been confirmed by field investigations; the interpretation of grade-area and (or) grade of 1 2 EXPERIMENTAL AND THEORETICAL GEOPHYSICS finite and elementary sources, particularly those visible on only one flight line, is difficult and is satisfactory only within an order of magnitude. The method of interpretation, based on a semiempirical approach, is applicable to measurements made with scintillation detectors of broad spectral energy response. For other than essentially identical radiation detection instruments, the necessary constants which specify the buildup factor for any specific detector can be established by empirical tests of the response to known thick uranium sources. INTRODUCTION Airborne radioactivity surveying is now widely and successfully used, primarily to prospect for uranium. In the majority of airborne surveys the sought-for target is a radioactivity anomaly, a sharp local increase in radiation intensity. Data on anomalies are usually reported on a qualitative basis (Stead, 1955). To advance airborne surveying from the qualitative to the semiquantitative estimation of natural-source parameters,, a greater knowledge of air-scattered gamma-ray intensity at considerable air distances from naturally occurring thick uranium sources is necessary. The scope of the knowledge must be such that for any specific instrument of gamma-ray detection and measurement the observable data for a given anomaly, such as the peak intensity, the area under the curve, and the shape of the curve, can be correlated with the principal characteristics of a natural source, namely the strengh in terms of the equivalent uranium oxide content and the configuration in terms of the surface dimensions. Inasmuch as naturally occurring sources are usually poorly defined in area and composition, and the radiation effects are obscured by surrounding sources, a purely empirical study would present great difficulties in determining the salient features of the radiation intensity from a given source type. It therefore seems more practicable to investigate numerically and analytically the features of certain simple source types, never found in nature, but nevertheless covering the entire range of variation in shape and size found in natural sources. The following sequence of action presents itself: Determination of the radiation intensity, theoretically or experimentally, from an elementary source from which other sources can be constructed. Determination of the radiation intensity from simple sources by distribution of the elementary source over suitable geometrical configurations. Investigation of the relationship between the source characteristics, such as size, grade, shape, and the observable data such as peak intensity reading and area under the counting-rate meter curve for several sources to establish criteria for distinguishing the different source types. SCATTERED GAMMA RATS FROM THICK TJRANTUM SOURCES 3 Relation of source characteristic directly to the observable data without reference to (unknown) distance, with the criteria for distinguishing source types established. Reduction of information gained in the previous steps to a simple recipe suitable for actual field applications. This report is devoted primarily to the establishment of the expression for the elementary-source intensity, to a comparison of experimental results with existing theoretical knowledge, and to the effect on the apparent peak intensity of the finite cone of response and resolving time of a counting-rate meter. Characteristics of selected source types are established and a possible mode of interpreting airborne radioactivity measurements in terms of natural-source parameters is outlined. ACKNOWLEDGMENTS The writer is deeply grateful to L. V. Spencer, of the National Bureau of Standards, for a long enlightening discussion on the nature of gamma-ray scattering and on the format and contents of the paper. The section entitled "Comparison with theory" was inserted upon his suggestion. The writer is also grateful to F. J. Davis, of Oak Ridge National Laboratory, who compiled most of the data and to R. H. Ritchie, of Oak Ridge National Laboratory for many fruitful discussions. He is indebted to N. Lazar of Oak Ridge National Laboratory for determining the equilibrium spectrum of uranium. The work herein reported is part of an investigation carried on by the U. S. Geological Survey on behalf of the Division of Research of the U. S. Atomic Energy Commission. GAMMA-RAT INTENSITY FROM ELEMENTARY AND BROAD SOURCES DETERMINATION OF EMPIRICAL RELATIONS As the fundamental properties of gamma radiation are well known for the energy range observed in natural sources, the ideal method of interpretation would be based on theoretical computation of the radiation intensity emanating from several sources, by solving the Boltzmann equation for gamma-ray transport in two-media. This solution, in general, is a function of three space variables, two angular variables and an energy variable. The advantage of the computational approach is that the results do not have to be resolved in terms of the response characteristics of a particular detector, and that the response of any detector, if its spectral and angular characteristics are known, can be computed. No satisfactory solutions to the general two-media problems have yet been published, although the U. S. Geological Survey and the Atomic Energy Commission Computing Facility at New York University are now engaged in solving the two-media 428734 57 2 4 EXPERIMENTAL AND THEORETICAL GEOPHYSICS problems with plane symmetry. However, Fano (1953a, 1953b) and Spencer and Fano (1951) have made extensive analytical studies, and a vast quantity of numerical solutions to one-medium problems in plane and spherical geometry exists (Goldstein and Wilkins 1954), from which one may predict trends of solutions in two-media problems. Moreover, for moderate energy gamma rays, two-media problems with plane symmetry can be reduced to equivalent one-medium problems. The general procedure for solving the Boltzmann equation was developed by Spencer and Fano. A topical summary and pertinent bibliography can be found in recent articles by Fano (1953a, 1953b). However, the simplest approach is a semiempirical one, wherein an experimentally determined or assumed form of radiation-intensity law for an elementary source is integrated over a suitable geometric configuration to obtain the intensities from various sources. Peirson and Franklin (1951) performed such an integration assuming an inversesquare exponential law which not only neglects the effect of scattering but also the multitudinous lines of the uranium gamma-ray spectrum. Carmichael and others (Steljes and others, 1952) used the inversesquare law but took air scattering into account by experimentally determining the "effective absorption coefficient" by measuring the radiation from radium sources. Cook (1952) assumed an "effective" energy and utilized "effective" computed cross-section and the inversesquare law. However, there is no priori reason why any "effective" quantity computed or measured in one source-to-medium orientation should be applicable to others. To avoid this difficulty measurements were made on infinitely thick sources, wherein the integration in depth is already performed in the data, and the d

Scattered gamma rays from thick uranium sources