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### NARROW

**Follow your search**

Abstract The goal of this book is to provide information about the principles, understanding, and applicability of the gravity exploration method. This book is intended to be suitable for classroom instruction and as a reference for anyone engaged in geophysical exploration, including those whose specialties might be in another discipline but who would benefit from an understanding of how gravity exploration can help them solve exploration problems. For many decades, the 1971 SEG book by L. L. Nettleton (Geophysical Monograph Series No. 1, Elementary Gravity and Magnetics for Geologists and Seismologists ) has helped to fill this need, but it is limited in scope (as its title implies) and is, of course, out of date, especially with respect to modern exploration technology. This little book has been a best seller, however, and it resides in the libraries of thousands of geologists and geophysicists. It contains several classical and practical examples of how the gravity method can be applied, and we have borrowed liberally from these where they retain their long-held value. In 1995, Richard J. Blakely published Potential Theory in Gravity and Magnetic Applications . This book covers in depth much of which the Nettleton monograph lacks: the principles of potential theory and the mathematical basis for the forward and inverse techniques of interpretation. Our book is intended to fill a need that is oriented more toward exploration than the Nettleton monograph or the Blakely book, with more information about the underlying principles and technology than the former and clearer orientation toward the explorationist's

#### Principles of Attraction and Earth’s Gravity Field

Abstract Consider two small masses, M 0 and M 1 whose radii are very small in comparison with the distance r between the masses (Figure 1 ). Newton’s universal law of attraction states that each mass attracts the other by a force F whose amplitude F is in direct proportion to the product of their masses and inversely proportional to the square of the distance between them: where k is the universal gravitational constant equal to 6.67 × 10 -11 m 3 /kg·s 2 in MKS units (i.e., distances measured in meters, mass in kilograms, and time in seconds) or 6.67 × 10 -8 cm 3 /g·s 2 in cgs units (centimeters-grams-seconds). The force caused by M 1 acting at and on M 0 is directed along r toward M 1 ; an equivalent force acting on M 1 by M 0 also is directed along r but in the opposite direction, toward M 0 . The resulting force F is a vector quantity given by whose magnitude is stated in equation 1 and whose direction is in the direction toward the causative body. The negative sign is introduced to indicate that r is measured from the source mass to the point of observation, whereas the force F is directed in the opposite direction (i.e., toward the source). Figure 1. Attraction between two small masses separated by distance r with f the unit vector directed from gravitational source to the observation point. We will consider M 0 to be a mass residing at our point of observation and M 1 to be the source mass causing a field Abstract Consider two small masses, M 0 and M 1 whose radii are very small in comparison with the distance r between the masses (Figure 1 ). Newton’s universal law of attraction states that each mass attracts the other by a force F whose amplitude F is in direct proportion to the product of their masses and inversely proportional to the square of the distance between them: where k is the universal gravitational constant equal to 6.67 × 10 -11 m 3 /kg·s 2 in MKS units (i.e., distances measured in meters, mass in kilograms, and time in seconds) or 6.67 × 10 -8 cm 3 /g·s 2 in cgs units (centimeters-grams-seconds). The force caused by M 1 acting at and on M 0 is directed along r toward M 1 ; an equivalent force acting on M 1 by M 0 also is directed along r but in the opposite direction, toward M 0 . The resulting force F is a vector quantity given by whose magnitude is stated in equation 1 and whose direction is in the direction toward the causative body. The negative sign is introduced to indicate that r is measured from the source mass to the point of observation, whereas the force F is directed in the opposite direction (i.e., toward the source). Figure 1. Attraction between two small masses separated by distance r with f the unit vector directed from gravitational source to the observation point. We will consider M 0 to be a mass residing at our point of observation and M 1 to be the source mass causing a field

Abstract In the previous chapter, we investigated the gravitational acceleration g and found that it can be derived from a scalar potential U . Based on these definitions, we now investigate the gravitational attraction of a number of mass distributions and derive some important consequences.

Abstract The measurement of the earth’s gravity field, whether in absolute or relative terms, is one of mankind’s greatest engineering achievements, the accuracy of which can be on the order of one part in one billion of the earth’s total field. During a period of more than one century, numerous instruments have been invented, many of which have met with large commercial success. It is not within the scope of this book to review the extensive history of gravity instruments or to give details of instruments that are not now in use. A complete description of all gravimeters mentioned in this chapter and many others not mentioned here can be found in Nabighian et al. (2005), along with their advantages and limitations. In this chapter, we discuss absolute and relative instruments, gravity gradiometry, field operations, measurement uncertainty, and ambiguity related to survey design.

Abstract Equation 15 of Chapter 3 is, in theory, a unique formula for performing the forward calculation that produces the gravity anomaly caused by a subsurface density distribution. On the right side of that equation, under the integral, are the density ρ and the geometric components of an element of mass to be summed over the entire geologic body. In this chapter, we examine the nature of density in exploration, its determination, and finally, how a lateral density contrast is required to cause an observable anomaly.

Abstract Lateral variations in the density of rocks cause variations in the gravity field measured at the surface, and our central problem in gravity exploration is to discover the nature of subsurface rocks, their constituents, their structure, and their distribution. Toward this end, we use the theory and tools developed and described in the first five chapters. In general, the observed gravity value g o is equal to the sum of the gravity anomaly g a caused by the geologic masses we wish to study and the contribution resulting from “noise,” g N . For present purposes, we will define the noise contribution, as the sum of all unwanted effects, where g p represents all the effects caused by variations in position, elevation, speed of the instrument, and so forth, for which standard corrections apply; g g represents geologic noise effects caused by unknown or uncertain geologic features other than our target(s) of interest (discussed in Chapters 7 and 8); g i represents untreated instrumental noise, such as nonlinear drift components in the instrument; and g d includes survey design noise (aliasing), as shown in Figure 10 of Chapter 4 . In the data-reduction phase of gravity work, our goal is to identify and remove the effects that make up the first term on the right side of equation 1 , g p , and to evaluate the potential magnitudes of the last two terms, g t and g d . The intended result is an anomaly field in which all the unwanted contributions to measured gravity have been partly

#### Anomaly Interpretation Guidelines and Limitations

Abstract We have studied the mathematical basis for the generation of gravity anomalies (Chapter 3 ), gravity instrumentation that enables gravity surveys and generally available surveying methods for obtaining them (Chapter 4 ), density variations and methods for determining rock density (Chapter 5 ), and the reduction of gravity data in static and dynamic settings (Chapter 6 ), which is intended to eliminate often very substantial measured effects that are unrelated to the gravitational sources we wish to analyze. Both relative-and absolute-gravity measurements are available in gravity exploration. Six generalized purposes of gravity surveys can incorporate one or both methods of measurement: 1) determination of the earth’s shape 2) determination of missile trajectories, a military application now seldom used 3) tidal and earth elasticity studies 4) other time-dependent applications (such as the monitoring of reservoirs) 5) determination of physical constants 6) determination of the subsurface geology or other characteristics of the earth’s structure The last of these, the study of the subsurface, requires identification of the anomalies associated with the geologic sources of interest (anomaly separation) and an explanation of those anomalies in terms of the geology that is the purpose of the investigation. We will now turn to those activities. In this chapter, we examine the guidelines and limitations of anomaly interpretation. In Chapter 8 , we examine inversion, a special case of interpretation. In Chapter 9 , we illustrate case histories to demonstrate practical results of interpretation. As we have seen in Chapter 3 , three features of the causative bodies must be present to produce

Abstract We have seen previously that the calculation of the gravity anomaly resulting from a given geologic structure, the so-called forward or direct problem, is relatively straightforward and can be done with a high degree of accuracy. In the most general case, the gravitational attraction is given by expression 15 of Chapter 3 : Expression 1 is usually written in compact form as follows: where ρ(Q ) is the density function at a point Q ( ξ,η,ζ ) inside volume V (usu-ally the lower half-space), and is referred to as a Green’s function and gives the vertical component of gravitational attraction at observation point P( x, y, z) of an element of mass at distance r at point Q. In the above expression, and (ζ-z)/r is the direction cosine between r and the z -axis. It is worth mentioning that the forward problem has a unique solution, i.e., g z is determined completely from a knowledge of ρ(Q) and G z (P, Q). The inverse problem is defined as an automated numerical procedure that constructs a model of subsurface density distribution from measured data using all prior information independent of data. In other words, given g z and G(P,Q) in the above equation, we are asked to determine ρ(Q) . In contrast, however, to the forward problem, the typical inverse problem usually does not possess a unique solution. The interpreter must decide among several solutions that satisfy the known or assumed geology for the area under investigation while also fitting the observed data within certain tolerances. That is because we have one Abstract We have seen previously that the calculation of the gravity anomaly resulting from a given geologic structure, the so-called forward or direct problem, is relatively straightforward and can be done with a high degree of accuracy. In the most general case, the gravitational attraction is given by expression 15 of Chapter 3 : Expression 1 is usually written in compact form as follows: where ρ(Q ) is the density function at a point Q ( ξ,η,ζ ) inside volume V (usu-ally the lower half-space), and is referred to as a Green’s function and gives the vertical component of gravitational attraction at observation point P( x, y, z) of an element of mass at distance r at point Q. In the above expression, and (ζ-z)/r is the direction cosine between r and the z -axis. It is worth mentioning that the forward problem has a unique solution, i.e., g z is determined completely from a knowledge of ρ(Q) and G z (P, Q). The inverse problem is defined as an automated numerical procedure that constructs a model of subsurface density distribution from measured data using all prior information independent of data. In other words, given g z and G(P,Q) in the above equation, we are asked to determine ρ(Q) . In contrast, however, to the forward problem, the typical inverse problem usually does not possess a unique solution. The interpreter must decide among several solutions that satisfy the known or assumed geology for the area under investigation while also fitting the observed data within certain tolerances. That is because we have one Abstract We have seen previously that the calculation of the gravity anomaly resulting from a given geologic structure, the so-called forward or direct problem, is relatively straightforward and can be done with a high degree of accuracy. In the most general case, the gravitational attraction is given by expression 15 of Chapter 3 : Expression 1 is usually written in compact form as follows: where ρ(Q ) is the density function at a point Q ( ξ,η,ζ ) inside volume V (usu-ally the lower half-space), and is referred to as a Green’s function and gives the vertical component of gravitational attraction at observation point P( x, y, z) of an element of mass at distance r at point Q. In the above expression, and (ζ-z)/r is the direction cosine between r and the z -axis. It is worth mentioning that the forward problem has a unique solution, i.e., g z is determined completely from a knowledge of ρ(Q) and G z (P, Q). The inverse problem is defined as an automated numerical procedure that constructs a model of subsurface density distribution from measured data using all prior information independent of data. In other words, given g z and G(P,Q) in the above equation, we are asked to determine ρ(Q) . In contrast, however, to the forward problem, the typical inverse problem usually does not possess a unique solution. The interpreter must decide among several solutions that satisfy the known or assumed geology for the area under investigation while also fitting the observed data within certain tolerances. That is because we have one Abstract We have seen previously that the calculation of the gravity anomaly resulting from a given geologic structure, the so-called forward or direct problem, is relatively straightforward and can be done with a high degree of accuracy. In the most general case, the gravitational attraction is given by expression 15 of Chapter 3 : Expression 1 is usually written in compact form as follows: where ρ(Q ) is the density function at a point Q ( ξ,η,ζ ) inside volume V (usu-ally the lower half-space), and is referred to as a Green’s function and gives the vertical component of gravitational attraction at observation point P( x, y, z) of an element of mass at distance r at point Q. In the above expression, and (ζ-z)/r is the direction cosine between r and the z -axis. It is worth mentioning that the forward problem has a unique solution, i.e., g z is determined completely from a knowledge of ρ(Q) and G z (P, Q). The inverse problem is defined as an automated numerical procedure that constructs a model of subsurface density distribution from measured data using all prior information independent of data. In other words, given g z and G(P,Q) in the above equation, we are asked to determine ρ(Q) . In contrast, however, to the forward problem, the typical inverse problem usually does not possess a unique solution. The interpreter must decide among several solutions that satisfy the known or assumed geology for the area under investigation while also fitting the observed data within certain tolerances. That is because we have one

Abstract In this book,we have studied the mathematical basis for understanding gravity anomalies, the gravitational nature of the earth on and in which we make our measurements, gravity instrumentation which enables gravity surveys, gravity inversion which provides for a tool by which we can determine possible (in some cases probable) sources of gravity anomalies, and the reduction of gravity data in static and dynamic settings which is intended to eliminate substantial measured effects that are unrelated to the geologic sources we wish to analyze. We have listed briefly the reasons and generally available methods for performing gravity surveys. Now we turn to gravity interpretation, the purpose of which is to improve our understanding of the subsurface in geologic terms. We enjoy a robust literature on the successes of the gravity method (failures tend to go unreported) embracing a very wide range of geologic and engineering targets, and one approach is to list those to show the sometimes remarkable effectiveness of the gravity method. Our purpose in this book, however, is to provide the reader of the gravity-exploration method with a basic understanding from which one can proceed to (1) determine if the method is applicable toward an improvement in one’s understanding of the geologic problem under investigation, (2) optimally plan a survey by which the appropriate data can be obtained, (3) properly reduce the data to the desired anomaly field, (4) separate the observed anomaly field into components in an effort to isolate the target(s) of interest and, (5) if possible, determine

Abstract The Fourier transform is a mathematical operation that decomposes a function into its constituent frequencies. This appendix will give a brief review of Fourier-transform theory as a tool for mapping functions of time or distance (space) into functions of frequency or wavenumber. In gravity exploration, we are concerned mostly with functions that depend on distance (e.g., gravity profiles or maps), in contrast with seismic exploration, in which the main output (seismic-record trace) is represented as a function of time. For a complete coverage of this topic, the reader is referred to the excellent textbooks by Papoulis (1962) and by Bracewell (1965).

Abstract The goal of this book is to provide information about the principles, understanding, and applicability of the gravity exploration method. This book is intended to be suitable for classroom instruction and as a reference for anyone engaged in geophysical exploration, including those whose specialties might be in another discipline but who would benefit from an understanding of how gravity exploration can help them solve exploration problems. For many decades, the 1971 SEG book by L. L. Nettleton (Geophysical Monograph Series No. 1, Elementary Gravity and Magnetics for Geologists and Seismologists ) has helped to fill this need, but it is limited in scope (as its title implies) and is, of course, out of date, especially with respect to modern exploration technology. This little book has been a best seller, however, and it resides in the libraries of thousands of geologists and geophysicists. It contains several classical and practical examples of how the gravity method can be applied, and we have borrowed liberally from these where they retain their long-held value. In 1995, Richard J. Blakely published Potential Theory in Gravity and Magnetic Applications . This book covers in depth much of which the Nettleton monograph lacks: the principles of potential theory and the mathematical basis for the forward and inverse techniques of interpretation. Our book is intended to fill a need that is oriented more toward exploration than the Nettleton monograph or the Blakely book, with more information about the underlying principles and technology than the former and clearer orientation toward the explorationist's geologic goals than the latter.

#### Effects of low-pass filtering on the calculated structural index from magnetic data

**Journal:**Geophysics

**Publisher:**Society of Exploration Geophysicists

#### Electrical and EM methods, 1980–2005

**Journal:**The Leading Edge

**Publisher:**Society of Exploration Geophysicists

#### Metalliferous mining geophysics—State of the art in the last decade of the 20th century and the beginning of the new millennium

**Journal:**Geophysics

**Publisher:**Society of Exploration Geophysicists

#### Unification of Euler and Werner deconvolution in three dimensions via the generalized Hilbert transform

**Journal:**Geophysics

**Publisher:**Society of Exploration Geophysicists

The front matter contains the title page, copyright page, dedication page, and table of contents.

INTRODUCTION The immediate objective of a geophysical survey is to obtain some information about the interior spatial distribution of one or more of the earth's physical properties from a limited set of measurements of a related physical field made on the earth's surface (or another accessible place). In the case of an electromagnetic (EM) induction survey, the most relevant physical property is the electrical conductivity, and it is sensed by means of a time-varying magnetic and/or electric field. The procedure of converting field measurements to a physical property distribution is termed modeling or interpretation, and the formal corresponding mathematical process is termed inversion. Geophysical inversion is difficult in the best of circumstances because of numerous intrinsic ambiguities. For EM methods in particular there is an additional problem. The basic laws that relate the EM field to the physical property distribution are well known (Maxwell's equations) and a quantitative and calculable relationship between the physical measurements and the property structure can be established for certain idealized cases. However, we still lack practicable modeling capabilities that enable quantitative prediction of the EM field configuration produced by an arbitrary physical property distribution of even moderate complexity. Geologic scenarios are extremely varied, and few actual cases can be described accurately in terms of simple geometric forms like plane horizontal layers. Thus, only rarely can we feasibly turn geophysical observations directly into a reliable picture of earth structure simply by application of an automatic process. Generally, a human interpreter is still needed to guide the interpretation process, and this human needs to have a good qualitative understanding of how physical earth structure can interact with EM fields. In addition the interpreter should be able to mentally extrapolate beyond calculable cases and to select more important features of the data from less important ones. Our objective in this tutorial paper is to assist readers in developing such an ability by discussing the various physical processes which arise in some simple situations.