RU2431873C2 - Processing gravimetric survey data - Google Patents

Abstract

FIELD: physics.

SUBSTANCE: described is a method of processing potential field measurement data obtained from surveying the Earth's potential field in order to determine map data for mapping the field. The method comprises steps where potential field measurement data are entered. Potential field measurement data include data which give the set of potential field measurements and corresponding positions. Each position gives the potential field measurement position in three-dimensional space; the set of relationships between potential field measurements and positions is determined. Each relationship links the potential field measurement with the function of the corresponding position in three-dimensional space, multiplied by the field mapping parameter; and an essentially self-consistent set of field mapping parameters for the set of relationships is determined in order to determine mapping data.

EFFECT: improved data processing methods.

29 cl, 4 dwg

Description

The present invention relates to improved methods for processing potential field measurement data obtained by aerial reconnaissance, for example gravimetric reconnaissance, and to improved data collection methods that are provided by improved data processing methods.

Traditionally, aerial reconnaissance of a potential field, for example gravimetric reconnaissance, is carried out according to a grid scheme. The grid is defined by orthogonal sets of parallel lines (flight paths) on a two-dimensional surface that envelops the underlying relief. The envelope surface satisfies the limitation of the minimum height (i.e., the minimum height above the ground at which the aircraft is allowed to fly) and the restriction on the maximum aircraft ascent / descent speed, usually about three percent. This approach is suitable for a flat terrain, but for a hilly or mountainous terrain, the surface on which the plane flies can vary within two to three kilometers from, say, the bottom of the underlying valley to the top of the mountainous / reconnaissance area, so a different approach is needed.

It is useful to be able to collect potential field data, in particular gravimetric data, near the ground, i.e. at low altitude. In gravimetric reconnaissance, the nearby mass provides high and low (spatial) frequency data, while the influence of a deeper mass is observed mainly at low frequencies. In the search for underlying anomalies, the intermediate mass has a predominant influence, and to ensure an accurate representation of the deep features, it is desirable to have a good representation of the surface features in order to be able to subtract, in particular, high frequencies (which prevail in the energy spectrum). For example, a signal with a wavelength λ weakens with a height z according to the law exp ( -kz ), where k = 2π / λ, whence it can be estimated that the component of a signal with a wavelength of 200 meters from the mass at a depth of 100 meters weakens approximately 20 times from its initial value on the surface of the earth (and additionally decreases exponentially with increasing height), while it can be seen that longer wavelengths decrease much more slowly. In the general case, the size and position of the reconnaissance are selected according to the wavelength scale corresponding to the signature assumed in accordance with the size and depth of the target.

From the above consideration it follows that in the general case it is desirable to be able to carry out aerial reconnaissance at a low altitude, but in practice aircraft limitations and a flight scheme tied to a grid can impose significant restrictions. A gridded flight pattern is necessary because traditional methods for processing gravity data are based on the assumption of a constant height. In a broad sense, the assumption is that for a deep source, the height of the aircraft is approximately constant, and the deviation from this assumption is considered only as a small correction. In addition, traditional methods for processing gravimetric reconnaissance data rely on regularly placed data elements, usually in the power of two, which makes it possible to use the (fast) Fourier transform, thereby setting the requirement for orthogonal sets of parallel flight paths. It is necessary that flight routes be located on a common surface, since existing methods assume, for example, that if two routes intersect, then they intersect at the same height. An additional problem with existing flight routes arises when the reconnaissance area is not exactly rectangular, for example due to local terrain. In this case, in order to be able to apply traditional methods, the data elements are “clogged”, for example, by interpolation or extrapolation to generate a regular set of data elements in a rectangular area. Then the wavelengths (or, in particular, the wave numbers) used for the Fourier analysis are determined by the maximum dimensions x and y (length and width) of the clogged rectangular region.

In view of the aforementioned disadvantages of traditional methods, improved methods for processing potential field intelligence data and reconnaissance flight schemes are required.

According to a first aspect of the present invention, there is provided a method for processing potential field measurement data obtained from prospecting a potential field of the earth to determine map data for mapping a field, the method comprising the steps of entering potential field measurement data, the potential field measuring data comprising data defining a plurality of measurements potential field and corresponding positions, and each position sets the measurement position of the potential field in three-dimensional space; determining a set of relations between potential field measurements and positions, each relationship relating a potential field measurement to a function of the corresponding position in three-dimensional space multiplied by the field mapping parameter; and determine, in essence, a self-consistent set of field mapping parameters for a set of relationships to determine, thus, the cartographic data.

Potential field data may include gravimetric data (gravitational field measurement data), gravitational gradiometer data (magnetic field gradient measurement data), vector magnetometer data, true magnetic gradiometer data, or similar data. Field mapping parameters (coefficients or parameters allowing to describe the potential field) can be used to generate similar data of the potential field and, according to embodiments, in general, the parameters are determined by the choice of parameter values that specify the data of the potential field, for example, the gravitational field or the gradient of the gravitational field, which most accurately approximate potential field measurements. This may be, for example, minimizing the mean square error or other similar optimization.

According to embodiments, the ratios comprise a system of equations that can be represented, for example, by a matrix, and the definition contains a solution to these equations. Preferably, the equations are excessively bounded, and the solution comprises a solution through a noise reduction procedure, such as least squares optimization. Preferably, the ratios are such that they have the form of a field of real (gravitational) potential, so that the noise, which usually does not have this kind, is ultimately filtered out in the optimization procedure. Thus, preferably, the (three-dimensional) position function satisfies the Laplace equation. In a number of representative examples of the method, there may be about 10K parameters and 100K positions.

The cartographic data may simply contain a set of field mapping parameters (coefficients or potential field parameters), since this data can be used to generate a range of potential field data (for example, gravitational field data or a gravitational field gradient) depending on the desired height, coverage area and / or mapped surface. However, the method may further comprise determining the desired field, usually on the surface, from a set of field mapping parameters for generating the map, i.e. direct calculation of potential field data from a set of field mapping parameters. According to the explanation below, embodiments of the method provide for generating the same type of potential field data that is measured, at least implicitly, when determining the parameters of the field mapping using a procedure that aims to minimize or otherwise optimize the differences between the calculated and measured values. That this works regardless of whether the potential field data contains, say, gravimetric data or gravitational gradiometer data, can be seen using one of Green's theorems. In addition, knowing one type of data of the potential field, for example, the gravitational field or the gradient of the gravitational field, it is possible to determine the other by integration / differentiation, as well as the scalar potential.

In one embodiment of the method, an equivalent data source representation of a potential field is applied. In this embodiment, values of surface density (or mass) are found for a combination of massive surface elements that together create a gravitational (or other) field that best approximates the measured gravitational (or other) field. The surface in the general case, but not necessarily, is flat, and it, for example, can be selected to approximate the surface of the earth in the area of exploration. Having found the values for these massive elements, one can use simple direct calculation to predict the scalar potential, or the gravitational field, or the gradient of the gravitational field, for example, to generate any desired map of the reconnaissance area. Typically, direct calculation is performed to determine one or more field components on a plane mapping plane.

In general terms, according to embodiments of this method, the square of the difference between the measured field and the field determined from the masses of the equivalent source (the gravitational field is measured / calculated or the gradient of the gravitational field) is a function of mass errors. Thus, taking the partial derivative of this function with respect to, separately, the mass of each surface element, we compose a system of equations in which only the masses of all massive surface elements are variables (provided that the measurement position with respect to the massive surface element, r - r ′ , is known ) It is convenient to present this system of equations in the form of a matrix and solve it with respect to the values of massive surface elements. Since the number of measurements is usually much larger than the number of equations in the system (i.e., the number of massive elements), for example, at least five or ten times more, the system of equations is excessively limited. This is useful since the values of massive surface elements will in no way correspond to noise; instead of the optimization procedure, for example, the least squares approximation is used to determine the values of massive surface elements, which reduces the noise. In addition, due to the use of the physical model of the gravitational field, the equations obey the Laplace equation, which allows us to approximate the gravitational field, rather than noise.

) каждой двухмерной составляющей (

), это представление все же является наиболее общим и подчиняется уравнению Лапласа (при дифференцировании множителей высотно-зависимого коэффициента и сокращении двухмерных составляющих). Разложение можно обрезать в той или иной точке, в зависимости от нужной точности представления, например, определяемой количеством переменных, сделанных зависимыми. Можно применять другие разложения, например по сферическим гармоникам, которые полезны для более обширных областей, в частности, когда кривизной земли нельзя пренебречь.In the second embodiment of the method, the modified Fourier basis function method is applied. According to this method, two-dimensional Fourier series expansion is used to represent the measurement data, but due to multiplication by a height-dependent coefficient (

) of each two-dimensional component (

), this representation is still the most general and obeys the Laplace equation (when differentiating the factors of the height-dependent coefficient and reducing the two-dimensional components). The decomposition can be cut off at one point or another, depending on the desired accuracy of the representation, for example, determined by the number of variables made dependent. Other decompositions can be applied, for example, in spherical harmonics, which are useful for more extensive areas, in particular, when the curvature of the earth cannot be neglected.

также известно. Таким образом, при разложении в ряд Фурье (например, согласно приведенному ниже уравнению (3)) каждый элемент данных можно в итоге рассматривать по отдельности, и, как и в первом варианте осуществления, описанном выше, формируется система уравнений, которую можно решить относительно коэффициентов разложения в ряд Фурье. Эти коэффициенты затем можно использовать для определения (путем прямого вычисления) гравитационного поля или градиента гравитационного поля на любой двухмерной поверхности, которую нужно картографировать. Очевидно, что в этом (и предыдущем) варианте осуществления данные можно выбирать произвольным образом, поскольку элементы данных фактически не связаны между собой - все, что необходимо, это набор измерений и соответствующих (x, y, z) позиций, чтобы иметь возможность определения гравитационного поля или градиента гравитационного поля на любом другом наборе точек, в частности на поверхности или плоскости, то есть карте. Кроме того, отсюда следует, что, с использованием традиционных методов, нет необходимости забивать данные измерений для построения прямоугольника. В принципе, элементы данных можно рассматривать как участок произвольной формы двухмерной области максимальных размеров, определяемых максимальными длинами волны для разложения в ряд Фурье в направлениях x и y (хотя, как можно видеть, данные измерений не обязаны лежать на двухмерной поверхности). Отсюда следует, что значения k _m и k _n можно выбирать независимо от размеров области разведки (здесь k - волновое число, т.е. 2π/λ, тогда как при традиционной разведке максимальная длина волны должна соответствовать длине или ширине прямоугольной области разведки).In the general case, the expansion coefficients are determined as follows. At position r, the measured potential field (gravitational field or gradient of the gravitational field) is known, and for a particular pair of values of k _m and k _{n, the} value

also known. Thus, when expanding in a Fourier series (for example, according to the equation (3) below), each data element can be considered separately, and, as in the first embodiment described above, a system of equations is formed that can be solved with respect to the coefficients Fourier series expansion. These coefficients can then be used to determine (by direct calculation) the gravitational field or the gradient of the gravitational field on any two-dimensional surface that needs to be mapped. Obviously, in this (and previous) embodiment, the data can be arbitrarily selected, since the data elements are practically not interconnected - all that is needed is a set of measurements and corresponding ( x , y , z ) positions in order to be able to determine the gravitational field or gradient of the gravitational field on any other set of points, in particular on a surface or plane, that is, a map. In addition, it follows that, using traditional methods, there is no need to clog measurement data to construct a rectangle. In principle, data elements can be considered as a part of an arbitrary shape of a two-dimensional region of maximum dimensions determined by the maximum wavelengths for expansion in a Fourier series in the x and y directions (although, as you can see, the measurement data does not have to lie on a two-dimensional surface). It follows that the values of k _m and k _n can be chosen regardless of the size of the reconnaissance area (here k is the wave number, i.e. 2π / λ, whereas in traditional reconnaissance, the maximum wavelength should correspond to the length or width of the rectangular reconnaissance area).

According to another aspect of the invention, there is provided a data processing system for processing potential field measurement data obtained by prospecting a potential field of the earth, for determining cartographic data for mapping a field, the system comprises a data storage device for storing potential field measurement data, wherein the potential field measurement data contains data, defining a set of measurements of the potential field and the corresponding positions, and each position sets the measurement position of the sweat ntsialnogo field in three-dimensional space; a program storage device for storing a processor control code; and a processor connected to the data storage device and the program storage device for downloading and executing a control code, the code comprising a code instructing the processor to input measurement data of a potential field; determine the totality of the relationships between the potential field measurements and the positions, each relationship correlating the potential field measurement with the function of the corresponding position in three-dimensional space, multiplied by the field mapping parameter; and determine, in essence, a self-consistent set of field mapping parameters for a set of relationships to determine, thus, the cartographic data.

According to an additional aspect of the invention, there is provided a method for processing measurement data obtained in aeronautical gravimetric reconnaissance to provide data for a gravitational field map, the measurement data comprising a collection of gravitational potential field measurements, each of which has a measurement position in three-dimensional space, the method comprises the steps of use the measurement data to estimate the coefficients by which the function of the three-dimensional position in the harmonic expansion is multiplied, for defining, therefore, a representation of the gravitational field in the area of exploration for a map of the gravitational field.

The invention additionally provides a method for processing measurement data obtained in aeronautical gravimetric reconnaissance to provide data for a map of the gravitational field, the measurement data containing a set of measurements of the gravitational potential field, each of which is associated with a measurement position in three-dimensional space, the method comprises the steps of using the data measurements to evaluate a set of massive elements, each of which is multiplied by a function of a three-dimensional position in the representation of ivalentnogo source gravitational field to thereby provide data for the map of the gravitational field.

The invention further provides a method for mapping a gravitational field, the method comprising the steps of introducing measurement data obtained in aeronautical gravimetric reconnaissance, the measurement data comprising a collection of potential gravitational field measurements, each of which has a measurement position in three-dimensional space; determining a set of relations between potential field measurements and positions, each relationship relating a potential field measurement to a function of the corresponding position in three-dimensional space multiplied by the field mapping parameter; and map the gravitational field, determining, essentially, a self-consistent set of field mapping parameters for a set of relationships.

Embodiments of the above methods further comprise reconnaissance of the field to obtain measurement data of the potential field by flying around a set of routes that do not have to be parallel or form a rectangular grid.

As mentioned above, embodiments of the above method can be applied, if desired, to virtually randomly selected data. Although random sampling may be inconvenient from a practical point of view, it is nevertheless obvious that, since the methods described here are generally not limited, aerial reconnaissance routes can be chosen so as to obtain better initial data, in particular, at the expense of possibly more low flight, limited only by general safety considerations and aircraft capabilities. Thus, for example, in a broad sense, the traditional set of routes can be supplemented by flights along the lines of the valleys and / or modified, for example, by curving one or more flight routes to repeat the mountainous terrain.

Although routes do not have to intersect at substantially the same height (“crossover”), crossovers are nonetheless useful for reducing noise and low-frequency drift, as they provide two highly correlated measurements of similar sections. However, unlike traditional reconnaissance methods, routes are not required to cross at the same altitude. In addition, various crossing patterns are possible, for example, in a valley, two piecewise linear or serpentine routes can meander in opposite directions to ensure a sequence of crossings along the routes.

Therefore, according to an additional aspect of the invention, there is provided a method for conducting aerial reconnaissance of a potential field, the method comprising the steps of conducting an airplane along a set of routes and measuring potential field data at points on routes in which the set of routes has one or more of the following features: two routes intersect at heights differing by at least 50 meters; in the intelligence area, routes in the same general direction are not more than 5 degrees parallel; routes include curved routes; routes from a set of routes taken together, essentially, do not lie on the surface; the routes from the set of routes taken together define a surface in which at least one of the routes defines one of two orthogonal directions on the surface, so that the rates of change of height with distance in different orthogonal directions of the surface differ by more than 5 percent.

According to embodiments of the above methods, the two routes intersect at heights differing by more than 50, 100, 150 or 200 meters. Routes can be straight, piecewise linear or curved and, in general, adjacent flight routes can deviate from parallelism by more than two degrees, three degrees, five degrees, ten degrees or more. As noted above, routes taken together are not required to essentially lie on the surface, in particular due to the lack of a “substantially constant height” restriction. However, one convenient method of constructing a set of routes for such aerial reconnaissance involves providing traditional reconnaissance with its subsequent modification towards approaching the ground, in particular, in lowlands where better coverage is desired.

A typical way of providing traditional reconnaissance involves the construction of a two-dimensional surface enveloping the terrain on which reconnaissance is to be carried out. At high points of the underlying terrain, the surface height is usually determined by the minimum permitted aircraft altitude (for safety), and then the surface height decreases due to the aircraft’s inherent limitations of ascent / descent, usually of the order of two to three percent. Because routes are limited to a rectangular grid, these restrictions apply in two orthogonal directions. Unlike the embodiments of the above method, such a restriction needs to be applied in only one direction (in one dimension, and not in two). As a result, a one-dimensional envelope can be used to determine flight routes. Thus, according to the embodiments of the method described here, the set of routes taken together defines the surface on which the route lies, defining one or two orthogonal directions, and in the other direction of the surface it is allowed to have a rate of change of height with a distance exceeding the allowed speed of ascent / descent of the aircraft for example, more than three percent, five percent, ten percent, twenty percent or more.

The invention also provides a data carrier carrying aircraft navigation data for such a set of potential field aerial reconnaissance routes.

The invention further provides a processor control code for implementing the above methods, in particular on a storage medium, such as a disk, CD or DVD-ROM, in programmable memory, such as read-only memory (firmware), or on a storage medium, such as optical media or electrical signal. The code (and / or data) for implementing the embodiments of the invention may contain source, object, or executable code in a traditional programming language (interpreted or compiled), for example C, or assembler code, code for configuring and controlling ASIC (specialized integrated circuit), or FPGA (Field Programmable Gate Array), or code in a hardware description language, such as Verilog (trademark) or VHDL (hardware description language for high-speed integrated circuits). It will be apparent to those skilled in the art that such code and / or data may be distributed among a number of components communicating with each other.

The following are additional aspects of the invention .

A method of reconnaissance of a potential field from the air, for which the aircraft is equipped with a set of equipment for geophysical measurements, including one or more instruments for measuring the potential field, for example, a vector gravimeter, gravity gradiometer, magnetometer, magnetic gradiometer or other devices, and according to which the plane flies an irregular set of disconnected, not at the same level, non-linear flight routes that cover the reconnaissance area, preferably with the least the possible distance between the surface and the aircraft for each flight line and with approximately uniform coverage of the reconnaissance area (such lines are consistent with the safe operation of the aircraft). Preferably, according to this method, the magnitude of the potential field of the land of interest is determined using algorithms that work with the measurement data obtained using the device for measuring the potential field, collected along the intelligence lines as is, without the need to align the data, bring the data to a common horizontal plane or to attach data to the grid, and such data include the measurement of the magnitude of the potential field and (instantaneous) position and, optionally e, the height of the instrument (s) for measuring the potential field.

The method of reconnaissance of a potential field from the air, described above, but in which the flight pattern is slightly modified in order to achieve an acceptable number of “crossings” per unit area, and in this case, “crossover” is the point where the flight lines of an aircraft with different heading directions are nominally intersect at the same point in space.

The method of reconnaissance of a potential field from the air described above, where some lines from a set of essentially parallel, but not necessarily straight lines, are deliberately made wriggling to increase the number of crossings with other lines in this set that run in parallel.

The method of reconnaissance of a potential field from the air described above, where all lines are drawn in order to ensure the maximum (possible) number of crossings over the entire reconnaissance area (taking into account restrictions, for example, on the total / length / flight time). None of the lines of intelligence is required to be parallel to any other line of intelligence, nor is any of the lines required to be straight, and in the general case, many lines will not cross the entire area of intelligence from edge to edge.

The method of reconnaissance of a potential field from the air, described above, but in which the aircraft carries out reconnaissance according to a more traditional pattern, for example, according to a reconnaissance pattern with a two-dimensional envelope or constant height or some other pattern that entangles the flight lines and connects them so that they intersected at each crossing. (For example, navigation data can specify the exact intersection, although in practice the pilot achieves this only with an accuracy of, for example, 10 m or 20 m.)

The method of reconnaissance of a potential field from the air, described above, in which the data is "aligned" before processing. Alignment here is a general term that encompasses methods that include one or more of: reducing noise, removing low-frequency drift, matching the low-frequency spectrum of adjacent lines, correlating data with a fixed-height plane, etc. Data can also be snapped to the grid before processing.

The method of reconnaissance of a potential field from the air, described above, where the first stage of the analysis involves the removal or adjustment of data that can in no way be caused by any geological structures that are the subject of research or geomorphology (relief) in the area of exploration. The influence of the relief can also be used to adjust data at any stage of processing before calculating the gravitational potential of the earth.

The method of reconnaissance of a potential field from the air described above, where an exact DEM (digital elevation model) is created using a lidar (laser radar) in conjunction with IMU (inertial measuring unit), as well as with DGPS (differential global positioning system) to correct the lidar data for flat movement. DEM and DGPS data can also be used to correct potential field measurements for terrain. Similarly, the data of acceleration, altitude, orientation, angular velocity and angular acceleration of the aircraft can also be used to adjust the output of the equipment for measuring the potential field. Any on-board or remote sensor can be used to provide position and movement information for an airplane and / or equipment for measuring potential fields.

Therefore, it is preferable to equip the aircraft with various additional standard geophysical reconnaissance aircraft, for example, GPS, DGPS, altimeter, altitude, pressure, hyperspectral scanner, electromagnetic measurement system (EM), transient electromagnetic measurement system (TDEM), vector magnetometer, accelerometer , gravimeter and other devices, including other potential field measuring devices.

The method of reconnaissance of a potential field from the air, described above, in which the output signals of the equipment on the reconnaissance aircraft are corrected using the equipment on a stationary or mobile base station, for example, according to best practice at this time. Such equipment may include GPS equipment and magnetic equipment and high-quality ground-based gravimeters.

The method for reconnaissance of a potential field from the air described above, in which the data collected according to any of the above methods are combined with any ground or satellite reconnaissance data to improve analysis, and such data includes terrain, spectral, magnetic or other data.

These and other aspects of the invention will be further described solely by way of example, with reference to the accompanying drawings, in which:

FIG. 1 is an aircraft with aerial reconnaissance data and an example of a data processing system adapted to implement an embodiment of the method of the invention;

FIG. 2 is a flowchart of a processing procedure for measuring potential field data for implementing an embodiment of the method of the invention;

FIG. 3 is a flowchart of a procedure for generating flight data for aerial reconnaissance of a potential field according to an embodiment of the method of the invention; and

FIG. 4 is an illustrative set of flight routes for aerial reconnaissance of a potential field, the data of which can be processed according to embodiments of the invention.

Theoretical background

First, we turn to the theoretical foundations that allow a better understanding of the invention.

Potential field data includes, but is not limited to, gravimetric data, gravitational gradiometer data, vector magnetometer data, and true magnetic gradiometer data. Such data can be mathematically described by a number of relations that determine the nature of the change in values depending on spatial coordinates, taking into account various types of measurements. Elements and representations of a potential field can be derived from a scalar quantity.

For a gravitational field, the corresponding potential is the scalar potential of the gravitational field, Φ ( r ), defined as

where r , ρ ( r ′), G - respectively, the position of measurement of the gravitational field, mass density at position r ′ and the gravitational constant. The gravitational field intensity, expressing the effect of the gravitational field, is equal to the spatial derivative of the scalar potential. The gravitational field is a vector, because it has a direction that everyone knows - gravity acts downward. It can be represented by three components with respect to any selected Cartesian coordinate system:

Each of these three components changes in each of these three directions, as a result of which the gradient of the gravitational field is a tensor having nine components:

The mathematical theory of potential fields and fundamental equations and relations arise from an analysis of the properties of a scalar potential function, its derivatives, its Fourier transforms and other mathematical quantities.

According to one of Green's theorems, if any of the spatial derivatives of the scalar potential (including the scalar potential itself) is known on a closed surface, then the value of this spatial derivative is known at all points of the volume bounded by this surface. It follows that if this quantity is known at all points, then by differentiation and integration it is possible to obtain all other derivatives of the scalar potential, including the scalar potential itself, and all its derivatives are actually known at all points of the volume, when only one of the derivatives is known on the surface, covering this volume. This suggests that a complete measurement of any component of any derivative of the scalar potential allows us to calculate any other component of any derivative of the scalar potential. It follows that, at least theoretically, it does not matter what quantity to measure, and the choice of equipment is determined solely by which device measures the desired value with the highest signal-to-noise ratio.

, когда r→0) в конце концов дает:Differentiation of the scalar potential of the gravitational field described above (after solving some issues related to

when r → 0) finally gives:

which in areas free of matter reduces to the Laplace equation, an important fundamental relation in the theory of gravity:

Harmonic functions satisfy the Laplace equation, and many of their properties can be used in the analysis of data collected during the exploration of a potential field.

Data can be analyzed and processed using various methods that work with the data collected during exploration as a starting point, but which then change the data and / or their format so that all values associated with the measured values are on a regular two-dimensional a grid located on a horizontal plane of analysis of a fixed height, the processes used are called "alignment" and "snap to the grid."

Snap to the grid is a geophysical method of numerical processing, the basic principle of which is:

- dividing the reconnaissance area into rectangular cells, the sides of which are usually aligned with the main directions of reconnaissance,

- replacing the actual measurement data with data that is completely "equivalent" to the measurement data, but which are assigned values at the points in the middle of each cell.

Such data is called “gridded” data. There are many ways to make sure that data “conceived” as representing measurement data is truly “equivalent” to measurement data. There are also many ways to select the size of each cell, but all of them are associated with an average partition of lines drawn in two orthogonal directions. When reconnaissance lines are not drawn regularly, as described here, the idea of gridding, although not necessary, can still be used, but there are much more options for selecting cell size and orientation.

When data has this format, it is much more convenient to subject them to mathematical transformations. No data involved in these processes is required to satisfy the Laplace equation. The data are considered as a set of numbers, and statistical and other methods are applied to the numbers to obtain the best estimate of the potential field on the horizontal plane of analysis.

The data can be reduced to a two-dimensional Fourier series so that, in addition to the requirement that the data be at a fixed height, there is a requirement that each data line have 2 ⁿ data elements, that the fast Fourier transform method can be applied, and that the data be collected in orthogonal directions.

The general view of the representation in the form of a two-dimensional Fourier series for the gradient of the gravitational field can be represented as the sum of two-dimensional spatial sinusoidal waves in the form:

where the wave numbers k _m , k _n are related to the size of the reconnaissance area, L _x , L _y in the x , y directions, respectively:

This decomposition is suitable only at a constant height. However, we will later describe the dependence of the coefficients g _zz ( k _m , k _n ) on the wave number and height, which together define the two-dimensional Fourier transform of the gravitational field gradient.

Detailed Description of Preferred Embodiments

Data does not need to be processed as described above if the properties of gravitational or magnetic potential fields are used. The following description is about the gravitational field, but it can easily be extended to magnetic fields.

First of all, we will make a few statements regarding the gravitational field.

1. The gravitational field outside the body can be modeled in all respects, as if it was generated by matter entirely located in an infinitely thin layer on the surface of the body, which exactly repeats the outline of the surface of the body. Such a layer defines an equivalent source, i.e. a source of gravity, which creates essentially (theoretically exactly) the same gravitational signature as the body itself. There are many ways to specify equivalent sources, they can be similar to those described above or can be strictly horizontal, they can be completely or partially above or below the surface of the earth or can be located in another way, but they all have the same property, namely they generate the same gravitational field like earth. Further information can be found in R.J. Blakely, "Potential Theory in Gravity and Magnetic Applications", Cambridge University Press, 1995.

2. The gravitational field outside the body can also be uniquely written as a sequence of modified two-dimensional basic Fourier functions, which is suitable for all positions outside the body. This function is a pronounced harmonic function and is reproduced below. Its shape is the most general and can represent any possible distribution of mass in the body.

According to preferred embodiments, we measure G _zz as a function of the r _measure position using a gravitational gradiometer and work with it without the need to generate other elements of the gravitational field gradient tensor. This can be used to generate a representation of the underlying mass distribution. Here we describe two methods that can be applied, namely, the equivalent source method and the modified Fourier basis function method. It follows from the above Green's theorem that the underlying mass distribution can, in principle, be deduced from G _zz , although the Green's theorem is not used explicitly in the methods described here.

Equivalent Source Method

In this embodiment, the surface of the reconnaissance area is divided into small areas with a side usually of the order of 50 m - they are called plates (hereinafter massive elements). It is easy to directly calculate the gravitational field of each Blakely plate (ibid.), The mass of which is regulated until the best general agreement with the measurement data is obtained. This mass determination is carried out using the standard least squares approximation procedure. The approximation is carried out by comparing the data in the true measurement position with the gravitational field generated by the proposed equivalent source in the same true measurement positions. This process is mathematically rigorous and does not involve any artificial adjustments to the data to match the horizontal rectangular area of intelligence.

After obtaining such an approximation, it is considered as a primary data set. In the course of the entire subsequent analysis to determine the geological structure, the differences between the gravitational field that any given geological structure would generate and the field generated by an equivalent source are compared and minimized. One real advantage of the method is that the best approximation comes from the distribution of mass, albeit artificial, and therefore the solution to the best approximation will automatically satisfy the Laplace equation. This is the difference from the traditional method described above, which creates the best numerical approximation, but does not impose an additional restriction that the data must satisfy the Laplace equation, i.e. that it should come from the real distribution of mass.

The equivalent source method is not required to use a surface consistent with topography, it can use sources that cover any surface that can be at a constant height, above or below the true surface of the earth, can intersect the true surface of the earth, etc. The choice of a surface corresponding to topography is likely to lead to a smaller variation in the mass of individual plates, but the overall result, in principle, will not be much different for any reasonable choice of surface.

Similarly, the plates can be of any size and any shape, they do not even have to be of the same size - indeed, the analysis will be more effective if we allow a change in their size and geometry depending on how quickly the topography in each area changes. The mathematical complexity of the process is determined solely by the number of plates used and how many of these plates are used in the analysis at each position in the field of exploration. One advantage of this method is that for some components of the gravitational field or gradient of the gravitational field, you can use only plates in the data element area, and this significantly reduces the complexity of the analysis. It is clear that this analysis is carried out in space.

After generating an equivalent source, you can predict any derivative of the scalar potential of the gravitational field on any surface by direct calculation. This process is useful both in terms of analysis and in terms of visualization.

In particular, taking into account the mass of each surface element, direct calculation is used to predict the value that the measured value at each measurement point would receive if this value were a component of the gravitational field vector or the gravitational field gradient tensor. In general, it is obtained by summing the form shown below. Here we use gg to denote the measured value, which, as indicated above, is G _zz in some preferred embodiments.

(one)

In the above Equation, F denotes the Green function (Blakely, ibid., On page 185, incorporated by reference) and r _mass-element sets the position of the massive element (for example, its center of gravity or some other given point). Function F is standard and known to those skilled in the art (and can be deduced for any geometry of massive elements). For example, the Green's F function for a rectangular prism is defined in Blakely, ibid., On page 187, enabled by reference; it has 8 members, each of which corresponds to the top of a prism.

In connection with this relation, it is important to indicate that the function "F" is known, but the mass of each element is not. The calculated value in the general case will not coincide with the measured value, and according to one approach we compose the following sum:

(2)

The value of S ultimately determines the total quadratic error S (noise and modeling errors), and by minimizing it, we can find the best approximation gg _calculated . This can be done through standard procedures, for example using Matlab (RTM).

Summarizing the above proof, only the actual masses of all massive elements and, of course, the measurement noise associated with the measurement at each point are unknown for S. Best approximation i.e. the best estimate of the values of these massive elements is obtained if we require that S be minimal in relation to the mass variations of each element. After obtaining the correct coefficients, S is simply the sum of the squared noise terms associated with each measurement, and this is the minimum value that S can take. Differentiating S by the mass of each massive element, i.e. the first derivative of S with respect to m _mass-element must be zero for each massive element. The result is a system of equations in which only the masses of all massive surface elements are variables and where the number of equations is equal to the number of massive elements involved in the approximation procedure. It is convenient to present this system of equations in the form of a matrix and solve it with respect to the values of massive surface elements. Since the number of measurements is usually much larger than the number of equations in the system (i.e., the number of massive elements), for example, at least five or ten times more, the system of equations is excessively limited. This is useful since the values of massive surface elements will in no way correspond to noise; instead of the optimization procedure, for example, the least squares approximation is used to determine the values of massive surface elements, which reduces the noise. In addition, due to the use of the physical model of the gravitational field (real massive elements), the equations obey the Laplace equation, which allows us to approximate the gravitational field, rather than noise.

In practice, massive elements spaced more than a predetermined distance can be virtually neglected, for example, by weighing massive elements according to the distance and setting the weight to zero outside the threshold distance. This threshold distance is usually several kilometers, for example between 1 and 10 kilometers, although it depends to some extent on geography (for example, you may need to increase the distance to cover a large mountain nearby). The result of weighing massive elements to neglect those that are located beyond the threshold distance is that the matrix representing the difference between the calculated and measured values is a sparse matrix. This is useful because such a matrix can contain, for example, from 100K to 500K data elements, and processing costs are significantly reduced if most of its elements are equal to zero.

It is clear to the skilled person that the S value specified above is just one option for fitting the calculated data to the measurement data, and there are many other options. When the plane for the equivalent surface for massive elements is specified, the independent parameters are the masses of the massive elements (since the distance function is known); it is clear to the specialist that there are many numerical methods that can be used to approximate these independent parameters, including, for example, iterative numerical search. One method that has proven useful in practice is to use a variation of Equation 2, which uses a module instead of a quadratic function.

After finding the massive elements, direct calculation (i.e., summing the contributions of the massive elements) allows you to find other components of the scalar potential and, by differentiation, other components of G. The obtained values of G can be compared with the geological model (referred to here as the “interpretation”) to determine the underlying geological structure.

The method of modified basis Fourier functions

) двухмерного преобразования Фурье гравитационного поля переписан в виде произведения коэффициента, не зависящего от позиции (C _mn) и высотно-зависимого коэффициента (

). Т.е.

. В явном виде можно записать гравитационное поле любого распределения массы в формеIn the second embodiment of the method, the modified Fourier basis function method is applied. According to this method, two-dimensional Fourier series expansion is used to represent the measurement data, but each two-dimensional coefficient A _{mn of} each component (

) the two-dimensional Fourier transform of the gravitational field is rewritten in the form of the product of a coefficient independent of position ( C _mn ) and a height-dependent coefficient (

) Those.

. In explicit form, we can write the gravitational field of any mass distribution in the form

In the language of Fourier transforms, A _mn is the two-dimensional Fourier transform of the gravitational field. This representation is the most general, and each component of the expansion that represents the gravitational field in explicit form obeys the Laplace equation (when differentiating the factors of the height-dependent coefficient and reducing the two-dimensional components). Thus, the altitude dependence of each Fourier coefficient is revealed, and it is also clear that the representation of the gravitational field, provided by the knowledge of the coefficients C _mn , allows you to completely determine the gravitational field at any point in space where there is no mass. The decomposition provided by this modified Fourier series can be cut off at one point or another, depending on the desired accuracy of the representation.

также известно. Каждое волновое число выражает гармоническое пространственное изменение базисной функции Фурье, например, каждый коэффициент с данным волновым числом k _m =2π/λ_m будет периодически изменяться в пространстве с периодом λ_m. Дополнительное свойство метода Фурье состоит в том, что для каждого из независимых направлений каждое волновое число будет целым кратным минимального волнового числа, которое соответствует длине волны, в общем случае эквивалентной размеру области разведки.At position r, the measured potential field (gravitational field or gradient of the gravitational field) is known, and for a particular pair of values of k _m and k _n , known as wave numbers, the value of each basis function of the modified Fourier series

also known. Each wave number expresses a harmonic spatial change in the basis Fourier function, for example, each coefficient with a given wave number k _m = 2π / λ _m will periodically change in space with a period of λ _m . An additional property of the Fourier method is that for each of the independent directions, each wave number will be an integer multiple of the minimum wave number, which corresponds to a wavelength that is generally equivalent to the size of the reconnaissance area.

Other decompositions can be applied, for example, in spherical harmonics, which are useful for more extensive areas, in particular, when the curvature of the earth cannot be neglected.

In the general case, the expansion coefficients are determined almost in the same way as described above for the equivalent source method. By choosing the maximum wavelength of interest for each direction and the orientation and origin of the coordinate system for the measurement, one can determine the value of the basis functions at each point in space. After that, the same function of the squared differences S is calculated for the measured quantity, and the best values of the coefficients C _{mn are} determined by minimizing such a function with respect to the variations of C _mn . Thus, as in the first embodiment described above, a system of equations is formed that can be solved with respect to the Fourier series expansion coefficients. These coefficients can then be used to determine (by direct calculation) the gravitational field or the gradient of the gravitational field on any two-dimensional surface that needs to be mapped. It will be shown that in this (and previous) embodiment, the data can be arbitrarily selected, since the data elements are practically not interconnected - all that is needed is a set of dimensions and corresponding ( x , y , z ) positions in order to be able to determine gravitational field or gradient of the gravitational field on any other set of points or indeed on a plane, that is, a map. In addition, it follows that there is no need to clog measurement data to construct a rectangle. In principle, data elements can be considered as a part of an arbitrary shape of a two-dimensional region of maximum dimensions determined by the maximum wavelengths for expansion in a Fourier series in the x and y directions (although, as you can see, the measurement data does not have to lie on a two-dimensional surface). It follows that the values of k _m and k _n can be chosen regardless of the size of the reconnaissance area (here k is the wave number, i.e. 2π / λ, whereas in traditional reconnaissance, the maximum wavelength should correspond to the length or width of the rectangular reconnaissance area).

In particular, the idea outside the course of the Fourier series is to solve the problem expressed by Equation (1) in the Fourier domain, and not in the spatial domain. Further we will assume that g _zz is a measured quantity (also denoted above as G _zz ).

The gravitational field of any body or mass distribution can be expressed in the most general form:

(3)

Where

In Equation (3), the coefficients g _zz ' ( k _m , k _n ) formally do not depend on the height and wave number, they depend only on the studied geology. Note the formal similarity of Equation (3) with the general representation of the two-dimensional Fourier series presented above. The expressions are identical, which is what we need only if

A strong dependence on the height and wave number of standard Fourier transforms is observed, i.e. coefficients g _zz ′ ( k _m , k _n ). That is why it is impractical from a practical point of view to carry out the standard Fourier transform of the data collected during reconnaissance with variable height. It is also clear why it is impossible to recalculate “up” data from point to point; recalculation works only if the exact frequency composition of the quantity is known. You can also see that each component of the expansion of Equation (3) has a separate altitude dependence.

However, the method of modified Fourier basis functions described here does not attempt to implement the Fourier transform on its own - it is, as described above, not a mathematical approach.

можно присвоить значение, которое является точным, когда позиция измерения известна. Дело в том, что мы выбираем значения k, как описано ниже, и r(x,y,z) известно. По существу, выбираются максимальное и минимальное значения для k _x и k _y, например, путем построения вокруг (или немного внутри) района разведки воображаемого прямоугольника, который приблизительно представляет район разведки, и размеры прямоугольника задают максимальную длину волны (значения k). Минимальные значения можно выбирать, например, в зависимости от приближенной средней высоты разведки, например кратного средней высоты разведки между 0.5 и 3. Дело в том, что масштаб длин вариаций зависит от высоты разведки, и, в общем случае, минимальное значение выбирается для представления вариаций, которые ожидаются или наблюдаются на средней высоте разведки, превышающие пороговую значимость, с учетом вычислительной мощности. Для иллюстрации идеи вышеупомянутый член exp(-kz), где z= высота разведки, уменьшен приблизительно в e^-6 раз для длин волны, равных высоте разведки.This process provides that all data elements are processed in the same way and that

You can assign a value that is accurate when the measurement position is known. The fact is that we choose the values of k , as described below, and r ( x , y , z ) is known. Essentially, the maximum and minimum values for k _x and k _y are selected, for example, by constructing around (or slightly inside) the reconnaissance area of an imaginary rectangle that approximately represents the reconnaissance area, and the dimensions of the rectangle specify the maximum wavelength ( k values). The minimum values can be selected, for example, depending on the approximate average reconnaissance height, for example, a multiple of the average reconnaissance height between 0.5 and 3. The fact is that the scale of the lengths of the variations depends on the reconnaissance height, and, in general, the minimum value is chosen to represent the variations that are expected or observed at an average intelligence height that exceeds threshold significance, taking into account the computing power. To illustrate the idea, the aforementioned term exp (- kz ), where z = reconnaissance height, is reduced approximately e ^-6 times for wavelengths equal to reconnaissance height.

известны в каждой точке измерения данных. После этого неизвестными являются коэффициенты g _zz′(k _m,k _n), и процесс аппроксимации однозначно становится только процессом получения наилучших оценок коэффициентов.Then we have a system of equations based on Equation (3) in an amount equal to the number of data elements used, due to which the measured values of the gravitational field gradient, including noise, and the quantity

known at every data measurement point. After that, the coefficients g _zz ′ ( k _m , k _n ) are unknown, and the approximation process uniquely becomes only the process of obtaining the best estimates of the coefficients.

According to Equation (3), this gives the calculated g _zz , and by analogy with Equation (1), one can derive a variant of Equation (2). This provides a system of equations in an amount equal to the number of unknowns, which in this case are the values of the coefficients g _zz . This is done in the same way as in the equivalent source method, i.e. the coefficients are determined by the least squares approximation procedure. An important point is that in this form, the coefficients g _zz ′ ( k _m , k _n ) do not have an explicit dependence on the height and wave number.

This method has a similar advantage over the distribution of equivalent sources in that the solution is harmonic, since each term in the expansion of Equation (3) is clearly harmonic. Hardware noise is not harmonic, so this method, even by itself, has the ability to significantly eliminate noise in the process.

This method, like the equivalent source method, does not need to bind data to a regular grid. One unexpected additional advantage of the method is that, in contrast to the Fourier series method itself, it is not limited to the wavelengths that can be used for analysis. This is an implicit result, depending on the suitability of the method of modified Fourier series, in the most general expression, in any area that may be of interest. The process involves selecting the maximum wavelengths of interest in two orthogonal directions of the reconnaissance plane, which leads to the maximum wavelength of interest in each direction, λ _{x max} , λ _{y max} . This wavelength reflects the minimum wave number in each direction, defined as

All wave numbers in the expansion of Equations (3) are their multiple integers. In this way:

An additional advantage is that this method does not have to have degree 2 as the number of data elements to use in the analysis of each line, which is necessary according to the fast Fourier transform method. This eliminates the need to type data to achieve this.

In contrast to the equivalent source method, where the analysis is carried out in the spatial domain, the analysis of Fourier series is carried out in the frequency domain. By frequency we mean the spatial frequency, which indicates how many periods a given component has a unit distance measure, and this is expressed by the wave numbers described above - the larger the wave number, the greater the number of periods per unit distance and the shorter the repetition distance. The proposed method does not work explicitly in any field, it only allows you to compile a system of equations from which you can calculate the best estimates of the unknowns.

Fourier methods in practical applications usually require measurements in a rectangular region, and the minimum wave numbers represent the largest wavelengths that can be used to represent the data - the largest wavelengths clearly express the size of the reconnaissance area in each direction. When the intelligence area does not meet this criterion, data is usually generated in a process called stuffing so that the transformed dataset matches it.

The modified Fourier basis function method has many advantages over traditional Fourier analysis. For example:

1. It is not necessary to carry out Fourier transforms at all - we know that there will be a standard format, and the coefficients in the expansion of Equations (3) must be determined by the best approximation process, and not by calculating the Fourier transforms in explicit form.

2. The wave numbers to be used are not required to be integer multiples of the size or shape of the reconnaissance area. The fact is that we know the form of the Fourier transform, and we determine the coefficients through the above-described best approximation process.

Perhaps the most impressive result is that intelligence data can be collected at inconsistent heights. The traditionally used two-dimensional Fourier transforms must be carried out at a constant height, and the Fourier transforms included in Equation (3) are highly dependent on the height. This functional dependence is explicitly expressed in Equation (3), and the coefficients g _zz ′ ( k _m , k _n ) no longer depend on the height.

Overview

The embodiments of the methods described here make full use of the actual measurement data, and both are mathematically rigorous; they do not damage the data by linking them to a regular grid of constant height, the generated solutions are harmonic, and the data is not required to have a power of two as the number of data elements in two orthogonal directions.

In the general case, the process involves the use of all data from each data element and tries to generate an equivalent surface mass distribution or a set of coefficients of the modified Fourier series with the best approximation of the data in the field of exploration.

This is a fundamental difference from the processing method, in which it is assumed that the data are collected from a fixed height, even if this is not true, and new data is generated from the measurement data for the sole purpose of generating data on a regular two-dimensional grid. This gridded dataset assigns values to measurement data that is not measured and assigned to positions where the aircraft did not collect data, although this is incorrect.

Errors arising in such a process, with a high degree of probability, acquire significant dimensions if, in this situation, the approximation of a fixed height is weak. They are also great if the pilot tries to fly as close to the ground as possible to maximize the signal from small features located relatively close to the surface of the earth - these features cause the appearance of short-wave components in the expansion in the modified Fourier series. Finally, the errors are not so large in the presence of large instrumental noise, since the errors associated with extrapolation are smaller than the errors associated with the device.

In FIG. 1 shows an example of an aircraft 10 for prospecting a potential field to obtain data for processing in accordance with the method described above. The aircraft 10 contains an inertial platform 12, on which a gravity gradiometer 14 is installed, which provides intelligence data of the potential field to the data collection system 16. The inertial platform 14 is rigidly connected to the inertial measuring unit (IMU) 18, which also provides data collection system 16 typically containing orientation data (e.g., pitch, roll and yaw data), angular velocity and angular acceleration data, and airplane acceleration data. The aircraft is also equipped with a GPS 20 differential system and a LIDAR 22 system or similar system to provide data on the height of the aircraft above the underlying terrain. The aircraft 10 can also be equipped with other equipment 24, for example, a magnetometer, a TDEM system and / or a hyperspectral imaging system, which again feed their signals to the data acquisition system. The data acquisition system 16 also receives signals from conventional aircraft equipment 26, which may include, for example, altimeter, air and / or ground speed data, etc. The data acquisition system 16 may provide some initial data preprocessing, for example, to adjust lidar data for the movement of an airplane and / or for combining data from IMU 18 and DGPS 20. The data collection system 16 may be provided with a communication line 16a and / or non-volatile storage 16b to provide storage of potential data collected A la and positions for further processing. A network interface (not shown) may also be provided.

Data processing for generating cartographic data for prospecting for a potential field is usually (but not necessarily) carried out offline, sometimes not in the country where the intelligence was collected. The shown data processing system 50 comprises a processor 52 connected to a data and code storage device 54, an input / output system 56 (for example, containing interfaces for a network and / or storage media and / or other communication means), and to a user interface 58, for example containing a keyboard and / or mouse. The code and / or data stored in the memory 54 can be transferred to a removable storage medium 60. During operation, the data includes data collected during the exploration of a potential field, and the code contains a code for processing this data to generate map data, for example, in accordance with the procedure shown in FIG. 2 described below.

In FIG. 2 illustrates an illustrative procedure implemented on a data processor, which may, according to embodiments, comprise a general-purpose computer system for processing aerial reconnaissance data in accordance with the methods described above. Thus, in step S200, the procedure inputs the measurement data of the potential field, for example, a gravitational gradiometer, and the corresponding data of the three-dimensional position. Optionally, some pre-processing may be applied in step S200a, for example, to remove anomalies and / or to reduce (or increase) or select the data to be processed.

In step S202, the procedure constructs an excessively bounded system of equations relating potential field data, three-dimensional position data, and a set of field mapping parameters. In particular, the procedure builds a system of equations that correlate the measurement of the potential field with the function of the corresponding three-dimensional position ( s ( r - r ′)), multiplied by the field mapping parameter. Preferably, the procedure uses a representation of the potential field, in particular a position function that obeys the Laplace equation, for example, through the above-described equivalent source or a modified basic Fourier function. Optionally, at this stage (S204), these terrain corrections may be included. The procedure solves this system of equations (S206), for example, by the traditional least squares method to determine a substantially self-consistent set of field mapping parameters. They actually provide a map of the prospected potential field and therefore constitute one preferred procedure output. Then (S208), a direct calculation can be performed using these parameters to generate the desired map of the potential field on the surface, for example, a surface approximating a plot of land, where and when it is required.

For traditional aeronautical gravimetric reconnaissance, it was not necessary to fly very close to the ground, since the instruments were relatively insensitive and were additionally configured to perceive only large wavelengths. Exploration was carried out at a more or less constant height or at a height at which it would be reasonable to assume that the data comes from a constant height.

However, for any reconnaissance using new, highly sensitive gravitational gradiometer systems, which are also capable of resolving much shorter waves, it is advisable to fly as close to the ground as possible to maximize the signal, in particular, contained in short-wave components. It is unlikely that these types of reconnaissance adequately met the criterion of constant height, but all modern analysis methods are based on the fact that this is so.

However, you can use the equivalent source method or the modified Fourier transform to process the data and combine it with a fundamentally new flight method to explore the potential field.

In its most general form, the method involves flying around a completely disparate set of reconnaissance lines, collecting data from lines and using data and the absolute position of their collection, obtaining the best approximation parameters for the masses of plates of an equivalent source or for the components of the modified Fourier transform.

Reconnaissance lines do not have to be straight, do not have to be horizontal, do not have to go in orthogonal directions, lines in approximately orthogonal directions do not have to intersect. Ideally, flight routes should follow the terrain as accurately as possible without any other restrictions. Of course, any other flight method is possible, taking an intermediate position between this reconnaissance flight method and methods involving flight routes intersecting at right angles at a constant height, and any reconnaissance may include elements of any flight method. The power and mathematical precision of analytical methods makes these flight procedures possible.

Obviously, data collected using this flight method can be further processed before and after using any of the above processes. You can use any existing methods of reducing noise or combining data. Topographic effects can be largely eliminated using high-quality DEM, in fact, any processes associated with more traditional data processing can be used.

An airplane can be any geophysical exploration aircraft capable of flying at low altitudes. In practice, the aircraft will be loaded with as much equipment as it can carry, based on safety requirements and a reasonable flight time. The equipment selected will measure signals related to geology and signals related to plane motion. The latter are used, in particular, for gravimetric reconnaissance, for the correction of measurements made by equipment selected for measuring geological properties.

In FIG. Figure 3 shows a logical flowchart of a procedure for generating aerial reconnaissance data defining a flight pattern for reconnaissance of a potential field, the results of which can be processed using the methods described above.

At step S300, the procedure enters terrain data and, for example, through a user interface, data defining a desired reconnaissance area. Then, in step S302, the procedure builds an envelope surface on top of the selected terrain to determine a reconnaissance flight pattern containing a set of flight paths. The construction of the envelope surface may be subject to restrictions on the maximum slope in any direction on the surface, and initially flight routes may follow a regular pattern. Then, however, in step S306, the procedure adjusts the surface and / or flight paths to adapt the routes to the surface. Here the restriction on the maximum speed of ascent / descent (determined on the basis of the characteristics of the aircraft) comes into force, but it should be applied only along the route. Thus, in other directions, for example, orthogonal to the route, the inclination of the surface may exceed the value specified by this restriction. Additionally or alternatively, in step S308, the procedure adjusts the surface and / or flight paths to more accurately adapt the routes to the surface of the underlying terrain. To do this, it is necessary to allow the routes to be curved, non-parallel, significantly different in height at the intersection (for example, more than 50 meters, 100 meters or 200 meters) lying on a surface whose inclinations exceed the maximum ascent / descent speed of the aircraft, or not lying on the same surface. After carrying out such an adaptation, the procedure outputs aerial reconnaissance data (S310) defining a specific set of flight routes. The pilot can then use this data to pilot the aircraft in accordance with a specific reconnaissance scheme.

Obviously, unlike traditional grid-fixing systems, such methods allow you to specify flight paths along the valleys, near the bottom of the valley, where other methods will be limited by the minimum approach of the aircraft to the ground in such a situation, due to the combination of the grid-attached circuit and the maximum speed lifting / lowering the aircraft. It is also obvious that in the general case it is possible to specify a set of routes following the terrain, since the methods described here allow you to process the data of such aerial reconnaissance. The advantage is that the data obtained by such methods are much more accurate due to the significant decay rate of the amplitude of the perturbations of the potential field with height above the surface of the earth.

In FIG. Figure 4 shows an example of an airborne reconnaissance route, data from which can be processed using the methods described above. The figure shows examples of the types of routes along which these methods allow you to fly.

On flat areas, all flight strategies converge, but on hilly or truly mountainous areas, the proposed method has significant advantages. In such areas, each part of the reconnaissance area is analyzed relatively independently, and a flight strategy is developed over that area.

In such situations, the exploration area is analyzed for its topography, and an aerial reconnaissance strategy is developed based on the geological targets of interest and how the area can be circled to best identify these geological targets. If, as in the usual case, it is necessary to fly as close to the ground as possible at all reconnaissance points, then reconnaissance lines will become fragmented with relatively little connectivity. The aircraft can only rise and fall at a given speed, and an appropriate clearance is necessary to safely pass over the ridges of the mountains. Lines “down” or “up” along the valleys will not intersect with the lines “crossing” the valleys, or they will intersect with much fewer intersections. Crossovers are generally considered important for getting rid of low-frequency noise (often called drift), and this is another consideration to consider when designing intelligence.

Equipment desirable for standard reconnaissance includes a gravity gradiometer; gravimeter; inertial measuring unit (IMU); GPS lidar; magnetic gradiometer; magnetometer; altimeter; radar altimeter; barometer; spectrometer; hyperspectral image builder; EM TDEM navigation software; data collection equipment.

When a flight strategy is developed, actual reconnaissance and data collection is performed. The analysis uses real data from the potential field measurement system, this data is corrected for any known artifacts associated with the measurements (for example, aircraft tilt, aircraft accelerations, pressure artifacts, etc.), and then the data is analyzed as described above. The flight is carried out at low altitudes due to the strong altitude dependence of the measured signal, in particular, signals having small wavelengths, i.e. large wave numbers.

Surely, a specialist can offer many other effective alternatives. It should be understood that the invention is not limited to the described embodiments and encompasses modifications obvious to those skilled in the art, within the spirit and scope of the appended claims.

Claims (29)

1. The method of reconnaissance of the potential field of the earth to determine the cartographic data for mapping the field contains the steps at which
perform airborne gravimetric reconnaissance of the potential field of the earth in three dimensions and obtain measurement data of the potential field;
enter the measurement data of the potential field, and the measurement data of the potential field contain data specifying a set of measurements of the potential field and the corresponding positions, and each position sets the measurement position of the potential field in three-dimensional space,
determine the set of relations connecting the measurement of the potential field with the function of the corresponding position in three-dimensional space, multiplied by the field mapping parameter, and
define, in essence, a self-consistent set of field mapping parameters for a set of relations for determining, thus, the cartographic data. 2. The method according to claim 1, wherein the cartographic data comprises a set of field mapping parameters. 3. The method according to claim 1, wherein the cartographic data comprises data mapping a field on the surface, the method further comprises determining a field on the surface from a set of field mapping parameters. 4. The method according to claim 1, 2 or 3, in which the ratios contain joint equations, and in which at the stage of determining the field mapping parameter, the joint equations are solved. 5. The method according to claim 4, in which the number of measurements of the aggregate of the potential field is greater than the number of joint equations, and in which the noise reduction procedure is used at the solution stage. 6. The method according to claim 1, 2 or 3, in which the ratios are set by means of a sparse matrix, and in which, at the stage of determining the parameters of the field mapping, a numerical method is used. 7. The method according to claim 1, in which the function of the corresponding position essentially satisfies the Laplace equation. 8. The method according to claim 1, in which the field is represented by a set of massive elements, each of which has a corresponding mass and a corresponding position, in which each field mapping parameter contains a mass position, and in which the function of the corresponding position is a function of the difference between the measurement position of the potential field and position of the massive element. 9. The method according to claim 1, in which the field is represented by harmonic decomposition having a set of decomposition coefficients, and in which each field mapping parameter contains a decomposition coefficient. 10. The method according to claim 9, in which the coefficients in the view are essentially independent of the height above ground. 11. The method according to claim 1, in which the measurement data of the potential field contain one or more of the gravimetric data and the data of the gravitational gradiometer, and in which the field represents the gravitational field. 12. A medium carrying a processor control code for implementing the method according to claim 1. 13. A data processing system for processing data of potential field measurements obtained by prospecting a potential field of the earth for determining cartographic data for mapping a field, comprises
a data storage device for storing measurement data of the potential field, the measurement data of the potential field containing data defining a set of measurements of the potential field and corresponding positions, each position setting the measurement position of the potential field in three-dimensional space,
a program storage device for storing a processor control code and
a processor connected to a data storage device and a program storage device for loading and executing a control code, the code comprising a code instructing the processor
enter the measurement data of the potential field,
determine the totality of the relationships between the potential field measurements and the positions, each relationship correlating the potential field measurement with the function of the corresponding position in three-dimensional space, multiplied by the field mapping parameter, and
define, in essence, a self-consistent set of field mapping parameters for a set of relations for determining, thus, map data. 14. A method for conducting aeronautical gravimetric reconnaissance to provide data for a map of the gravitational field in which aeronautical gravimetric reconnaissance of the potential field of the earth is performed in three dimensions and the measurement data of the potential field are obtained;
moreover, the measurement data contains a set of measurements of the gravitational potential field, with each of which a measurement position in three-dimensional space is associated, use the measurement data to estimate the coefficients by which the function of the three-dimensional position in the harmonic expansion is multiplied to determine, therefore, the representation of the gravitational field in the exploration area for maps of the gravitational field. 15. The method according to 14, in which the harmonic decomposition contains the expansion in a Fourier series, and in which the function of the three-dimensional position contains a function having the form equivalent to

, where x, y and z define a position in three-dimensional space, k _m and k _{n are} positive, and

. 16. The method according to 14 or 15, in which the coefficients are formally independent of height. 17. A method of conducting aeronautical gravimetric reconnaissance to provide data for a map of the gravitational field in which aeronautical gravimetric reconnaissance of the potential field of the earth is carried out in three dimensions and the measurement data of the potential field are obtained;
moreover, the measurement data contain a set of measurements of the gravitational potential field, each of which is associated with the measurement position in three-dimensional space,
use an equivalent source representation of a gravitational field containing a set of massive elements having an appropriate mass and corresponding position,
determine the calculated value of the potential field in each position of the measurement;
multiply the difference function between the measured position and the position of the massive element by the corresponding mass and
use the measurement data to estimate the masses and aggregate of massive elements for a map of the gravitational field. 18. A method of mapping a gravitational field comprises the steps of
enter the measurement data obtained in aeronautical gravimetric reconnaissance carried out in three-dimensional space, and the measurement data contain a set of measurements of the gravitational potential field, each of which is associated with the measurement position in three-dimensional space,
determining a set of relations between potential field measurements and positions, each relationship relating a potential field measurement to a function of the corresponding position in three-dimensional space multiplied by the field mapping parameter, and
map the gravitational field, defining, in essence, a self-consistent set of field mapping parameters for the totality of ratios. 19. The method according to claim 1, further comprising the step of exploring the field using an aircraft to collect measurement data to determine the totality of the relationships, and in which, at the reconnaissance stage, a set of routes having one or more of the following features are flown around:
two routes intersect at heights differing by at least 50 m,
in the reconnaissance area, routes in the same general direction are not parallel by more than 5 °,
routes include curved routes,
routes from a set of routes taken together, essentially, do not lie on the surface,
heights with distance in different orthogonal directions of the surface differ by more than 5%. 20. The method according to 14, further comprising the step of exploring the field using an aircraft to collect measurement data to determine the totality of the relationships, and in which, at the reconnaissance stage, a set of routes having one or more of the following features flies around:
two routes intersect at heights differing by at least 50 m,
in the reconnaissance area, routes in the same general direction are not parallel by more than 5 °,
routes include curved routes,
routes from a set of routes taken together, essentially, do not lie on the surface,
the routes from the set of routes taken together define a surface in which at least one of the routes defines one of two orthogonal directions on the surface, so that the rates of change of height with distance in different orthogonal directions of the surface differ by more than 5%. 21. The method according to 17, further comprising the step of exploring the field using an aircraft to collect measurement data to determine the totality of the relationships, and in which, at the reconnaissance stage, a set of routes having one or more of the following features flies around:
two routes intersect at heights differing by at least 50 m,
in the reconnaissance area, routes in the same general direction are not parallel by more than 5 °,
routes include curved routes,
routes from a set of routes taken together, essentially, do not lie on the surface,
the routes from the set of routes taken together define a surface in which at least one of the routes defines one of two orthogonal directions on the surface, so that the rates of change of height with distance in different orthogonal directions of the surface differ by more than 5%. 22. The method according to p. 18, additionally containing a stage in which they scout the field using an aircraft to collect measurement data to determine the totality of the ratios, and in which, at the stage of exploration, a set of routes are circled that have one or more of the following features:
two routes intersect at heights differing by at least 50 m,
in the reconnaissance area, routes in the same general direction are not parallel by more than 5 °,
routes include curved routes,
routes from a set of routes taken together, essentially, do not lie on the surface,
the routes from the set of routes taken together define a surface in which at least one of the routes defines one of two orthogonal directions on the surface, so that the rates of change of height with distance in different orthogonal directions of the surface differ by more than 5%. 23. A medium carrying a processor control code for implementing the method according to any one of claims 14, 15, and 17-20. 24. The method for conducting aerial reconnaissance of a potential field comprises the steps of conducting an airplane through a set of routes and measuring potential field data at points on routes in which the set of routes has one or more of the following features:
two routes intersect at heights differing by at least 50 m,
in the reconnaissance area, routes in the same general direction are not more than 5 ° parallel,
routes include curved routes,
routes from a set of routes taken together, essentially, do not lie on the surface,
the routes from the set of routes taken together define a surface in which at least one of the routes defines one of two orthogonal directions on the surface, so that the rates of change of height with distance in different orthogonal directions of the surface differ by more than 5%. 25. A data carrier carrying navigation data defining a set of aerial reconnaissance routes of a potential field according to paragraph 24. 26. A method for generating aerial reconnaissance data comprises the steps of:
determining a reconnaissance flight pattern by applying a surface to the terrain to be reconnoitered, in accordance with the condition of the maximum speed of ascent / descent of the aircraft, and
generating aerial reconnaissance data for a plurality of routes essentially on the surface, and
in which the method further comprises adjusting the surface and / or one or more routes to reduce the height of one or more routes, so that in at least one direction on the surface, orthogonal to the route, the condition of maximum speed of ascent / descent has been exceeded. 27. The method of generating aerial reconnaissance data according to claim 26, wherein the aerial reconnaissance data sets a method for conducting aerial reconnaissance of a potential field, comprising the steps of conducting an airplane along a set of routes and measuring potential field data at points on routes in which the set of routes has one or several of the following features:
two routes intersect at heights differing by at least 50 m,
in the reconnaissance area, routes in the same general direction are not more than 5 ° parallel,
routes include curved routes,
routes from a set of routes taken together, essentially, do not lie on the surface,
the routes from the set of routes taken together define a surface in which at least one of the routes defines one of two orthogonal directions on the surface, so that the rates of change of height with distance in different orthogonal directions of the surface differ by more than 5%. 28. A medium carrying a processor control code for implementing the method of claim 26 or 27. 29. A data carrier carrying aircraft intelligence data according to paragraph 26 or 27.

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