JP6653517B2 - Three-dimensional data processing method, three-dimensional data processing program, and three-dimensional data processing device - Google Patents

Description

  The present technology relates to a three-dimensional data processing method, a three-dimensional data processing program, and a three-dimensional data processing device.

  As a method of representing a position in a three-dimensional space, a method using an orthogonal coordinate system based on predetermined X axis, Y axis, and Z axis, or a polar coordinate system represented by one radial and two declinations is used. There is a way. In addition, there are various methods for handling events such as rotation of an object in space and propagation of waves. For example, an event can be represented using a matrix for performing a coordinate transformation of a vector from one coordinate space to another coordinate space. Further, an Euler angle expressing one angular displacement by a plurality of rotations around three axes perpendicular to each other may be used. There is also a method of defining a quaternion by extending a complex number to express three dimensions. As a technique using a quaternion, for example, a technique has been proposed in which an operation path of a manipulator is interpolated to control the operation (Patent Document 1).

JP 2004-284004 A

  By the way, when expressing a direction in space, for example, the conventional method is difficult for the user to grasp. For example, understanding an event by multiplying it by a transformation matrix requires enormous effort and also makes it difficult for the user to grasp the essence of the event. In the case of the Euler angle, since the axis serving as the rotation reference changes after three rotations, it is difficult for the user to intuitively grasp the event. In addition, since the angular displacement can be expressed by three rotations around an arbitrary axis, it is difficult for the user to intuitively grasp the event even if the expression indicating a certain direction is not uniquely determined. Regarding quaternions, it is difficult to grasp the relationship with the space, and an operation rule for defining three imaginary numbers is provided, so that it is difficult for the user to understand.

  The present invention has been made in view of the above-described problem, and has as its object to represent and process a three-dimensional space in a manner that is easy for a user to grasp spatially.

In the three-dimensional data processing method according to the present invention, the three-dimensional polar coordinates A = r · e ^{iφ + jθ} (where i ² = −1, j ² = −1, i · j = 0, j · f (φ) = j · f (0), φ is the declination from the real axis on the real axis−i-axis plane, θ is the declination from the real axis−i-axis plane, and f (φ ) Indicates the position of an object using a term having a variable φ, and the computer executes information processing in a three-dimensional space.

  As described above, by providing unique constraints on the imaginary numbers i and j, the three-dimensional polar coordinates can be expressed as a complex function of a space including the real axis, the imaginary i-axis, and the imaginary j-axis.

The information processing in the three-dimensional space, add, subtract, multiply, and divide against radial rotation of the polarization angle direction, may include a fine min radial direction or polarization angle direction. With these processes, the calculation results match even under the above-mentioned restrictions.

  In addition, the step of acquiring waveform data relating to seismic waves from sensors at a plurality of observation points, and the distance between each observation point and the epicenter and the epicenter using three-dimensional polar coordinates based on a difference between times when the plurality of waveform data are observed. The step of estimating the position of may be further executed by a computer. This makes it possible to easily estimate the epicenter using the three-dimensional polar coordinates using the virtual imaginary numbers.

The contents of the means for solving the above problems can be combined as much as possible without departing from the problems and technical ideas of the present invention. Further, a program that causes a computer to execute the above means, and an apparatus including a processing unit that executes the above means may be provided. The program may be provided by being recorded on a computer-readable recording medium. The computer-readable recording medium refers to a recording medium in which information is accumulated by electrical, magnetic, optical, mechanical, or chemical action, and can be read by a computer. Among such recording media, those removable from a computer include, for example, optical disks, magneto-optical disks, flexible disks, magnetic tapes, memory cards, and the like. HDD (Hard Disk Drive) as a recording medium fixed to the computer,
Examples include an SSD (Solid State Drive) and a ROM (Read Only Memory).

  ADVANTAGE OF THE INVENTION According to this invention, a three-dimensional space can be represented and processed in the aspect which a user can easily grasp spatially.

It is a figure for explaining polar coordinate display in three-dimensional space. It is a figure for explaining the relation between hypocenter e and observation point m. It is a figure for explaining refraction of a seismic wave in a boundary of a stratum. FIG. 4 is a diagram for explaining measured waveform data. It is a figure for explaining a seismic wave which propagates beyond a boundary of a stratum. It is sectional drawing for demonstrating the seismic wave which propagates beyond the boundary of a stratum. It is sectional drawing for demonstrating the seismic wave which propagates beyond the boundary of a stratum. It is a block diagram showing the outline of a system. It is a functional block diagram showing an example of a three-dimensional data processing device. FIG. 2 is a device configuration diagram illustrating an example of a computer. It is a process flow which shows an example of a hypocenter estimation process.

ここで、図１に点Ａを示すとおり、ｒは動径であり、原点Ｏからの距離を示す。また、φは、Ｘ−Ｙ平面上におけるＸ軸からの偏角である。θは、Ｘ軸上の点を原点Ｏを中心に偏角φだけ回転させた回転後の点及びＺ軸が含まれる平面上におけるＸ−Ｙ平面からの偏角である。換言すれば、θは点ＡからＸ−Ｙ平面へ下ろした垂線の足をＨとしたとき、原点Ｏ及び点Ａを通る直線と原点Ｏ及び点Ｈを通る直線とのなす角である。また、φは原点Ｏ及び点Ｈを通る直線とＸ軸とのなす角である。すなわち、本発明で用いる三次元極座標のｒ、φは一般的な動径、偏角であるが、θはＺ軸からでなくＸ−Ｙ平面からの偏角とする。 <Overview of processing>
According to the polar coordinate display in the three-dimensional Euclidean space, the coordinates of a certain point A can be expressed as in the following Expression 1.

Here, as shown by a point A in FIG. 1, r is a moving radius and indicates a distance from the origin O. Φ is a declination from the X axis on the XY plane. θ is a point after rotation of a point on the X-axis by the argument φ around the origin O and an argument from the XY plane on a plane including the Z-axis. In other words, θ is an angle formed by a straight line passing through the origin O and the point A and a straight line passing through the origin O and the point H, where H is a perpendicular foot lowered from the point A to the XY plane. Φ is an angle between a straight line passing through the origin O and the point H and the X axis. That is, r and φ in the three-dimensional polar coordinates used in the present invention are general radial and declination angles, but θ is a declination angle not from the Z axis but from the XY plane.

ただし、ｉ及びｊは虚数であり、
ｉ^２＝−１
ｊ^２＝−１
ｉ・ｊ＝０
ｊ・ｆ（φ）＝ｊ・ｆ（０）
であるものとする。 In the complex function display of the three-dimensional polar coordinates according to the present invention, the above-described point A with respect to a predetermined coordinate (origin) is represented as in the following Expression 2. Here, a space consisting of one real axis and two imaginary axes is considered.

Where i and j are imaginary numbers,
i ² = -1
j ² = -1
i · j = 0
j · f (φ) = j · f (0)
It is assumed that

  It may be easier for a user to intuitively understand a polar coordinate system than to use a rectangular coordinate system. In other words, in the case where the direction such as the rotation of an object in a space or the propagation of a wave is expressed, by using a distance and an angle from a predetermined reference (origin), the user may be able to grasp the event at a glance. is there. In the present invention, the above definition is adopted, and in a predetermined application, three-dimensional polar coordinates can be handled by a complex function.

これは、実軸、虚数ｉ軸及び虚数ｊ軸からなる空間の複素関数によって点Ａを表したものである。すなわち、点Ａ（r・cosφ・cosθ，r・sinφ・cosθ，r・sinθ）という一般的な三次元極座標の変数ｒ、φ、θを用いて表したＸ−Ｙ−Ｚ直交座標系の成分（Ｘ，Ｙ，Ｚ）表示と一致する。 (Euler's formula)
By using Equation 2, the following Equation 3 holds.

This represents the point A by a complex function in a space consisting of a real axis, an imaginary i-axis, and an imaginary j-axis. That is, a component of an XYZ orthogonal coordinate system expressed using variables r, φ, and θ of a general three-dimensional polar coordinate called a point A (r · cosφ · cosθ, r · sinφ · cosθ, r · sinθ) It matches the (X, Y, Z) display.

(Calculation for radial and declination)
As shown in Equation 4, addition and subtraction can be performed on the radius r. That is, there is an additive property.

なお、α＝１／β（β≠０）とする。 In addition, as shown in Equation 5, multiplication and division can be performed on the moving radius r. That is, there is homogeneity.

Note that α = 1 / β (β ≠ 0).

In addition, as shown in ^Equation 6, the operation of rotating by Δφ in the direction of declination φ can be calculated by multiplying by ^eiΔφ .

Similarly, as shown in ^Equation 7, the operation of rotating by Δθ in the declination θ direction can be calculated by multiplying ^eiΔθ .

(differential)
The derivative in the radial direction is obtained as shown in Expression 8.

The derivative in the φ direction is obtained as shown in Expression 9.

Similarly, the derivative in the θ direction is obtained as shown in Expression 11.

As described above, the derivatives in the φ direction and the θ direction are the original functions. For example, in the case of a trigonometric function, when a derivative is obtained, the sine and the cosine are exchanged with each other, but the exponential function described above makes it easier for the user to handle .

As described above, the application of Euler's formula, the four arithmetic operations on the radial radius r, the rotation of the declination φ from the X axis on the XY plane, the point after rotation and the Z axis on the plane including the Z axis rotation of the deflection angle theta, the calculation finely minutes say, it is possible to display complex function of the three-dimensional polar coordinates. Since it can be represented as a complex function of a space composed of a real axis, an imaginary i-axis, and an imaginary j-axis, it is easy for the user to grasp the position and direction in the space.

<Embodiment>
INDUSTRIAL APPLICABILITY The present invention can be used for three-dimensional information processing in various fields such as architecture, civil engineering, vibration, fluid, electromagnetism, and aviation. Here, as an example, a method of estimating the epicenter of an earthquake will be described.

Ｒ_ｍは、震源からｍ地点までの距離である。ΔＴ_ＰＳ（ｍ）は、ｍ地点におけるＰ波とＳ波との到達時刻の差である。また、ｖ_ｐは、現地の地盤におけるＰ波の速度、ｖ_ｓは、現地の地盤におけるＳ波の速度である。 (principle)
FIG. 2 is a diagram for explaining the relationship between the epicenter e and the observation point m. In this embodiment, at three or more observation points that are not linear (m, m + 1, and m + 2 in the example of FIG. 2), the acceleration, velocity, or displacement is continuously measured in association with time to acquire waveform data. I do. In this embodiment, the ground surface is treated as a plane, and the observation points are assumed to be on the same XY plane (also referred to as “ground surface”). You may make it set. The number 12 is the difference between the arrival times of the P wave and S wave at the observation point m with the case ground is uniform between the epicenter e and observation point m, the formula expressed using the distance between the seismic source e is there.

R _m is the distance from the epicenter to the point m. ΔT _PS (m) is the difference between the arrival times of the P wave and the S wave at the point m. In addition, v _p, the speed of the P wave in the local ground, v _s is the velocity of the S wave in the local ground.

By transforming equation ( 12) , the distance R _m from the epicenter to the point _m is obtained as in the following equation ( 13) .

By the way, when the epicenter e and the observation point m on the ground surface are separated to some extent, the ground between the two points is not usually uniform and includes a plurality of strata. Also, the speed at which seismic waves propagate varies from stratum to stratum. Then, the seismic wave is refracted at the boundary of the stratum where the propagation speed of the seismic wave is different. FIG. 3 is a schematic longitudinal sectional view when two types of strata exist between the epicenter e and the observation point m. As shown in FIG. 3, the formation rate of the traveling wave propagation is V _1, the speed of the traveling wave propagation may exist and strata is V _2, the speed V ₁ and V ₂ and seismic progresses The relationship with the angle is as shown in Expression 14 according to Snell's law.

Here, placing the provisional coordinates of source e is unknown and _{(X e, Y e, Z} e). Also, setting the origin O of the provisional on the surface of the earth, it is assumed each observation point coordinates _{(X m, Y m, Z} m) of. At this time, the position vector M at the point m starting from the epicenter e is represented by Expression 15 when expressed using polar coordinates.

Then, the functions shown in the following Expressions 16 to 19 are established by the vector to the point m when the epicenter e is the starting point. The declinations φ and θ are declinations to point m when the epicenter e is the origin. When the point m is on the ground surface, _Zm is 0.

Incidentally, T _m is a predetermined waveform (e.g., the maximum value in a predetermined period of the amplitude of the S wave as shown by the arrows in FIG. 4) time time was observed, T _e is the predetermined waveform generated in the epicenter, t _m Is the time required for a given waveform to propagate to point m. Also, v is the speed at which the S wave propagates. FIG. 4 is an example of data obtained by measuring the amplitude of a body wave (including a P wave and an S wave). Derivation of Expression 18 from Expression 16 based on Expression 15 is as follows: i ² = −1, j ² = −1, i · j = 0, j · f (φ) = j · f (0), and φ is a real axis− The angle from the real axis on the i-axis plane, θ is the angle from the real axis-i-axis plane, and f (φ) is satisfied under the constraints of a term having a variable φ.

Up to this point, R _m is obtained by Expression 13 . Further, X _m , Y _m, and Z _m can also be obtained based on a difference in longitude, latitude, and sea level with respect to an arbitrary origin O. Further, v can be estimated as the velocity of the S wave in the local formation. Also, t _m can be estimated based on R _m and v. Similarly, _{T e can} also be estimated based on _R m, v, and _{T m.} Here, _Xe , _Ye , and _Ze are variables.

However, when a seismic wave passes through a plurality of strata, it is refracted at the boundary of the stratum as shown in Expression 14 , so that the seismic wave does not reach the observation point m via the shortest distance from the epicenter e. FIG. 5 is a schematic diagram illustrating an example in which a seismic wave is refracted at a boundary of a stratum. For example, when there are two types of strata, the Z coordinate of the stratum boundary can be expressed as follows by a function of polar coordinates from the epicenter e.

At this time, the number of intersections J _m of the seismic waves and the formation of the boundary surface that propagate from the epicenter e to the observation point m 2
Set as 1 .

Then, the deflection angle after refraction at the stratum boundary surface is φ _jm2 (the angle between the X axis on the XY plane) and θ _jm2 (the angle between the XY plane and the plane including the Z axis and the perpendicular foot H). And the derivative in the φ direction (Equation 9) and the derivative in the θ direction (Equation 11), and Snell's law (Equation 14 ), the following Equations 22 and 23 hold. That is, the value of a boundary point J _m phi and θ is changed. The propagation speed of seismic waves in the stratum below the boundary surface is V ₁ , and the propagation speed of seismic waves in the stratum above the boundary surface is V ₂ .

6, the refraction of seismic waves shown in FIG. 5 is a diagram showing a plane containing a perpendicular foot H of source e, from the intersection J _m and J _m of the boundary surface and seismic to the XY plane. Since the observation point m is not on the same plane, the apparent magnitudes of R _m2 and θ _m2 shown in FIG. 6 are not accurate. Boundary schematically the boundary surface between the plane, shows a straight line intersecting seismic source e, from the intersection J _m and J _m of the boundary surface and the seismic and the plane containing the foot H of a perpendicular to the XY plane. The angle between the vertical Z-axis and the normal to the boundary can be represented by a derivative in the θ-direction.

FIG. 7 is a diagram showing the refraction of the seismic wave shown in FIG. 5 on an XY plane. Schematically by the boundary surface between the plane in the example of FIG. 7, XY plane parallel shows a straight line intersecting the plane passing through the point J _m. In this case, the angle between the Y axis and the normal of the boundary can be represented by a derivative in the φ direction.

In addition, since the sum of the two vectors whose directions have changed due to refraction matches the observation point m, the following equation 24 holds. The change in the traveling direction as shown in Expressions 22 to 24 is expressed in polar coordinates, which makes it easier for the user to spatially grasp. Further, along with the processing of estimating the epicenter, the user may be presented with a display as shown in Equations 22 to 24 and FIGS. 5 to 7.

The unknowns R _m1 , φ _m1 , θ _m1 , R _m2 , φ _m2, and θ _m2 in Equation 24 can be obtained from Equations 16 to 23 . Expression 19 in the case where the seismic wave passes through two strata using Expressions 16 to 18 can be expressed as Expression 25 .

Further, the function of the _{R m} is considered to be undetermined value including an error, the variable _X e, defined by the following equation 26, shown in several 27 _{relationship, Y e, Z e, X} m1, Y m1, Z m1 I do.

Then, consider a t _m of the equation 25 as a variable that defines the function in the following Expression 28.

Note that n is the number of observation points. Ψ (t _me ) shown in Expression 28 is a time until the seismic wave arrives based on the distance R _m (R _m1 + R _m2 ) from the epicenter calculated from the observed value and the velocity of the seismic wave, and the hypothetical earthquake occurrence time T _This is a value obtained by summing the difference from the time from _e to the arrival at the observation point for a plurality of observation points. Then, varying the variable, combination of variables that the Ψ minimizes _{(X e, Y e, Z} e, T e) is determined. The variables may be approximated by randomly varying them by, for example, the Monte Carlo method, or may be obtained by other methods. Thus, the position of the epicenter can be estimated based on the distance from the epicenter estimated from the time difference when the same earthquake waveform was observed. As the number m of the observation point increases, measurement error included in the process of calculating the R _m is reduced, it is possible to estimate the seismic position accurately.

(Constitution)
FIG. 8 is a block diagram illustrating an outline of a system according to the present embodiment. The system in FIG. 8 includes a three-dimensional data processing device 1 and a plurality of sensors 2 (2a, 2b, 2c,... In the example of FIG. 8).
The three-dimensional data processing device 1 and the sensor 2 are connected to each other. The sensor 2 continuously measures acceleration, velocity, or displacement in association with time, and transmits waveform data to the three-dimensional data processing device 1. The three-dimensional data processing device 1 estimates the position of the epicenter based on the difference between the arrival times of the received waveform data.

FIG. 9 is a functional block diagram illustrating an example of the three-dimensional data processing device 1 according to the present embodiment. The three-dimensional data processing device 1 includes a data storage unit 101, a setting acquisition unit 102, a waveform data acquisition unit 103, a position estimation unit 104, and a result output unit 105. It is assumed that the data storage unit 101 previously stores information indicating the position of the sensor 2, information indicating the configuration of the stratum, the speed at which the waveform travels in each stratum, and the like. It is assumed that the coordinates of the position of the sensor 2 are calculated in advance based on a predetermined origin. For example, the coordinates are converted into spatial coordinates based on the latitude and longitude at the point where the sensor 2 is installed and the latitude and longitude of the point determined at the predetermined origin. Further, the data storage unit 101 holds the waveform data acquired from the sensor 2. Further, the setting acquisition unit 102 acquires, from the data storage unit 101, information such as the position of the sensor 2 and the speed at which the seismic wave travels in the stratum existing around the sensor 2. The waveform data acquisition unit 103 acquires waveform data observed by the sensor 2. The waveform data is, for example, data indicating acceleration, velocity, or phase, and can be observed by an existing sensor. In addition, the position estimating unit 104 obtains a combination of variables that minimizes Expression 27 shown in the description of the principle, and estimates the coordinates of the epicenter. In addition, the result output unit 105 outputs the estimated position of the epicenter and the like to a monitor or the like connected to the three-dimensional data processing device 1. The result may be output to another device via a network, for example.

(Device configuration)
FIG. 10 is an apparatus configuration diagram illustrating an example of a computer. The three-dimensional data processing device 1 is a computer as shown in FIG. A computer 1000 illustrated in FIG. 10 includes a CPU (Central Processing Unit) 1001, a main storage device 1002, an auxiliary storage device 1003,
A communication IF (Interface) 1004, an input / output IF (Interface) 1005, a drive device 1006, and a communication bus 1007 are provided. The CPU 1001 performs a process according to this embodiment by executing a program (also referred to as “software” or “application”). The main storage device 1002 caches programs and data read by the CPU 1001, and expands a work area of the CPU. The main storage device is, specifically, a random access memory (RAM) or a read only memory (ROM). The auxiliary storage device 1003 stores a program executed by the CPU 1001, setting information used in the present embodiment, and the like. The auxiliary storage device 1003 is, specifically, an HDD (Hard-disk Drive) or an SS.
D (Solid State Drive), flash memory, and the like. The main storage device 1002 and the auxiliary storage device 1003 function as the data storage unit 101 of the monitoring device 1. The communication IF 1004 transmits and receives data to and from another computer. The communication IF 1004 is specifically a wired or wireless network card or the like. The three-dimensional data processing device 1 may be connected to the sensor 2 through a communication IF 1004 via a network such as the Internet. The input / output IF 1005 is connected to the input / output device and receives an operation from a user or presents information to the user. The input / output device is, specifically, a keyboard, a mouse, a display, a touch panel, or the like. The drive device 1006 reads data recorded on a storage medium such as a magnetic disk, a magneto-optical disk, and an optical disk, and writes data on the storage medium. The above components are connected by a communication bus 1007. A plurality of these components may be provided, or some of the components (for example, the drive device 1006) may not be provided. Further, the input / output device may be configured integrally with the computer. Also, a program executed in the present embodiment is provided via a portable storage medium readable by the drive device 1006, a portable auxiliary storage device 1003 such as a flash memory, a communication IF 1004, and the like. It may be. Then, the computer shown in FIG. 10 operates as the three-dimensional data processing device 1 by the CPU 1001 executing the program.

(Earthquake estimation processing)
FIG. 11 is a processing flow illustrating an example of the hypocenter estimation processing. In the hypocenter estimation processing, the position of the hypocenter is estimated according to the above-described principle. First, the setting acquisition unit 102 of the three-dimensional data processing device 1 acquires setting data such as the position of a sensor and the speed at which a body wave is transmitted on the ground from the data storage unit 101 (FIG. 11: S1). These are input by the user in advance and stored in the data storage unit 101, for example.

  Further, the waveform data acquisition unit 103 of the three-dimensional data processing device 1 acquires waveform data from the sensor 2 (S2). The waveform data is stored in the data storage unit 101 in association with the observation time. The information indicating the time may be obtained by adding the information at each observation point, or may be determined by the waveform data acquisition unit 103 taking into account, for example, the time required for transmission from each observation point. Here, data as shown in FIG. 4 is obtained from each sensor.

Then, the position estimating unit 105 of the three-dimensional data processing device 1 estimates the coordinates of the epicenter (S3). In this step, the traveling direction of the seismic wave that changes at the boundary of the stratum is defined using the three-dimensional polar coordinate format. Then, while varying the coordinates of the epicenter, which is a variable, the coordinates of the epicenter that minimizes Ψ in Equation 27 described in the section of the principle are obtained. At this time, the calculation process or the calculation result may be displayed to the user using a three-dimensional polar coordinate format.

  Then, the result output unit 106 of the three-dimensional data processing device 1 outputs the estimated position of the epicenter (S4). The output destination may be a display device connected to the three-dimensional data processing device 1 or another computer.

<Others>
The present invention is not limited to the above-described example, and various modifications can be made without departing from the gist of the present invention.

  As described above, the complex function representation of the three-dimensional polar coordinates according to the present invention can be used in various fields such as architecture, civil engineering, vibration, fluid, electromagnetic, and aeronautical. According to such an expression, there is an advantage that it is easy for the user to easily grasp the position and the direction in the space. Therefore, it can be suitably used for operation of a device, movement of a 3D object in a virtual space, various other user interfaces, and information transmission means between users.

Reference Signs List 1 3D data processing device 101 Data storage unit 102 Setting acquisition unit 103 Waveform data acquisition unit 104 Position estimation unit 105 Result output unit 2 Sensor

Claims (4)

  A processing unit provided in the computer is a three-dimensional data processing method that performs a simulation for calculating a three-dimensional polar coordinate with a complex number,
  The processing unit, in the simulation,
  The coordinates (r · cosφ · cosθ, r · sinφ · cosθ, r · sinθ) in the three-dimensional Euclidean space are represented by a three-dimensional space in which three orthogonal axes are respectively associated with a real axis, an imaginary i-axis, and an imaginary j-axis.
Polar coordinate A = r · e between ^{iφ + jθ} (Φ is a declination from the real axis on the real axis-i-axis plane, θ is a declination from the real axis-i-axis plane)
  I for imaginary unit i ² To -1 and j ² Is replaced by −1, the term containing i · j is replaced with 0, and the term containing j · f (φ) is replaced with j · f (0) as the cancellation term.
  Simulates addition, subtraction, multiplication, division, rotation in the declination direction, and differentiation in the radial or declination direction
  3D data processing method. Acquiring waveform data relating to seismic waves from sensors at a plurality of observation points whose positions are known in advance,
A first distance at which the seismic wave propagates from the hypothetical hypocenter to a point on the boundary between the first and second strata, and a second distance at which the seismic wave propagates from the point on the boundary to the observation point. Represents the sum of the distance and the three-dimensional polar coordinates, the time from the hypothetical earthquake occurrence time to the observation of the seismic wave at the observation point, and the seismic wave reaches the observation point from the hypothetical hypocenter Searching for the hypothetical hypocenter and the hypothetical earthquake occurrence time using the waveform data at the plurality of observation points, such that the difference from the time until becomes smaller,
The three-dimensional data processing method according to claim 1, further comprising:   A three-dimensional data processing program for causing a processing unit provided in the computer to execute a simulation for calculating a three-dimensional polar coordinate with a complex number,
  In the simulation,
  The coordinates (r · cosφ · cosθ, r · sinφ · cosθ, r · sinθ) in the three-dimensional Euclidean space are represented by a three-dimensional space in which three orthogonal axes are respectively associated with a real axis, an imaginary i-axis, and an imaginary j-axis.
Polar coordinate A = r · e between ^{iφ + jθ} (Φ is a declination from the real axis on the real axis-i-axis plane, θ is a declination from the real axis-i-axis plane)
  I for imaginary unit i ² To -1 and j ² Is replaced by −1, the term containing i · j is replaced with 0, and the term containing j · f (φ) is replaced with j · f (0) as the cancellation term.
  Simulates addition, subtraction, multiplication, division, rotation in the declination direction, and differentiation in the radial or declination direction
  3D data processing program.   A three-dimensional data processing device including a processing unit that performs a simulation for calculating a three-dimensional polar coordinate with a complex number,
  The processing unit, in the simulation,
  The coordinates (r · cosφ · cosθ, r · sinφ · cosθ, r · sinθ) in the three-dimensional Euclidean space are represented by a three-dimensional space in which three orthogonal axes are respectively associated with a real axis, an imaginary i-axis, and an imaginary j-axis.
Polar coordinate A = r · e between ^{iφ + jθ} (Φ is a declination from the real axis on the real axis-i-axis plane, θ is a declination from the real axis-i-axis plane)
  I for imaginary unit i ² To -1 and j ² Is replaced by −1, the term containing i · j is replaced with 0, and the term containing j · f (φ) is replaced with j · f (0) as the cancellation term.
  Simulates addition, subtraction, multiplication, division, rotation in the declination direction, and differentiation in the radial or declination direction
  3D data processing device.

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