JP2017193841A - Ground estimation method - Google Patents

Abstract

An object of the present invention is to improve the accuracy of estimating ground characteristics. A ground estimation method for estimating a dominant frequency of ground having a hard basement below the ground surface, comprising constant microtremors in the horizontal x direction, constant microtremors in the horizontal y direction orthogonal to the horizontal x direction, A constant slight movement measurement step of measuring the vertical constant slight movement at a plurality of angular positions in which the horizontal x direction and the horizontal y direction are rotated in the horizontal plane; A spectrum calculation step of calculating spectrum Hx, spectrum Hy, and spectrum V from microtremors in the y direction and normal microtremors in the vertical direction, respectively; a dominant frequency estimating step of obtaining an angular position with the most similar shape from the V spectrum ratio, and estimating the dominant frequency of the ground based on the spectrum Hx, spectrum Hy, and spectrum V of the angular position; [Selection drawing] Fig. 7

Description

  The present invention relates to a ground estimation method.

  The ground always shakes slightly even when it is not in an earthquake (fine tremor). It is known that this microtremor can be measured and the characteristics of the ground can be detected from the measurement result. For example, in Patent Document 1, the ground period (in other words, the dominant frequency) is calculated from the constant fine movement of the two horizontal components (x, y) and the vertical component (z).

JP 2005-344309 A

  However, the above method is based on the premise that the hard base below the ground surface is not tilted. If the hard base is tilted, there is a problem that the characteristics of the ground (such as dominant frequency) cannot be detected stably. there were.

  The present invention has been made in view of the above-described conventional problems, and an object of the present invention is to increase detection accuracy of ground characteristics.

A main invention for achieving the above object is a ground estimation method for estimating a dominant vibration frequency of a ground having a hard base below the ground surface, wherein the fine movement in the horizontal x direction is orthogonal to the horizontal x direction. A microtremor measurement step for measuring microtremors in the horizontal y direction and microtremors in the vertical direction at a plurality of angular positions obtained by rotating the horizontal x direction and the horizontal y direction in a horizontal plane, and the plurality of angular positions. A spectrum calculation step for calculating a spectrum Hx, a spectrum Hy, and a spectrum V from the fine movement in the horizontal x direction, the fine movement in the horizontal y direction, and the fine movement in the vertical direction, respectively, and the spectrum at each angular position. An angular position having the most similar shape is determined from Hx and the spectrum Hy, or an Hx / V spectral ratio and a Hy / V spectral ratio, and the spectral position of the angular position is determined. Torr Hx, the spectral Hy, a ground estimation method characterized by having a predominant frequency estimation step of estimating the number of dominant frequency of the ground on the basis of the spectrum V.
Other features of the present invention will become apparent from the description of the present specification and the accompanying drawings.

  ADVANTAGE OF THE INVENTION According to this invention, the detection precision of the characteristic of a ground can be improved.

It is a schematic explanatory drawing of the measuring method of a constant fine movement. It is a figure which shows the measurement result of the shake (always fine movement) of each direction. 3A to 3C are schematic explanatory diagrams illustrating a procedure for calculating the H / V spectrum ratio. FIG. 4A is a diagram showing the Hx / V spectral ratio and Hy / V spectral ratio measured in the state of FIG. 1, and FIG. 4B is a diagram showing the H / V spectral ratio at that time. It is a figure which shows a state in case the base | substrate is inclined. FIG. 6A is a diagram showing the Hx / V spectral ratio and Hy / V spectral ratio measured in the state of FIG. 5, and FIG. 6B is a diagram showing the H / V spectral ratio at that time. It is a schematic explanatory drawing of the measuring method of the dominant frequency in this embodiment. 8A to 8D are diagrams showing changes in the shape of the Hx / V spectral ratio and the Hy / V spectral ratio when the microtremor meter 10 is rotated in the horizontal plane (about the x direction and the y direction). 9A to 9D are explanatory diagrams of the relationship between the direction of inclination of the base and the angular position (x direction, y direction) of the microtremor meter, and either the x direction or the y direction is perpendicular to the inclination direction. It is a figure in the case of becoming. 10A to 10D are explanatory diagrams of the relationship between the direction of inclination of the base and the angular position (x direction, y direction) of the microtremor meter, where the x direction and the y direction are both 45 degrees with respect to the inclination direction. It is a figure in the case of becoming. 11A to 11C are explanatory diagrams of a method for estimating the characteristics of the ground 1 (inclination direction of the base 3).

At least the following matters will become apparent from the description of the present specification and the accompanying drawings.
A ground estimation method for estimating a dominant vibration frequency of a ground having a hard base below a ground surface, the horizontal fine movement in the horizontal x direction, the fine movement in the horizontal y direction perpendicular to the horizontal x direction, and the vertical fine movement A fine movement measurement step for measuring fine movement at a plurality of angular positions obtained by rotating the horizontal x direction and the horizontal y direction in a horizontal plane, and a fine movement in the horizontal x direction for each of the plurality of angular positions; A spectrum calculating step for calculating spectrum Hx, spectrum Hy, and spectrum V from the fine movement in the horizontal y direction and the fine movement in the vertical direction, respectively, and the spectrum Hx and the spectrum Hy or Hx / V at each angular position. An angular position having the most similar shape is obtained from the spectral ratio and the Hy / V spectral ratio, and the spectrum Hx, the spectrum Hy, and the spectrum at the angular position are obtained. A predominant frequency estimation step of estimating the number of dominant frequency of the ground on the basis of the vector V, ground estimating method characterized by having become apparent.
According to such a ground estimation method, it is possible to improve the detection accuracy of the ground characteristics (dominant frequency) regardless of the inclination of the base.

In this ground estimation method, it is desirable that the rotation angle in the horizontal x direction and the horizontal y direction is less than 90 degrees.
According to such a ground estimation method, unnecessary measurement is not required.

  In this ground estimation method, in the dominant frequency estimation step, the H / V spectrum ratio is calculated by dividing the geometric mean of the spectrum Hx and the spectrum Hy by the spectrum V to calculate the H / V spectrum ratio. The frequency at which becomes the largest may be the dominant frequency.

  In this ground estimation method, in the dominant frequency estimation step, the square root sum of the spectrum Hx and the spectrum Hy is divided by the spectrum V to calculate the H / V spectrum ratio, and the H / V The frequency with the largest spectral ratio may be the dominant frequency.

  Also, a ground estimation method for estimating a tilt direction of the hard base of a ground having a hard base below the ground surface, the micro tremor in the horizontal x direction and the micro tremor in the horizontal y direction perpendicular to the horizontal x direction. And a microtremor measurement step for measuring microtremors in the vertical direction at a plurality of angular positions obtained by rotating the horizontal x direction and the horizontal y direction in a horizontal plane, and the horizontal x at each of the plurality of angular positions. A spectrum calculation step of calculating a spectrum Hx, a spectrum Hy, and a spectrum V from the continuous fine movement in the direction, the fine movement in the horizontal y direction, and the fine movement in the vertical direction, respectively, and the spectrum Hx and the spectrum Hy at each angular position, Or 45 degree rotation direction of the angular position where the shape of the Hx / V spectral ratio and Hy / V spectral ratio is most similar, or the front in each angular position An inclination direction estimating step of estimating an inclination direction of the hard base based on obtaining an angular direction in which the shapes of the spectrum Hx and the spectrum Hy or the Hx / V spectrum ratio and the Hy / V spectrum ratio are most different from each other; A ground estimation method characterized by having

  According to such a ground estimation method, it is possible to improve the detection accuracy of the characteristics of the ground (the direction of inclination of the base or the direction perpendicular to the inclination).

  In this ground estimation method, it is preferable that the inclination direction estimation process is executed at a plurality of points to estimate the inclination direction of the hard base.

  According to such a ground estimation method, the inclination direction of the hard base can be obtained more reliably.

=== First Embodiment ===
<< About the dominant frequency >>
<Regarding microtremor>
The ground (ground) is always shaking slightly, even during an earthquake. In general, fluctuations shorter than 1 second are caused by artificial vibration sources caused by human activities, and longer periods are caused by natural phenomena such as waves and atmospheric pressure changes. . These small vibrations are called microtremors.

  By measuring this microtremor, characteristics such as the ease of shaking of the ground during an earthquake can be detected. In addition, by analyzing the measured data, it is possible to estimate the ground structure (how hard the layer structure is).

  FIG. 1 is a schematic explanatory diagram of a method for measuring microtremors at all times. Moreover, FIG. 2 is a figure which shows an example of the measurement result of the shake (always fine movement) of each direction. In FIG. 2, the horizontal axis indicates time, and the vertical axis indicates the magnitude of shaking.

  When measuring the fine movement, the fine movement meter 10 is installed on the ground 1a (corresponding to the ground surface) of the ground 1 as shown in FIG. A hard base 3 (corresponding to a hard base) exists below the ground 1a of the ground 1.

  The microtremor meter 10 is a highly sensitive seismometer. The microtremor meter 10 is integrally provided with a three-component sensor of two horizontal components (x direction and y direction) and a vertical component (z direction) and a logger (recording device). In FIG. 1, the microtremor meter 10 has a ground 1a such that the positive in the x direction is east (negative is west), the positive in the y direction is north (negative is south), and the positive in the z direction is upward (negative is down). Is placed on top. The microtremor meter 10 simultaneously measures and records the magnitude (displacement, velocity, acceleration, etc.) of the shaking of each component in the x, y, and z directions. Thereby, as shown in FIG. 2, fine movement in each direction (always fine movement) is measured. For example, the east-west shaking (fine movement) of the ground 1 is measured as a component in the x direction (the uppermost figure of the three figures in FIG. 2) of the fine movement meter 10.

<About H / V spectral ratio>
Of the three-component observation records of microtremors observed at one point, a stable ratio that is not affected by the vibration source is obtained by taking the spectrum ratio obtained by dividing the horizontal motion spectrum (H) by the vertical (vertical) motion spectrum (V). It is said that the result will be obtained. This spectral ratio is called the H / V spectral ratio, and is used to estimate the frequency at which the ground 1 is likely to shake (dominant frequency).

  As shown in FIG. 1, when the microtremor meter 10 is installed on the ground 1a and the constant tremor of the three components x, y and z is recorded, the procedure for calculating the H / V spectrum ratio is as follows.

  3A to 3C are schematic explanatory diagrams illustrating a procedure for calculating the H / V spectrum ratio.

  First, frequency analysis is performed on the fine movement data (FIG. 3A) of each observed component (x, y, z). Thereby, as shown to FIG. 3B, each spectrum of x direction, y direction, and z direction is obtained. 3B, the horizontal axis indicates the frequency (Hz), and the vertical axis indicates the amplitude. Next, the horizontal motion (x and y) spectrum is divided by the vertical motion (z) spectrum. At this time, the calculation formula of the H / V spectrum ratio includes a method such as the following formula.

Here, Hx, Hy, and V are fine-spectrum Fourier spectra of a horizontal orthogonal two component (x, y) and a vertical component (z), respectively. Equation 1 is an equation in the case where the horizontal motion spectrum H is the geometric mean of the spectrum Hx and the spectrum Hy, and Equation 2 is the horizontal motion spectrum H being the square sum of squares of the spectrum Hx and the spectrum Hy. Is the expression of the case.
Thereby, the H / V spectral ratio is obtained as shown in FIG. 3C.

  4A is a diagram showing an example of the Hx / V spectral ratio and Hy / V spectral ratio measured in the state of FIG. 1, and FIG. 4B is a diagram showing the H / V spectral ratio at that time. It is. The Hx / V spectral ratio is the ratio between the horizontal x component spectrum Hx and the vertical z component spectrum V. The Hy / V spectral ratio is the horizontal y component spectrum Hy and the vertical z component spectrum V. Is the ratio.

  In FIG. 4A, the shape of the Hx / V spectral ratio is similar to the shape of the Hy / V spectral ratio (the dominant frequency is the same value). The dominant frequency of the H / V spectrum ratio (FIG. 4B) obtained from the spectra of these components is also the same value as the dominant frequency of FIG. 4A.

  Thus, when obtaining the H / V spectral ratio, the horizontal motion spectrum H is considered by combining the horizontal x component (spectrum Hx) and the horizontal y component (spectrum Hy). It is assumed that fine movement in the x direction≈fine movement in the y direction. However, actually, the base 3 (hard layer) may be inclined as shown in FIG. In addition, FIG. 5 is a figure which shows a state in case the base | substrate 3 inclines. In FIG. 5, the base 3 is inclined in the north-south direction, the north side is shallow and the south side is deep. In FIG. 5, the microtremor meter 10 is placed in the same direction as in FIG.

  6A is a diagram showing an example of the Hx / V spectral ratio and the Hy / V spectral ratio measured in the state of FIG. 5, and FIG. 6B is a diagram showing the H / V spectral ratio at that time.

  When the base 3 is inclined as shown in FIG. 5, the spectrum Hx in the x direction and the spectrum Hy in the y direction may be greatly different (the dominant frequencies do not match) as shown in FIG. 6A. In this case, if the H / V spectrum ratio is calculated using the spectrum Hx and the spectrum Hy as they are, the peak of the H / V spectrum ratio becomes unclear, and it may not be possible to obtain a stable dominant frequency (ground 1). The detection accuracy of the characteristics may be reduced).

  Therefore, in this embodiment, the detection accuracy of the characteristics (specifically, the dominant frequency) of the ground 1 is increased.

<< Measurement method of the dominant frequency of this embodiment >>
FIG. 7 is a schematic explanatory diagram of a method for measuring the dominant frequency in the present embodiment. In the present embodiment, the microtremor meter 10 is communicably connected to a computer (not shown) provided with a storage unit for storing various data and programs and an arithmetic processing unit for performing various calculations. Processing other than measurement is performed by the computer.

  In the present embodiment, measurement is performed by rotating the microtremor meter 10 every several degrees as shown in FIG. That is, the microtremors in the x direction, the y direction, and the z direction are measured at a plurality of angular positions obtained by rotating the x direction and the y direction on the horizontal plane (corresponding to the microtremor measurement step).

For example, as shown in the figure, from the state (x ₀ , y ₀ ) where the x direction is east and the y direction is north, (x ₁ , y ₁ ) → (x ₂ , y ₂ ) → (x ₃ , y ₃ ). Then, the fine movement of the two horizontal components and the vertical component at each angular position is measured.

  The computer receives microtremor data measured at each angular position, and frequency-analyzes them to calculate each spectrum in the x, y, and z directions (spectrum Hx, spectrum Hy, spectrum V) (spectrum calculation). Equivalent to the process). In the present embodiment, the microtremor meter 10 itself is rotated. However, data of two horizontal components in the x and y directions may be rotated and analyzed every several degrees.

  Next, the Hx / V spectral ratio and the Hy / V spectral ratio are obtained for each angular position, and the direction (angular position) in which the shape of the Hx / V spectral ratio and Hy / V spectral ratio at each angular position most closely matches is determined. locate. Since x and y are recorded as positive and negative, turning 90 degrees gives the same result as the spectrum at 0 degree. That is, the rotation angle may be less than 90 degrees. This eliminates unnecessary measurement.

8A to 8D are diagrams showing changes in the shape of the Hx / V spectral ratio and the Hy / V spectral ratio when the microtremor meter 10 is rotated in the horizontal plane (about the x direction and the y direction). 8A shows the shape at (x ₀ , y ₀ ), FIG. 8B shows the shape at (x ₁ , y ₁ ), FIG. 8C shows the shape at (x ₂ , y ₂ ), and FIG. 8D shows the shape at (x ₃ , y ₃ ). .

As can be seen from these figures, the shapes in the x direction and the y direction change according to the rotation. For example, in the case of the figure, when the angle position (x ₂ , y ₂ ) in FIG. 8C is reached, the shapes of the Hx / V spectral ratio and the Hy / V spectral ratio substantially coincide.

  In this way, the angle position where the shapes of the Hx / V spectrum ratio and the Hy / V spectrum ratio are most similar is obtained, and using the data of the angle position (spectrum Hx, spectrum Hy, spectrum V), the above-described formula 1 Alternatively, the H / V spectral ratio is obtained by Equation 2. Then, the frequency at which the H / V spectrum ratio is the largest is estimated as the dominant frequency (corresponding to the dominant frequency estimation step). Thereby, even if the base | substrate 3 inclines, the stable dominant frequency can be calculated | required.

  In the present embodiment, the angle position is determined by comparing the shapes of the Hx / V spectral ratio and the Hy / V spectral ratio, but it is most similar to the shape of the spectrum Hx and the spectrum Hy at each angular position. The angular position may be obtained. In this embodiment, the computer determines the angular position. However, for example, the worker may determine the angular position by viewing the shape.

  As described above, in the present embodiment, when estimating the dominant frequency of the ground 1 having the base 3 below the ground 1a, a plurality of horizontal two components (x direction and y direction) are rotated in the horizontal plane. At this angular position, microtremors in the x, y, and z directions are constantly measured. Then, from each microtremor, a spectrum Hx in the horizontal x direction, a spectrum Hy in the horizontal y direction, and a spectrum V in the vertical direction are calculated. Then, an angular position having the most similar shape is obtained from the Hx / V spectral ratio and the Hy / V spectral ratio at each angular position, and the dominant vibration of the ground 1 is obtained using the spectrum Hx, the spectrum Hy, and the spectrum V at the angular position. Estimate the number.

  Thereby, irrespective of the presence or absence of the inclination of the base | substrate 3, the stable dominant frequency can be calculated | required and the detection precision of the characteristic (dominant frequency) of the ground 1 can be improved.

=== Second Embodiment ===
In the above-described embodiment, the dominant frequency is calculated as the characteristic of the ground 1, but in the second embodiment, the direction of the inclination (inclination) of the base 3 of the ground 1 is obtained.

  That is, if the cause of the difference between the spectrum Hx in the x direction and the spectrum Hy in the y direction (or the Hx / V spectral ratio and the Hy / V spectral ratio) is due to the tilt of the base 3, the tilt direction of the base 3 and It is assumed that the difference in spectrum is the largest when measured in the perpendicular direction. Conversely, when measured in a direction that is symmetrically affected by the tilt of the substrate 3 (that is, an angular position rotated 45 degrees from the tilt direction), the spectrum Hx and spectrum Hy (or Hx / V spectrum ratio and Hy / V spectrum ratio) are obtained. Presumed to be closest.

  9A to 9D and FIGS. 10A to 10D are explanatory diagrams of the relationship between the inclination direction of the base 3 and the angular position (x direction, y direction) of the microtremor meter 10. Here, as in the first embodiment (FIGS. 5 and 7), the direction of inclination is the north-south direction, the base 3 is shallow on the north side, and the base 3 is deep on the south side.

  9A to 9D are diagrams in a case where one of the x direction and the y direction is perpendicular to the tilt direction. That is, one of the x direction and the y direction is perpendicular to the tilt direction (north-south direction), and the other is parallel to the tilt direction. In this case, the way of receiving the influence of the inclination of the base 3 is most different between the x direction and the y direction, and the difference in spectrum becomes large.

  10A to 10D are diagrams in the case where the x direction and the y direction are both 45 degrees with respect to the tilt direction. In this case, x and y are similarly affected by the inclination of the base 3. That is, the spectra of x and y are approximately the same.

  9A and 9C, FIG. 9B and FIG. 9D, and FIG. 10A and FIG. 10C, FIG. 10B and FIG. 10D, respectively, the wave data are inversion waveforms, and the spectrum (the magnitude of fluctuation for each frequency) Are the same.

  From the above, the direction rotated 45 degrees from the direction in which the spectrum Hx in the x direction and the spectrum Hy in the y direction (or Hx / V spectral ratio and Hy / V spectral ratio) substantially coincide (state of FIG. 8C). Is the inclination direction of the substrate 3 or the direction perpendicular to the inclination.

  Therefore, the 45-degree rotation direction of the angular position where the shapes of the spectrum Hx and the spectrum Hy (or the Hx / V spectral ratio and the Hy / V spectral ratio) are most similar, or the spectral Hx and the spectral Hy (at each angular position) Alternatively, it is possible to estimate the tilt direction of the substrate 3 and the direction perpendicular to the tilt direction (direction perpendicular to the tilt direction) from the angle direction in which the shapes of the Hx / V spectrum ratio and the Hy / V spectrum ratio are the most different. However, only one point of measurement can be understood to be either the tilt direction or the direction perpendicular to the tilt, and the tilt direction of the substrate 3 cannot be determined reliably.

  On the other hand, if the dominant frequency is measured at a plurality of (two or more) points, the inclination direction of the base 3 can be estimated more reliably. The dominant frequency increases as the base 3 is shallow, and decreases as the base 3 is deep. Therefore, by obtaining the dominant frequencies at a plurality of points by the above-described method and comparing the magnitudes, it is possible to know which base 3 is deep at each point. That is, it is possible to determine the inclination direction (depth direction) of the base 3 and the right-angle direction (direction perpendicular to the inclination direction).

  11A to 11C are explanatory diagrams of a method for estimating the characteristics of the ground 1 (inclination direction of the base 3).

  As shown in FIG. 11A, in this example, the x direction and the y direction are 45 degrees with respect to the inclination direction of the base 3 (the spectrum Hx and the spectrum Hy substantially coincide). However, if the measurement is performed only at the point P1, it cannot be determined whether the direction of the inclination is the direction shown in the figure or the direction orthogonal to the direction shown in the figure. Therefore, in this embodiment, measurement is performed at two points, point P1 and point P2.

  FIG. 11B is a diagram showing the H / V spectrum ratio at the point P1 and the H / V spectrum ratio at the point P2. P1 has a smaller H / V spectral ratio dominant frequency, and P2 has a higher H / V spectral ratio dominant frequency.

  From this result, it can be seen that the direction of inclination is the direction shown in FIG. 11A, and the base 3 is deep at the point P1 and the base 3 is shallow at the point P2, as shown in FIG. 11C. If the dominant frequency is the same, the inclination direction is a direction orthogonal to the direction connecting the points P1 and P2 (inclination direction shown in FIG. 11A).

  Thus, the inclination direction of the board | substrate 3 can be estimated by measuring in several points like this embodiment. Also in this case, the detection accuracy of the characteristics of the ground 1 (here, the inclination direction of the base 3) is improved by rotating the microtremor meter 10 to obtain a direction in which the spectra in the x direction and the y direction substantially coincide. Can do.

  In this embodiment, the 45-degree rotation direction in the direction in which the spectrum Hx and the spectrum Hy are most similar is estimated as the tilt direction. However, the tilt direction is estimated from the direction in which the spectrum Hx and the spectrum Hy are the most different. Also good.

=== Other Embodiments ===
As mentioned above, although embodiment of this invention was described, said embodiment is for making an understanding of this invention easy, and is not for limiting and interpreting this invention. Further, the present invention can be changed or improved without departing from the gist thereof, and needless to say, the present invention includes equivalents thereof. For example, the following modifications are possible.

  In the above-described embodiment and the like, the computer having the storage unit and the arithmetic processing unit is used except for the measurement of the fine movement at all times. However, the function of this computer is provided in the fine movement meter 10 and each processing is performed only by the fine movement meter 10. You may do it.

1 Ground 1a Ground 3 Base 10 Microtremor meter

Claims (6)

A ground estimation method for estimating a dominant frequency of a ground having a hard base below the ground surface,
A plurality of angles obtained by rotating the horizontal x direction and the horizontal y direction in the horizontal plane in the horizontal x direction, the fine direction in the horizontal y direction orthogonal to the horizontal x direction, and the vertical fine movement in the horizontal plane. Microtremor measurement process that measures at position,
A spectrum calculating step for calculating a spectrum Hx, a spectrum Hy, and a spectrum V from the fine movement in the horizontal x direction, the fine movement in the horizontal y direction, and the fine movement in the vertical direction for each of the plurality of angular positions;
From the spectrum Hx and the spectrum Hy at each angular position, or an angular position having the most similar shape from the Hx / V spectral ratio and the Hy / V spectral ratio, the spectrum Hx, the spectrum Hy, A dominant frequency estimating step of estimating a dominant frequency of the ground based on the spectrum V;
A ground estimation method comprising: The ground estimation method according to claim 1,
The ground estimation method, wherein a rotation angle in the horizontal x direction and the horizontal y direction is less than 90 degrees. The ground estimation method according to claim 1 or 2,
In the dominant frequency estimation step,
The geometric mean of the spectrum Hx and the spectrum Hy is divided by the spectrum V to calculate the H / V spectral ratio, and the frequency at which the H / V spectral ratio is the largest is the dominant frequency. The ground estimation method. The ground estimation method according to claim 1 or 2,
In the dominant frequency estimation step,
The square root sum of the spectrum Hx and the spectrum Hy is divided by the spectrum V to calculate the H / V spectrum ratio, and the frequency at which the H / V spectrum ratio is the largest is the dominant frequency. A ground estimation method characterized by A ground estimation method for estimating an inclination direction of the hard base of the ground having a hard base below the ground surface,
A plurality of angles obtained by rotating the horizontal x direction and the horizontal y direction in the horizontal plane in the horizontal x direction, the fine direction in the horizontal y direction orthogonal to the horizontal x direction, and the vertical fine movement in the horizontal plane. Microtremor measurement process that measures at position,
A spectrum calculating step for calculating a spectrum Hx, a spectrum Hy, and a spectrum V from the fine movement in the horizontal x direction, the fine movement in the horizontal y direction, and the fine movement in the vertical direction for each of the plurality of angular positions;
The spectrum Hx and the spectrum Hy at each angular position, or the 45 degree rotation direction of the angular position having the most similar shape of the Hx / V spectral ratio and the Hy / V spectral ratio, or the spectrum at each angular position An inclination direction estimating step of estimating an inclination direction of the hard base based on obtaining an angular direction in which the shapes of the Hx and the spectrum Hy or the Hx / V spectrum ratio and the Hy / V spectrum ratio are most different from each other;
A ground estimation method characterized by comprising: The ground estimation method according to claim 5.
A ground estimation method, wherein the inclination direction estimation step is executed at a plurality of points to estimate the inclination direction of the hard base.