RU2337382C1 - Method of short-term earthquake forecast - Google Patents

Abstract

FIELD: physics.

SUBSTANCE: method for short-term earthquake forecast includes registration of seismic background waves in two distanced points of base, registration of time when regular component of infrasound signal appears, defining fractal magnitude of amplitude-frequency response of the component, tracking time history of fractal magnitude, calculation of dynamic process time constant (T), forecast of expected shock characteristics: shock time t_y=4.7 T, shock magnitude lg t_y[day]=0.54 M - 3.37, hypocentre as cross-point of sight lines drawn from the base direction at angles

where B_x1(0), B _y1(0) are autocorrelation function values for signals at zero point on the planes (x, y) of first seismic receiver; B_x2(0), B_y2(0) are autocorrelation function values for signals at zero point on the planes (x, y) of second seismic receiver.

EFFECT: extension of earthquake forecast interval to 4 hours.

6 dwg

Description

The invention relates to geophysics and may find application in seismology when creating geophysical observation ranges in earthquake-prone regions of the planet.

To date, many long-term signs-precursors of the zone of the prepared earthquake have been identified [see, for example, in book. T. Rikitake “Earthquake Prediction”, trans. from English., World, M, 1979, table 15.13 p. 314-333]. Known signs have long intervals (years) of existence, but do not allow to accurately predict the moment of impact and its magnitude. Another class is short-term forerunners. They appear several days (hours) before the impact, but, due to the lack of technical means for measuring them, they cannot be detected in a timely manner. Among the most significant short-term precursor signs, measured by the global navigation positioning system (GPS, NAVSTAR,) is the buildup of the earthquake source before the impact. The buildup is accompanied by the propagation from the hypocenter of the focus of extra-long (with a period of ~ 10 ⁴ sec) lithospheric waves [see, for example, “Method for predicting earthquakes”, Patent RU No. 2170446, G01V, 9/00, 2001]. Also known is a sign of earthquake precursor, such as a change in the noise spectrum of the seismic background, the so-called “lull” immediately before the impact [see, for example. Patent RU No. 2181205, G01V, 9/00, 2002].

Reliable prediction can be provided by those registration methods that are based on measuring the root causes of the earthquake. Theoretically, there are several geophysical models that claim to justify the root causes of earthquakes [see, for example, “Short-term forecast of catastrophic earthquakes using radiophysical ground-space methods”. Conference reports, RAS, OIFZ them. O.Yu. Schmidt, M., 1998, pp. 14-16]. The true model of earthquake preparation should obviously reveal a new, absolute sign-precursor that accompanies all cases without exception.

One of the root causes of earthquakes is the loss of stability of the earth's crust when it is saturated with light gases (hydrogen, helium), which liberally liberate from the zone of the prepared earthquake on the eve of the impact.

Saturation of the earth's crust with a gas component leads to a change in its viscoelastic characteristics, due to which the elastic coefficients in the bonds infinitely increase in time, striving to ensure absolutely rigid adhesion and the formation of a block covering the entire zone of the prepared earthquake. As a result, due to the increase in the size of the vibrational elements, the noise spectrum of the seismic background of the zone of the prepared earthquake shifts to the infrasonic range. A class of membrane-type devices is known that makes it possible to measure infrasonic vibrations of the earth’s crust [see, for example, “Conductometric vibration sensor”. Patent RU No. 2055352, G01N, 27/02, 1996 - analogue].

The analogue device contains a sensitive element made in the form of a hollow sealed enclosure closed from the ends by elastic membranes in two cavities connected by a channel and filled with a conductive liquid (electrolyte). In the channel there are electrodes overlapping the channel cross section, parallel to each other, and the sensitivity axis, they are covered on both sides by counter electrodes. The sensitive element is rigidly fixed in the protective housing, and its submembrane cavities, using the connecting channel, communicate freely with each other. External influence leads to oscillations of the electrolyte relative to the electrodes, due to which the amount of electrolyte substance supplied to them changes, which changes the electrical resistance in the near-electrode region. In the background current flowing through the electrolyte, an alternating component appears, the amplitude and frequency of which are proportional to the external effect. The sensor has high sensitivity and linearity of the output characteristic in the field of infra-frequencies. It can be used in any spatial orientation, i.e. take measurements in mutually perpendicular planes. Based on the sensor, the industrial development of multicomponent infrasonic seismic receivers used in low-frequency acoustic reconnaissance equipment (ACAR) for oil and gas fields was performed [see, for example, Patent RU No. 2045079, G01V, 1/00, 1995].

, определяют гипотетический центр очага как точку пересечения на траверзе радиус-векторов с косинусом угла при вершинеThe closest analogue to the claimed is the "Method of short-term earthquake prediction", Patent RU No. 2181205, G01V, 9/00, 2002]. In the closest analogue method, seismic background waves are recorded in the form of a continuous sequence of discrete samples of the signal amplitude A (t) at two points spaced along the coordinates, the Fourier spectrum of the recorded function with the sample volume in each sample N≥2F _max / σ is calculated, the correlation interval τ is calculated , the beginning of the change in the parameter τ is recorded and, with its continuous monitoring, the delay time Δτ of the phase change of this feature between two points is recorded, the guide cosine of the traverse yes ultra-low focus waves

, determine the hypothetical center of the focus as the point of intersection on the beam of the radius vectors with the cosine of the angle at the vertex

the period T _{0 of the} parameter τ is calculated and the magnitude M≈110 / T ₀ ² (hour) and the impact time t _x ≈2.3T _{0 are} predicted by its magnitude, where:

F _max - the maximum frequency of the spectrum of the seismic background, Hz;

σ is the standard error of the calculation of the Fourier spectrum from a discrete sample of measurements;

a - the length of the base between two points, m;

V is the speed of seismic waves in the earth's crust, m / s;

B ₁ (0), B ₂ (0) are the values of the autocorrelation functions of the signal at zero for each point.

The disadvantages of the closest analogue include:

- the autocorrelation interval of the signal τ is determined, first of all, by the rate of change of the seismic background, therefore the measurement of the delay parameter Δτ is technically difficult to implement, since it practically does not depend on the size of the base;

- the indeterminable parameter V is included in the formula of the directing cosine - the velocity of lithospheric waves in the earth's crust, which can vary in the range from 1.2 to 2.5 km / s, which introduces a significant error in the result of determining the hypocenter;

- the inaccuracy of the regression dependencies for determining the magnitude and time of the impact, in particular, is known from the Gutenberg-Richter relations that the longer the time (T ₀ ), the greater the magnitude of the expected impact.

The problem solved by the claimed method is to extend the time interval of the predictive earthquake prediction, increase the accuracy and reliability of the predicted parameters by extracting hidden information from the amplitude-frequency characteristics of the infrasound signal based on the calculation of their fractal dimension and tracking the dynamics of its change.

The technical result is achieved by the fact that in the short-term earthquake prediction method, waves of seismic background are recorded at two points spaced on the measuring base, the registered signals are jointly processed by calculating their autocorrelation functions, additionally, registration is performed by two-coordinate (x, y) geophones in the infrasonic range, with the axis sensitivity of the geophones along the coordinate (x) is oriented in the direction of the base, the time of occurrence of the regular component is recorded st of infrasonic signal and determining the fractal dimension of its amplitude-frequency characteristic (AFC), track the dynamics of change of the fractal dimension of the response and finds the time constant (T) of the dynamic process, predict parameters expected earthquake: shock time counted from the moment of occurrence of infrasound signal, t _y = 4.7 T, magnitude M from the relation: log t _y [days] = 0.54 M - 3.37, the coordinates of the focus hypocenter are identified with the intersection point of the guiding cosines, measured from the direction of the base axis:

where B _x1 (0), B _y1 (0) are the values of the autocorrelation functions of the signals at zero in the x, y planes of the first geophone;

In _x2 (0), In _y2 (0) are the values of the autocorrelation functions of the signals at zero in the x, y planes of the second geophone.

The invention is illustrated by drawings, where

figure 1 - non-linear elastic-viscous model of the saturation of the earth's crust with a gas component;

figure 2 - one of the solutions of the nonlinear differential equation of the model in the form of a changing spectrum of oscillations of the focal zone;

figure 3 - amplitude-frequency characteristics of the seismic background of the focal zone of the infrasound range;

figure 4 - dynamics of changes in the fractal dimension of the recorded infrasound signal;

figure 5 - diagram of the direction finding source of the infrasound signal;

6 is a functional diagram of a device that implements the method.

The technical essence of the method is as follows.

It has been established [see, for example, “Short-term forecast of catastrophic earthquakes using radiophysical ground-space methods”. Conference reports RAS, OIFZ them. O.Yu. Schmidta, M., 1998, pp. 27-28, Fig. 1-2] that on the eve of the earthquake there is an active emanation of gases (hydrogen, helium, radon) from the earth's crust. Saturation of the earth's crust with a gas component leads to a change in its visco-elastic characteristics. A nonlinear elastic-viscous model of saturation of the earth's crust with a gas component is illustrated in Fig. 1. The mathematical model of the visco-elastic characteristics of the earth's crust was presented in the form of a system of differential equations:

i = 1 ,,,, n

The functions k _i (t) for all i are defined as

k _i (0) = 0

k _i (t) + α · dt with probability (1-p)

k _i = (t + dt) =

0 with probability p

p is the probability of dumping elastic bonds.

At the initial moment t = 0, the elements are motionless x _i = 0, i = 0 ... n + 1

The mass m _i oscillates x ₀ (t) = sin (ωt), the mass m _{i + 1 is} motionless x _{n + 1} (t) = 0.

The blocks of the earth's crust in the model are in contact through a system of sequential elements with an elastic connection. The frequency of natural vibrations of the mechanical system and the size of the vibrational “grains” depend on the stiffness coefficient k _i (t + α · dt), which varies with the degree of saturation of the earth's crust with a gas component. The differential equations of the model were solved according to a specially developed mathematical program. From the solution of the differential equations of the model it follows that the size of the grains increases from units of meters to several kilometers, and the frequency of the seismic background of the focal zone varies from the sound range (units of kHz) to the infrasound range (fractions of Hz). The change in the spectrum of the seismic background of the focal zone (as one of the implementation of the solution of the differential equations of the model) is illustrated by the graph of figure 2.

The very fact that a regular component of the infrasonic range appears in the spectrum of the seismic background indicates the beginning of the transition process to the release of energy by the energy-saturated focal zone.

Due to gas saturation, the elastic coefficients in the bonds increase unlimitedly in time, striving to ensure absolutely rigid adhesion, and the entire region of the prepared earthquake zone turns into a monolithic block. In this case, the frequency of natural vibrations of the block due to its large size (100-150 km in diameter) is 10 ^-3 ... 10 ^-4 Hz.

In Fig.2 is a plot of ultra-long lithospheric waves of the buildup of the focus, measured by means of the space navigation system GPS [see Patent RU No. 2170446, 2001], takes an interval of ~ 8 hours.

If we continuously monitor the seismic background in the infrasonic range (from 16 Hz), then we can extend the interval of proactive earthquake prediction by the time of the dynamic process of the buildup of the source before impact through this interval. Figure 2 is the middle section of the graph of the function with a lifetime of the order of 2 ... 4 hours. It is known [see, for example, R. Duda, P. Hart "Pattern Recognition and Scene Analysis", trans. from English., World, M., 1976, ch. Spatial differentiation], that the maximum information about ongoing processes is contained in the image of the object. Hidden information about the dynamic transient process of the focal zone contains the form (image) of the recorded signal, i.e. its amplitude-frequency characteristic (AFC). A sign of the shape of the signal function is the fractal dimension introduced by Mandelbrot [see, for example, Mandelbrot B. Fractals. Forms, Chance and Dimension. Freeman, San-Francisco, 1997]. The recorded frequency response of the infrasound signal is illustrated in Fig.3. Initially, the recorded signal contains a spectrum of infrasound frequencies. The frequency response of such a signal occupies a certain band (Fig. 3, a) with a comparable amplitude of each of the harmonics. Then the signal turns into a single oscillation with increasing amplitude (Fig.3, b). In technology, to remove the frequency response when changing the carrier, the so-called follow-up filters are used [see A set of vibration measuring equipment from Bruel & Kjair, ENDEVCO, Denmark, “Follow-up Filter”, model 2020].

In mathematics, the so-called Hausdorff dimension is used to determine the dimension of fractal formations [see, for example, P. A. Burrough, Fractal dimensions of landscapes and other environmental data. Nature, 294, 1981, p. 240].

By definition, the Hausdorff dimension is calculated:

where ε is the size of the resolution element with which the object is covered (segment length, square area, cube volume);

Ω _ε is the number of resolution elements of size ε containing all the attributes of the set.

The calculation of the fractal dimension of the frequency response of the infrasound signal (graph function of figure 3) was carried out according to a specially developed mathematical program.

The text of the program for calculating the fractal dimension of the frequency response.

The calculated values of the fractal dimension of the frequency response were:

D _f = 1.64 (graph of FIG. 3, a), D _f = 1.2 (graph of FIG. 3, b).

From mathematics, it is known that the function itself and the rate of its change are described by a differential equation of the first degree, the general solution of which is an exponential dependence [see, for example, N. S. Piskunov, “Differential and Integral Calculus for Technical Universities, vol. 1, textbook, 5- e ed. Science, M., 1964, p. 458]. The exponential dependence has the property that from its separate section you can restore the entire function by calculating the exponential time constant. It is also known that the tangent to the exponent at any point cuts off from the time axis (abscissa axis) a segment equal to the exponent constant (T). In particular, according to the implementation of the frequency response of FIGS. 3a, b, the constant of the exponent of the function of changing the fractal dimension of the frequency response was T≈2.6 [hour]. The graph of changes in the fractal dimension of the frequency response over time is illustrated in Fig.4.

According to the transient time constant, the characteristics of the expected earthquake are predicted.

Impact time is the time interval over which the fractal dimension of the frequency response with a probability of ≥0.99 tends to unity. For the exponent, this value is t _y = 4.7 T. For the graph of FIG. 4, t _y from the start of the detection of the infrasound signal was 12 hours.

The impact magnitude is found from the Gutenberg-Richter relation:

log t _y [day] = 0.54M-3.37.

The earthquake hypocenter is found by direction finding of the source of infrasound vibrations from two measurement points spaced on the base.

It is known that the direction of energy transfer by the wave process coincides with the phase front of the wave at a given point. The direction of the vector in space is determined by its projections on the coordinate axes. The projections of the vector of the energy transfer direction are proportional to the power of the signals recorded by the two-component seismic receiver in mutually perpendicular planes (x, y). The recorded signal powers are determined by the corresponding frequency response. The direction finding of the infrasound signal source from two spaced apart on the basis of two-coordinate geophones is illustrated in Fig.5.

The calculation of the direction is carried out according to the operations of the closest analogue by calculating the autocorrelation functions of the signals. The values of the autocorrelation functions at zero are equal to the power of the process, i.e. the sum of the powers of the constant (average) and variable (variance) components. Since the x-axis direction of the two-coordinate geophones is oriented in the direction of the base, the cosine guides to the source will be respectively (Fig. 5)

The hypocenter of the center of the expected earthquake is identified with the intersection point of the corresponding vectors constructed on a map of the area at angles (α, β) relative to the location of the measuring base.

An example implementation of the method.

The inventive method can be implemented according to the scheme of Fig.6. The functional diagram of the device of Fig.6 contains two two-component seismic receivers 1, 2 spaced in space by the distance of the measuring base 3, each of which contains two conductometric sensors 4, 5, the sensitivity axes of which are oriented in mutually perpendicular planes (x, y) connected to the inputs of the corresponding built-in amplifiers 6. 7. The outputs of the amplifiers are connected to the input of a series-connected channel switch 8, a servo filter 9, a threshold device 10, and an analog-to-digital converter I am 11, computer 12, consisting of elements: processor 13, random access memory 14, hard drive 15, display 16, printer 17, keyboard 18. The synchronization of the operation of the device elements is provided by a programmable measurement sampling circuit 19. Selectable signs of an earthquake precursor signal are the moment of the appearance of a regular infrasound signal (exceeding the set threshold level in element 10) and the shape of the recorded frequency response in each measuring channel. Preliminarily, the program for calculating the fractal dimension of the frequency response is written to the hard drive 15 of the computer 12, and the program of the sequence of operation of the channel switch, the ADC operation mode and the threshold device are sent to the programmable measurement sampling circuit 19. If the signal exceeds the set threshold level in the device 10, the frequency response is recorded and converted from the output of the follow-up filter to a digital form with the measurement register recorded and visually monitored on the display 16. After a statistically stable array of frequency response is set in each of the measuring channels, the signals are processed together the claimed operations of the method. The fractal dimension of the frequency response is determined and the dynamics of its measurement are monitored. The time constant (T) of the process of changing the fractal dimension is calculated, as illustrated by the graph of FIG. 4. The tangent to the graph of the function (Fig. 4) cuts off from the time axis a segment equal to the process time constant T = 2.6 hours. From the ratio 1-e ^{-t / T} = 0.99, we determine that t = 4.7 T = 12 hours. Expected impact magnitude: log (t _y = 0.5 days) = 0.54M-3.37; M = 5.8. According to the registered array of the AFC implementation, the constant component of the power and its dispersion σ ² in the measuring channels are determined.

According to the results of processing the measurement array, the guides of the cosines of the lines of sight for the locations of the geophones (Pinachevo, Moroznaya, Kamchatka Geophysical Test Site, RAS) amounted to:

The calculated hypothetical center of the outbreak is located in the Sea of Okhotsk ≈100 km east of the city of Okha (Sakhalin Island).

All elements of the device are existing technical developments and means of analogues. The device used elements of vibration measuring equipment from Bruel & Kjair, ENDEVCO (Denmark) of the following models: servo filter - model 2020; amplifiers - models 2626, 2628; channel switch, ADC, spectrum analyzer - multifunctional unit model 3560-L.

The effectiveness of the device is characterized by an increase in the interval of proactive forecast of an upcoming earthquake by a time of about 4 hours.

Claims (1)

A method for short-term earthquake prediction, in which seismic background waves are recorded at two points spaced on the measuring base, carry out joint processing of the recorded signals by calculating their autocorrelation functions, characterized in that the registration is carried out by two-coordinate (x, y) geophones in the infrasonic range, while the sensitivity axes the geophones along the coordinate (x) are oriented in the direction of the base, the time of appearance of the regular component of the infrasound signal is recorded determining the fractal dimension of its amplitude-frequency characteristic (AFC), track the dynamics of change of the fractal dimension of the response and finds the time constant (T) of the dynamic process, predicting expected earthquake parameters: impact time counted from the moment of occurrence infrasonic signal t _y = 4,7 T the magnitude M from the relation log t _y [days] = 0.54 M-3.37, the coordinates of the focus hypocenter are identified with the intersection point of the guide cosines, counted from the direction of the base axis:

where B _x1 (0), B _y1 (0) are the values of the autocorrelation functions of the signals at zero in the x, y planes of the first geophone; B _x2 (0), B _y2 (0) - values of the autocorrelation functions of the signals at zero in the x, y planes of the second geophone.

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