CA2328192C - Method for predicting seismic events - Google Patents

Abstract

A method for predicting seismic events wherein measurable and calculable parameters relating to alterations in the shape of the geoid, such as centripetal and tidal gravitational effects, and gravitational anomalies related to a buildup of energy at any given point in the earth are incorporated with observations from at least two previous, subsequent seismic events, to calculate the energy buildup required to result in a future seismic event.

Description

1 "METHOD FOR PREDICTING SEISMIC EVENTS"

4 The present invention relates to methods of predicting the occurrence of seismic events from changes in the earth's equipotential 6 gravitational surface due to polar motion. More particularly, accumulated 7 gravitation shift in geoids between successive polar motions is associated with 8 the accumulation in energy in the earth's crust which can be correlated to seismic 9 events.

12 The majority and most destructive of earthquakes or seismic events 13 are the tectonic quakes which are a result of a sudden release of energy 14 accompanying a shift or dislocation of the earth's crust (shallow) and in the upper mantle (deep).

16 Shifts in the earth's crust create a potential energy, which is 17 occasionally released in a seismic event. Due to the devastating results of 18 earthquakes, particularly those occurring in populated areas, there have been 19 concerted efforts to predict such events.

There are known areas of frequent seismic activity such as 21 geological locations having faults. Monitoring stations are provided at these 22 locations which, at best, provide warning of an immediately impending event.
23 Monitoring primarily consists of recording geophysical precursors such as P-wave 24 velocity, ground uplift, radon emission, rock electrical resistivity and water level 1 fluctuations. These precursors can have lead times of one day through to several 2 years depending upon the magnitude of the upcoming event.

3 Some approaches to obtaining more advance notice or prediction of 4 future events includes statistical analysis of the history of earthquakes in a given location so as to determine whether there is a recurrent, or cyclical pattern to the 6 events. These methods can provide a statistical value, for example, a 70%
7 probability of an event happening every 100 years, but still leave an uncertainty 8 of tens of years.

9 Generally however, there is a need for an earlier warning system and one which can be tied to known and independent factors.

13 Using the motion of the earth's poles, a series of successive geoids 14 can be determined. The shift between incremental geoids provides information necessary to determine changes in gravitational anomalies and ultimately the 16 accumulation in energy at a given geological location. Knowing the energy which 17 was released in a previous seismic event, the geoidal shift method of the present 18 invention can be used to monitor and predict a subsequent seismic event.

19 In a broad form of the invention, a method is provided for predicting seismic events comprising: determining a first geoid surface at first instance in 21 time; determining successive geoid surfaces for successive and incremental 22 instances in time; determining an incremental energy associated with each 23 incremental shift between the successive geoid surfaces; accumulating energy 24 associated with the incremental shifts; and comparing the accumulated energy with a pre-determined energy which has resulted in a seismic event as being 1 indicative of the likelihood of a future seismic event. Preferably, the pre-2 determined energy for a seismic event is determined by establishing measures of 3 the energy released in a previous seismic event.

BRIEF DESCRIPTION OF THE DRAWINGS

6 Figure 1 is a section through the center of the earth which illustrates 7 the effect of polar shift on the corresponding section through the geoid surface;

8 Figure 2 is a section through the center of the earth which illustrates 9 the effect of polar shift on the forces at a geographical location on the earth;

Figure 3 is a side view of a truncated ellipsoid earth illustrating 11 rotational planes and rotation vectors of a single mass on the surface of a geoid;
12 Figure 4 is a fanciful view to illustrate the tidal gravitational effects 13 of the sun and the moon;

14 Figure 5 is a plot of the polar motion of the earth over a selected time period of 1964-1968;

16 Figure 6a illustrates two geoids spaced in time with partial 17 indications of the many intermediate incremental geoids which could be 18 calculated therebetween and the magnitude of the change in gravitational effect;
19 Figure 6b is a pair of charts which respectively illustrate; a plot of the Ag over each time increment between two seismic events at t, and tn and 21 accumulates over time future event at tm, and a plot of the accumulation of 22 energy between events.

2 It is not new that gravitational anomalies affect the shape of the 3 equipotential surface of the earth. This undulating surface is also known as a 4 geoid. Effects which alter the shape of the geoid include the centripetal effect of the earth's rotation (an equatorial bulge) and tidal gravitational effects.
The 6 surface undulates due to local gravitational anomalies. While the surface of the 7 ocean provides a good approximation of the geoid, the shape of the geoid can 8 also be calculated over a land mass. These undulations are conventionally 9 determined as departures from the theoretical ellipsoid.

The geoid is associated with the earth's orientation which varies 11 according to an annual elliptical component and a Chandler circular component 12 with a period of about 435 days. The variation is due in part to annual spring melt 13 cycles and tidal effects which exert a torque on the earth. This torque results in 14 precession of the earth's rotational axis. The precession is not a steady process however, there being discontinuities or a lull in the precession each time the tidal 16 mass crosses the equatorial plane. Further, beyond the tidal precession, the 17 earth itself undergoes a free, Eulerian precession, some times called a "free 18 nutation" or the Chandler Wobble.

19 The earth's orientation or polar motion is monitored. One such monitoring service is the International Earth Rotation Service (IERS) located at 21 the U.S. Naval Observatory. It has been determined that the earth's axis has 22 scribed a conical path of about 23.5 in about 26,000 years.

23 The major sources of energy for seismic events are the gravitational 24 anomalies. Gravitational anomalies are generated by differences between the gravity equipotential surfaces and the centripetal force of the earth's rotation 1 (rC02). This value, of course, varies with latitude from zero at a pole to a maximum 2 at the equator (r=RcosT). A shift in axis of the earth's rotation changes the 3 radius of rotation (a vector of rotation force is a component of the gravitation 4 vector).

Variation of sea-level gravity from a theoretical ellipsoid was first set 6 forth, by mid-18th century scientist Alexis Clairaut, as a function of latitude.
7 Adoption of internationally agreed upon constants improved the accuracy of the 8 gravity calculations. Using the expression for gravity, relating mass and distance, 9 increased distance from the earth's center can be added to the calculation.
At sea level, the gradient is about -0.3086 milligal per meter of elevation increase.
11 Calculations for such uniform changes in elevation are also known as the Free-12 Air Anomaly. Pierre Bouguer, again in the mid-18th century, made corrections for 13 actual variations in topography. The resulting correction, about +0.20 milligal per 14 meter of elevation increase, was termed the Bouguer Anomaly. Further, there are well described variations in the crust of the earth, known as the Mohorovicic 16 discontinuities (Moho). Warping of these density interfaces also produce gravity 17 at the earth's surface.

18 Suffice it to say that the geophysics for determining the geoid 19 surface are known and the detailed mathematics are not reproduced herein.

The equipotential surfaces, or geoids, change continuously over 21 time and certainly as a function of the polar motion. While this is a continuous 22 process, a series of incremental geoid surfaces can be determined from the 23 empirical polar motion and tidal data.

1 The equipotential surfaces of the gravitation of successive geoids 2 intersect. A gravitational difference or shift Ag is represented by the difference 3 between successive geoids. Maximum shifts Ag are along the meridian of shift.
4 Minimums or zero Ag are found at intersection points of the two equipotential gravitational surfaces.

6 Adjustments can be made to correct for delay in change of the hard 7 body of the earth to compensate for the already changed rotation vectors.

8 The shift Ag can be expressed as a new surface over the earth.

9 The Ag shift represents forces applied to the earth at that point. The surface of the Ag shift is calculated in incremental steps. Integration of the Ag over time 11 represents the accumulation of energy for the earth at that point.

12 Further, secondary energy sources include, listed according to 13 magnitude, the moon's tidal wave and the sun's tidal wave. Another source of 14 unbalancing of the polar motion is the movements of the masses on the earth's surface by rivers and oceans.

16 The movements of the earth surface itself, such as mountain 17 growth, can be a reaction to the gravitational anomalies and have the same sign 18 as the anomaly. The plastic Mohorovicic discontinuity moves to compensate 19 gravity to a stable position or to minimize the anomaly. Additionally, thermal effects of the Earth are as a result of Pressure-Temperature-Melting point drop 21 function as described by Boyle-Mariotte's law.

22 The major horizontal earth movement energy in the earth is 23 generated by coriolis force and a gravitational sliding or downward motion.

1 The movement of the earth's masses obeys the law of mechanics 2 of continuum where every material point has its own force field application and is 3 not simply a hard, non-compressible body of flat form. These material point 4 forces are integrated by the volume to obtain a large scale mass movement estimation.

6 Earthquakes or seismic events are known to be caused by the 7 sudden release of energy within some limited region of the Earth. The energy is 8 largely a result of an accumulation of elastic strain. The release of the elastic 9 strain energy can produce major earthquakes.

By observing the point or region of the earth having two consecutive 11 earthquakes in time, one can determine the energy required to cause the 12 earthquake. This energy represents energy accumulated from factors including 13 those caused by the shift of axis of the earth between said events. From the 14 known energy level, one can predict a similar energy which will trigger or initiate a subsequent seismic event at that same location.

16 The energy due to polar motion can be estimated by summation of 17 the incremental shift Ag at that location. Accordingly, by extrapolating polar 18 motion and resulting shifts in geoid, one can predict the time of the next seismic 19 event and its magnitude.

The theoretical determination of locations and forces involved in 21 earthquakes can be obtained through mathematical modeling. Depending upon 22 the data available and the variables involved, the method varies in complexity.

23 In one embodiment, a simplified general formula is developed which 24 considers the energy sources, medium properties and geoid configurations. A

1 mathematical formula is derived with its end use applicable for computer-2 generated modeling.

3 Of all the possible energy sources, gravity and gravitation is 4 considered to be dominant. Other secondary sources are divided between independent sources such as the gravitational effects of the sun and the moon, 6 solar radiant heat, and dependent sources involving the transformation of energy 7 such as pressure to heat, and others.

8 The earth's rotation, is considered to be the major variable source 9 and is subject to rapid change. Rotational energy is handled as an equation of the shape of the geoid and the present drift of the geoid's axis of rotation.
11 Between time t, and time t2, there will be incremental geoid surfaces gi and g2.
12 The shift Ag is the difference therebetween, or 13 0g =Si-g2 ~1) 14 Having reference to Fig. 4, one can see that the geoid rotational surface is defined by equal vectors of rotation. The motion of a material point is 16 the dynamic earth's surface.

17 The known phenomena of drift of axis of rotation is defined as a 18 change in position of an imaginary axis of symmetry of rotation of the material 19 points where the radius is equal to zero.

During an earthquake, rapid movement of the earth's matter is 21 generated. This displacement or movement Ah is working against the plastic 22 properties of the earth at this point - the earthquake epicenter. As a result of a 23 rapid strain release, the geological medium breaks, and the energy released is in 24 a shock-wave form.

1 The value of the function representing the energy generated is the 2 seismic energy.

h 3 EQKFk(At ) (2) 4 where:
= Eq is referred to as the energy generated, 6 = Fk is the force, 7 = K is the coefficient of the medium property, reflecting the change 8 of potential energy of tension to the dynamic energy of rotation), 9 = Ah - is the displacement or throw of the fault, and = At - is the time of duration of the movement or accumulated time 11 in the case of multiple shock events.

13 From the law of the preservation of energy, the energy accumulated 14 Ea equals the energy released Eq.

E. = Eq (3) 16 This condition is satisfied when in the same geographical area, we 17 have repeated earthquakes after known time interval T, where T is greater than 18 zero. (T 0). Historically, one earthquake occurs at a first instance in time t1 19 and a successive earthquake occurs at a second instance in time t2.

The total potential energy Ep is that energy accumulated in elapsed 21 time T. After elapsed time T, following the seismic event, the potential energy Ep 22 is substantially zero due to the release during the earthquake. Smaller or minor 23 earthquakes having energy Eqo, may be a result of residual accumulated energy 24 of Ea - Eqo. As is later shown, the potential energy is a measurable and calculable element. From the known potential energy, we can find the total 26 stress-force that is required to produce the earthquake.

1 Geological media properties A, which can be termed media 2 property parameters, can be calculated using conventional methods of 3 determination such as drilling, seismic, gravity, etc. This gives one the ability to 4 adjust the solutions of systems of equations regarding one of the parameters.

One first models the earth's surface as a geoid surface and the 6 geoid as an ellipsoid of revolution. Now, assume that it is a plastically 7 deformable body whose equipotential surfaces are substantially parallel to the 8 geoid's surface. A graph of the model can be simplified to that shown in Figs. 2 9 and 3.

When, due to a shift in the axis of rotation, the equipotential surface 11 of the gravitation Vo, shifts to a position relative to the gravitated body of earth 12 surface-geoid, the estimate of the value of gravitation changes as AV.

13 AV =V, -V2 (4) 14 where = V; is the equipotential gravitation surface of the geoid before the 16 shift of axis, 17 = V'; is the equipotential surface of the geoid after the shift of axis, 18 = V is the potential energy accumulated at this point on the geoid, 19 and = AV is the difference between the new and the old equipotential 21 levels.

23 Where the geoidal surfaces at ti and t2 coincide, there is a minimal 24 change in the trajectory of the earth's crust. Where the geoidal surfaces vary, there is a gravitational anomaly and a shift in the velocity vector or trajectory of 26 the earth. This results in significant forces in the earth's crust.

27 At each point, there are two forces applied: F due to gravity and 28 K due to the centripetal force for g= F+K R. The centripetal force is applied in 1 the plane of rotation and perpendicular to the axis of rotation. Centripetal force 2 can be represented as K = wz p where p is the radius of the plane of rotation 3 and w is the angular velocity.

4 In an ideal situation:

AV = kAg (5) 6 where Ag - is the gravitation anomaly generated.

7 But in practice the solutions are more complicated.

8 The IERS and others have precisely documented the polar motion 9 for more than 100 years. From this, we can obtain the accumulated value of the total number of events, A, in a given area A
11 Va = EOV,. (6) H
12 The limit of this value is A
13 V! =LimLAV, (7) /-+oo i_1 14 The physical limit is reached when the potential (stress) energy is transformed into the dynamic (strain) energy and results in the earthquake.
16 Therefore these two values are equalized at this time by equation.
( ) 17 V,=.fk ~t ~h (8) 18 where fk is a specific function which can be estimated.

19 One plots the equipotential surfaces of the AV on a geoid surface.
Overlaps indicate multiplication of Ag in this point and signal a concentration of 21 energy. As stated, using historical data for the energy and the incident of the last 22 earthquake event, the next may be predicted.

1 Accordingly, by monitoring the accumulation of potential 2 gravitational energy Ea between two successive earthquakes at a geographical 3 location and between times t, and t,,, and by extrapolating the ongoing 4 accumulation of potential energy to some future polar motion at tm, we can predict the moment when the conditions are satisfied for a similar seismic event.

6 Having reference to Fig. 5, the polar motion for the period of time 7 between 1964 and 1968 are illustrated. It is hypothesized that a beat between 8 the annual and the 14 month cycles results in the occasional collapse or 9 approach of the generally circular polar motion.

Turning to Fig. 6a, an exaggerated shift of the geoids over time due 11 to polar motion (PI - Pn) illustrates how the net gravitational effects are increased 12 in some areas and decreased in others. As shown at point Z, the effect is 13 minimal at the intersection of the geoids. In Fig. 6b, the incremental changes in 14 Ag for incremental instances in time ti - tõ are plotted. At time tn, an earthquake event is indicated. By integrating Ag over time between t, - tn, and applying the 16 appropriate constants for determining energy, the energy Eq which was 17 necessary to cause the earthquake at that particular locale can be determined.

18 Having V,n as an anomaly produced from periodic functions such as 19 moon gravity and sun gravity waves Agm, the V, of Eqn. 8 can be adjusted.

Theoretical calculated values of Moon and Sun tidal gravity change 21 are:

22 for the moon, 23 0 g, =~ f M, P R-' ft2cos2 z, - 3)+PR' (5 cos3 z, - 3 cos z, ~(9) c c c c 1 and for the sun, 0 3 P Me sin3 Ir I z 2J
2 g _ 2 f M' c~ M, sin3 ic, r 3 (10) 4 where = Ag , Og - first differentials on the Earth radius of tidal gravity 6 potential.
7 = f - Gravity constant, 8 = Mc - mass of Moon, 9 = M - mass of Sun, = p = a(1- esinz yi~ - the distance from centre of earth to point of 11 measurement, 12 = cc - Average distance from centre of the earth to centre of the 13 moon, 14 = Rc the distance from centre of the earth to centre of the Moon on the moment of measurement, 16 = r - the radius - vector of the sun.
17 = sinnc,sing the equatorial horizontal parallaxes of moon and 18 sun, 19 = z - momentary geocentric distance of moon and sun and 21 cos z = sin 8 sin yr + cos S cos yr cos z (11) 22 Where 23 = S- Latitude of the Moon or Sun, 24 = r - Hourly angle of the Sun and Moon = - Geocentric latitude of the point of measurement.

27 The value of Ag is in range of hundreds of mgal compared to the 28 average of the earth's gravity being 980 gal (1 gal = 1 cm/s2).

1 The tidal correction can be made as follows:

A
2 , <_ EOV. +V(9) ;-1 3 Through satisfying this condition, one is able to determine or 4 predict an earthquake event in time and place. Past experiments have shown good correlation between seismic events and moon tide peaks.

6 There is a geological part of the methodology that is similarly 7 determinable applying similar techniques. The vector calculus equations that 8 actually define the gravity, gravitation and the elastic properties of the 9 Earthquake, vector movements of a solid point of the geoid and centripetal potential belong to the field of vector calculus and the theory of the earth 11 topography which are known to those of ordinary skill in the art.

Claims (2)

1. A method for predicting seismic events comprising:

(a) determining a first geoid surface at first instance in time;

(b) determining successive geoid surfaces for successive and incremental instances in time;

(c) determining an incremental energy associated with each incremental shift between the successive geoid surfaces;

(d) accumulating energy associated with the incremental shifts; and (e) comparing the accumulated energy with a pre-determined energy which has resulted in a seismic event as being indicative of the likelihood of a future seismic event.

2. The method of claim 1 wherein the pre-determined energy for a seismic event is determined by:

(a) identifying a first instance in time when a seismic event occurred at the geographical location;

(b) identifying a second instance in time when a second successive seismic event occurred at the geographical location; and (c) establishing measures of the energy released in the second successive seismic event.