Hello from Germany,

your question: What can we say about the largest possible event (earthquake) that could happen in an area based on data?

Hm, sorrowly we can`t look what happens under the lithosphere. We cannot send satellites to get a lithosphere-wheather forcast. But as you are busy with, we may look what are the events on the surfaces-movements and their strength along a timescale. I've done that and combined propability, frequency and heavyness of magnitudes > 2 (or less). Less than 2 we have a symmetrical shape of a density distribution (sceewed and with cutosis), more that 2 you can see a part of all counted events. As you can see in the picture there must be a link between frequency&strength and probabilty when observing the gradient. The beginning of the gradient - I hope , may indicate an incoming earthquake anywhere in Italy. Next step one should discover rapidly where to find the reason. The largest event - I mean - you would never find a definite aswer, as we all work on probapististics.

Marcus

Speaking purely from a probability perspective (with a touch of philosophy I suppose) and have NO knowledge of seismology, I'd say the biggest issue in making probabilistic estimates is time scale of available data. Suppose a much larger earthquake occurred long ago in the region prior to any collected data. There might be some evidence of a massive quake in the geological record and estimates might be made from that, which would be helpful. But what if such a much larger quake is not known for whatever region that is being studied? If a much larger time scale (which might include a regularly occurring massive earthquake that is as-yet unknown) overlaps with the current time scale predictions are being made from, then a quake which exceeds the predicted confidence interval could happen and could ultimately be much more probable, just not known. I guess the issue is that your predictions will only be as good as your sample.

Dear Markus

I appreciate input and comments. As regards the largest possible event - we try to estimate it. Along with the estimate we obviously have uncertainty. But It is a well known problem trying to find an estimate of a truncation point of a distribution. But interpretations differ so vastly and some workers use different methods and different arguments. Pisarenko used a fiducial probability that there is no upperbound, which is a theoretical heuristic. But Holschneider draws different interpretations from it, which are much more on the philosophical side, that discredits our usual (humanly) confidence in our estimates.

I will read Holschneider's paper again and make my question more exact in a moment

Yes Edward - you are right.

Earthquakes appear suddenly, if we talk about those with a Magn > 3. All events less than 3 do cover under a skewed Bell-curve with a certain curtosis. That depends on a permanent ground noise. One will discover that facts on each region on earth.

So statisticians will use either the Poisson distribution or a Richter-Gutenberg Distribution, depending of what they want to compare.

I would like to show that frequency - data - I have analyzed data of a year approx. 50.000 in 2016, 25.000 in 2018 data - do well cover under the same skewed curve. The requirement is that skewness and kurtosis are taken into account.

So one will discover that - in complete Italy there wil be an earthquake in a near future - depending on a certain relationship frequency&strength and probability. Yes, we will have a much larger quake that is not known for whatever region. But for all that knowledge we have of earthquakes we can make predictions - and more than that - politicians should make decisions about setteling - restrictions in endangered regions, or even for building safety.

Marcus

Great points raised Marcus and Petrus. We face similar issues in emergency medicine in making predictions. Poisson is very helpful and turns out to be quite accurate. We're lucky in that a year or more of data is typically enough for short to medium term planning for certain types of events (atypical patient arrivals, etc.) But we wouldn't really have a good way to predict some kind of mass casualty event that hasn't happened. I have sympathy for your endeavors in trying to make good predictions about something as complicated as earthquakes and the kind of planning under uncertainty it must entail. Kudos to you both for working on such a complicated problem.

Hello Participants,

I have added an Excel spread sheet containing an example given for 2 equations (eqb,eqbl I have published at Springer) based on Magnitudes samples you may test .... well, if you like?

May be you must change some Excel functions cause they appear in german language for example squareroot sqrt appears as Wurzel... and so on

Yours Marcus

Can you predict when YOU will start shaking (from different reasons- fear, excitement, frustration...)?

Try an "Earth = Being" perspective.

Anamaria Popescu, it is indeed a random (stochastic) process, PLUS we have uncertainties (gaps) in our knowledge. We are not looking to PREDICT the largest possible magnitude, but trying to ESTIMATE the least upper bound (supremum if you like) of the random process (excluding gaps in knowledge as far as possible). Some authors have made claims that it is impossible to estimate the least upperbound intrinsically, or that we are too optimistic in our estimates thereof.

Indeed this is a parameter of the distribution of a random process. But it IS very touchy subject in seismology and arguments are starting to go beyond the bounds of science and formal logic. The following reference is a prime example:

Holschneider, M., et al. (2011). "Estimation of the maximum possible magnitude in the framework of a doubly truncated Gutenberg–Richter model." Bulletin of the seismological society of America 101(4): 1649-1659.

I‘m still working on an answer, I think this Will Not satisfy ...

The problem of estimating the largest event derives from our lack of a unified field theory between quantum mechanics and the rest of physics. Currently, physicists use the Planck basis as the 'best basis for estimating events over periods of time,' because eventually we reach a discrete limit in which all events are quantized (this is the Planck scale ~10^-34m). After this point, we simply CANNOT predict events (even the act of measurement alters the system). Nonetheless, when we use this scale as our mathematical basis, we obtain the best picture possible (admittedly a fundamentally limited one). When we write down a unified field theory between quantum mechanics and the rest of physics, we will be able to (hopefully) obtain an even better picture than the 'Planck picture,' but I digress..

I ‘m still working on an answer, I think this Will Not satisfy ..

as you can see on the addes picture - a special view of data may help to predict:

shown are two lines: the number of shocks, the slope of probabilty along a timescale of the eqbl - equation. But herer we go with the opinion of Edward.G. Brown: But what if such a much larger quake is not known for whatever region that is being studied? If a much larger time scale (which might include a regularly occurring massive earthquake that is as-yet unknown) overlaps with the current time scale predictions are being made from, then a quake which exceeds the predicted confidence interval could happen and could ultimately be much more probable, just not known.

I have studied probabilistic jam of magnitude strength that may point to a future heavy earthquake:

1. a picture of recent earthquake Catania & its history

2. a picture of the region of Macerata

To be continued:

what does the analysis show?

Yes, you may estimate the probabilty of earthquakes in a region

No, you cannot predict earthquakes in time or for a special place

Yes, you can follow the growth of the number of the frequence

Why?

Most of events caused by production processes can be evaluted by a quality approval - because all the pieces you produce are produced on the same place at a mesurable moment. Not so for earthquakes. A collection of data you gain from all seismographs loose time- and place information. So the only distribution you may analyse is a general one all over the region.

What can you do?

Don`t settle in those regions or make the buildings stable against shocks!

To gain futher information of earthquakes one must study the movements of the underground we walk on. One may do this with a lot of magma-satellites? The result of it will be such one as we know of a wheather forcast. But I dont´t believe in that.

Marcus Hellwig I like where your analysis is going. It is making me think more and more about turbulent systems and the way in which the underground movements may be part of cycles; and how there could be 'tipping points' which could trigger large (larger?) earthquakes than had been previously or in places unexpected. So the origin of them could be longer time scales which overlap our own or even just a product of the turbulent activity, meaning that they are not regular per se, just part of the turbulent system. Fascinating problem to think about.

May be good idea. Must check whether magnitudes below 3 are signifikant and symmetically distributed. And perhaps turbulentes that appear overleaping that frequences in a certain rithm?

...should use Fourier Transformatio n to detect unsignificant data ?

Dear Marcus Hellwig. I always wondered about the use of Fourier transform to analyze "noise" in data that is not necessarily a time series. Can you recommend any reading?

Oh yes, to gain a complete overview & History of equations & explanations to enter the theme you may study „seventeen equations that changed the world“ Ian Stewart... there are lots of publictions....

I‘m on Holidays in Austria and still reading Ian Stewarts Books. I have addended a sketch about my idea when following Edwards thoughts....

As I have no Computer, I have to work with my brain and a ballpen to make sketches that shall explain my idea based on the thougths of Edward... I hope they explain themselves?

See Text above

Marcus, I think these are great and can see where you are heading, I think. Is it possible there could be some period doubling at play somehow?

I was doing some searching and came across this paper, which incorporates Fourier transformations. Article A model for aperiodicity in earthquakes

Edward: I tried to demonstrate some observations of a single region of Macerata/ Italy, where we have some data of Magnitudes along a timescale. Seems that doubling is not a complete Cluster - contemplation when analysing a couple of depending regions as we have in the earthquakezones around the Appeninmountains. That offers another question: Can we separate clusters reffering to its origin by using Fourier? See sketches

Very interesting thing! At least that leads to a solution concerning a separation of vibrations and its frequencie....

Petrus: a solution to detect the

largest possible event

in the meaning of continously observing earthquakes by taking samples and at least estimate the strength of the release-energy of a future jam. Let us see if Fourier gives an answer for separable clusters to identfy different origins of low magnitudes with high number in short time

seems to come closer

.... and there should be an answer for Mrs Popescu‘s question...

but step by step:

step 1:

The basis for the following investigation is a data collection from 2018 over 20000 data sets.

It is necessary to determine

estimated mean: estimated logarithmic variance: estimated logarithmic skew: estimated logarithmic kurtosis

Using the Probabilityfunction Eqbl (shown and analized in ISBN 978-3-658-21859-1)

Step 2 will follow soon...

Here are some explanations to the graphics shown above:

Here are some explanations to the graphics shown above:

Let`s have a look upon Macerata,

Petrus:

could we have predicted the strongest Magnitudes at the beginning of the year 2018?

We are going back to January 2018 to start the obsevation acoounting the knowledge of the data of 2017 (pic1) and having a look upon the trend a few weeks later (pic2) and the result of a trendanalisis (pic3)

Does that fit for all cases?

step 2

let`s have a look upon Campobasso

1.(pic 4), Manitudes along timeline of 2018.

2. (pic 5), ProbableTrendCampobassoJan2018

3. (pic 6) ProbableTrendCampobassoJan2018prevision

4. (pic 7) ProbableTrendCampobassoMarch2018

5. (pic 8) ProbableTrendCampobassoMarch2018previsionMarch

May be that we have evidence that a probabilistic trend analysis coupled with a theoretical density distribution may indicate future earthquakes, but further experiments are needed, so I will be conducting further observations and analysis on Italy in 2019.

Next step:

After earthquakes of a vertical seismogram we`ll get a spectrum after the Fourier transformation. Let`s see if we can get a filter for noise data to separate them from earthquake-shocks....

Can we estimate the maximum of magnitudes by means of trend development?

Perhaps... Let's take a look at the pictures showing all of Italy in different trends compared to the region of Catania, see pics below:

What does it mean? Yes, probabilistically we can estimate the future magnitudes if we have sufficient data from the past.

Last step:

Unfortunately, I did not have access to data on the earthquake frequencies, so I was only able to determine a Fourier analysis on the number of magnitudes within a time interval. In the end, the analysis remains that a trend towards strong earthquakes with a certain probability is recognizable if there is a sufficiently high amount of data from the past is available.

What can I do now: I`m going to observe what developing will be in Italy week by week, starting 1st Jan 2019.

ok, here we go - and let`s have a comparison-look on Jan 2016:

We find

- a more dense frequence of data of magn than at Jan 2019.

- a shift of Fourier combined with the shift of the mean value

Now, let`s have a comparison-look onto one region: Macerata 2016/2019

Note the differences between the red circles. In Jan2016 we had a significant deviation from a longtermed distribution. In Jan2019 Magnitudes are tending to increase (see Fourier-panel).

Since now to the followers a picture will be shown to demonstrate the status each week, see Italy, Macerata, Perugia:

Continuation: Comparision 2016 / 2019

Let´s have a look upon Italy and Perugia!

We have a sight shift on the distributions, but a significant shift on the picture that shows the combination of Probability, Fourier and the shown sum of the seismic energy based on the Magnitudes-scale.

Continuation: Perugia 11 days later, movements seem to keep calm?

stato intermedi, probabilità tra 1,5 e 4

Report 2019-03-13: Movements seemed to be getting less

Report 2019-03-20: as long as we have no difference between blue-bell-curve and black-bell-curve, we have not an increase of Magn-strength

Report 2019-03-27: as long as we have no difference between blue-bell-curve and black-bell-curve, we have not an increase of Magn-strength

Report 2019-04-03: as long as we have no difference between blue-bell-curve and black-bell-curve, we have not an increase of Magn-strength, a comparison between Jan and Apr 2019 is added

Report 2019-04-11: as long as we have no difference between blue-bell-curve and black-bell-curve, a comparison between Fourier Feb / Fourier Apr is also added

Report 2019-04-17: as long as we have no difference between blue-bell-curve and black-bell-curve, a comparison between Fourier Feb / Fourier Apr is also added

Whilst the discussion of the useful help of a Fouriertransformation keeps to be open

Mr

Deepak Bhalchandra Gode, Directorate of Census Operations, Mumbai, India

“In the understanding there is no need of i in Fourier transformation, the fourier-series it self is a series of complex number, together with cos and sin.

In the derivation of Fourier transformation formula suddenly imaginary number i was introduced (see a derivation), why? No explanation. In my opinion i imaginary number was just misleading and it really changed/stopped the understanding of Fourier transformation.”

Report 2019-04-24: We have a remarcable closure of black and blue-bell-curve and a significant shift of (Fourier x NumeroMagn * Magn*Probabilitá) = Fourier x NumberMagn * Magn * Probability from 2,8 till 3,5. We`ll see what will happen!

Intermediate Report:Looking at March & April 2019 we have also a remarcable

Trend of occurence of damage & probability of occurence of damage expecting a join at middle of May

Report 2019-05-02: Still we have an unchanged situation...and last not least neither I´m convinced that we can define a final answer for:

- a maximum Magnitude.

I will close my work here hoping that other methods can help to preview.

The only answer Eqbl can give is "the permanent earthquake risk = probability x released energy given in tons of TNT", see second pic.

If anyone would like to continue my work, he may request - and I would like to send him the excel-spread sheet.

Finally I present to you a comparison-pic for the earthquake - releasable energy - risk between two regions: India (Mr Deepak Bhalchandra Gode was so kind leaving a dataset to analyze India´s earthquakes) & Italy. As you can estimate:

Never anybody can give an answer for the problem of estimating the largest possible event

That´s my final sentence.

An overview may help to give an impression of the risk of earthquakes of the last month for most of the italian provinces in between magn > 2,5 & Magn

Giving you a monthly Fourier-Report of Magnitudes evolution (7MonthSequence; red circled areas) may show that Magn are tending to become 4. We`ll see next months...

Giving an impression of trends, divided by Italy and 3 Provinces - it is obviously that a remarable %-trend-difference is found in the combination of low number and a highscore of Magnitudes. So - do those have the highest influence of the monthly/ yearly evolution of eathquakes?

I have just develloped a comparison for Italiy earthquakes between 2016 and 2019.

you may have a look on both. I mean - italian observers could have previewed a heavy earthquake at september 2016 since they had measures of april 2016.

Take also a look at both scales...

If looking at the history of 2016 and at the innitials of 2019....

are Italy earthquakes upper Magn >= 2,4 collecting releasable jam-energy for a next big shock 4 month later from now?

The shown picture demonstrates the difference between two years of a collection of Magn data:

Italy_Earthquakes_Summary of Magnitudes_Densities_2016_2019

As a negative base data of 2016 will be used to compare earthquakes risk of the sum of released energy (RSRE). That means: observing the increase till a jam of RSRE of 6,54 * 10^11 should be meaningful... I´ll do so

Marcus Hellwig Thank you for sharing your comparison and presentation of your data! Going to try to look at it and see what I can learn from it.

Only now have I had the chance to look at it and saw how much you shared. I had a lot on my plate and some health issues, but have time now. Will say more if I made sense of all the data (not saying it is not well presented, but I want to get a feel for what is going on)

......I‘m going to continue this Research observing and comparing data from 2016 and 2019...

Petrus

..so what I want to discover: Analysing data most of earthquake researchers suppress Magn lower than 2. Oppositly I´m going to treat them all. Why all?

As I`m familiar with statics and dynamics - I think it is worth to analize them all, because a lot of lower Magn - but with a high number of appearance - store dynamic energy until a time of release, thats what I have called "jam". So that a jam finally released in a riskful region - as an earthquakeshock - is most likely.(e.g. : pdf Compare2016_2019).

The main-questions I´m going to follow by further asking is - may be your question will be resloved with it :

1st : How strong must be a "jam of lower measurements of seismological movements" to be released in an earthquake that destroyes structures like buildings?

2nd : Which are the regions where likelyhood points to an earthquake risk caused by a so called "jam"?

Therefore I´m collecting earthquake-data of italian regions until the analyzes points to an incoming jam.

The equations I have elaborated and used will help - I hope...

Could´nt be previewed ? Earthquakes 2016, check data comparison 2016/ 2019