Monday, October 21, 2013

Battering Rams: Estimating the energy of the 7.2 magnitude earthquake that destroyed Bohol's churches


"Little Boy" atomic bomb
"Little Boy" atomic bomb
(Disclaimer: Since I am not a geologist but only a physicist, I would appreciate if somebody can correct my assumptions and computations. Computations and opinions are solely mine and may not necessarily reflect those of the Department of Physics of Ateneo de Manila University and of the Manila Observatory.)

According to Philippine Star, Dr. Renato Solidum of Phivolcs reported that "a magnitude 7 earthquake has an energy equivalent to around 32 Hiroshima atomic bombs".   I verified his estimate in Earthquake Energy Calculator and constructed the following table:

Table 1: Energy equivalent of earthquake magnitudes in Richter scale
Magnitude (R) Seismic Moment Energy (J) Seismic Radiated Energy (J) Hiroshima Bombs
7.0 $3.899420\times 10^{19}$ $1.995262\times 10^{15}$ 31.8
7.1 $5.508077\times 10^{19}$ $2.818383\times 10^{15}$ 45.0
7.2 $7.780366\times 10^{19}$ $3.981072\times 10^{15}$ 63.5

So a 7.0 quake is equivalent to 32 Hiroshima-type bombs, as Dr. Solidum said.  But a 7.2 quake is 64 nuclear bombs!

Little Boy A-Bomb Drop Hiroshima Ruins 11x14 Silver Halide Photo Print

Numbers always have assumptions behind them.  These earthquake energies do not mean that 32 "Little Boy" (Hiroshima-type) nuclear bombs were dropped from a plane and destroyed all the churches upon impact.  There is still another parameter that the media failed to ask: the depth of the quake epicenter.  According to USGS, the epicenter's depth is about 20 km and not 0 km (ground level).  This means that you make a well 20 km deep, put all the 32 Hiroshima-type bombs there, one on top of each other, cover the well with soil and stones, then detonate the bombs.  BOOM!  The island of Bohol would then shake and the churches would be leveled to a heap of ruins.  Actually, a similar procedure was done by France when they detonated nuclear bombs at the Moruroa Atoll, but the depth of the well is less than 1 km:
France abandoned nuclear testing in the atmosphere in 1974 and moved testing underground in the midst of intense world pressure which was sparked by the New Zealand Government of the time, which sent two frigates, HMNZS Canterbury and Otago, to the atoll in protest for a nuclear free Pacific. Shafts were drilled deep into the volcanic rocks underlying the atolls where nuclear devices were detonated. This practice created much controversy as cracking of the atolls was discovered, resulting in fears that the radioactive material trapped under the atolls would eventually escape and contaminate the surrounding ocean and neighboring atolls. A major accident occurred on 25 July 1979 when a test was conducted at half the usual depth because the nuclear device got stuck halfway down the 800 metre shaft.[2] It was detonated and caused a large submarine landslide on the southwest rim of the atoll, causing a significant chunk of the outer slope of the atoll to break loose and causing a tsunami affecting Mururoa and injuring workers.[2] The blast caused a 2 kilometre long and 40 cm wide crack to appear on the atoll.[2] (Wikipedia: Moruroa)

Richter's Scale: Measure of an Earthquake, Measure of a Man
A. Richter Scale and Radiated Energy

In order to relate the energy $E$ of an earthquake to the Richter scale $R$, we use the formula
\begin{equation}
E = 10^{1.5 R + 4.8}
\end{equation}
Let's try for $R=7.0$:
\begin{equation}
E = 10^{1.5(7.0)+4.8} = 10^{15.3} = 10^{0.3}10^{15} = 1.995262\times 10^{15} J,
\end{equation}
where $J$ stands for Joules, a unit of energy. Notice that energy value corresponds not to the seismic moment energy but to the seismic radiated energy.  Since  Phivolcs says that the magnitude is 7.2 while USGS says it is 7.1, we will just stick to the value of 7.2, which gives
\begin{equation}
E = 10^{1.5(7.2)+4.8} = 10^{15.6}= 3.981\times 10^{15} \approx 4\times 10^{15} J.
\end{equation}

Seismic Wave Propagation and Scattering in the Heterogeneous Earth : Second Edition
Seismic Wave Propagation and Scattering in the Heterogeneous Earth : Second Edition
B. Earthquake Power and Intensity as Function of Distance from Epicenter

For simplicity, let us assume that the 7.2 magnitude quake happened in 1 second.  This means that the power at the source is
\begin{equation}
P = \frac{E}{\Delta t} = \frac{4\times 10^{15} J}{1 s} = 4\times 10^{15} W,
\end{equation}
where the $W$ stands for Watts, a unit of power. If the seismic wave spreads out equally in all directions, then the average intensity at the distance $r$ from the quake epicenter is
\begin{equation}
I_r = \frac{P}{4\pi r^2},
\end{equation}
(c.f. Young and Freedman 2004, p. 567). This simply means that the farther you are from the epicenter, the quake intensity decreases. One way to imagine this is to take a balloon.  Blow some air into it, then draw some equally spaced dots on the surface, about 1 cm apart.  If you blow more air into the balloon, the balloon expands.  The number of dots remain the same, but the number of dots per square centimeter decreases.  In the same way, for earthquakes, the power remains the same, but the power per unit area decreases as you go farther from the epicenter.

Intensity of a spherical wave
Intensity of a spherical wave as a function of distance from source (Source: Hyperphysics)

Since the earthquake epicenter is 20 km deep, we set $r=20\times 10^3 m$ and solve for the intensity $I_r$:
\begin{equation}
I_r = \frac{4\times 10^{15} W}{4\times 3.14\times 400\times 10^6\ m^2} = 7.96\times 10^5 W/m^2 \approx 8\times 10^5 W/m^2.
\end{equation}
Since we assumed that the duration of the quake is $1s$, then the energy $E_r$ absorbed per square meter by the church buildings per square meter is
\begin{equation}
I_r\Delta t = 8\times 10^5 J/m^2 = \frac{E_r}{A},
\end{equation}
where $A= 1 m^2$.  Hence,
\begin{equation}
E_r = 8\times 10^5 J.
\end{equation}

Joint Scientific Papers of James Prescott Joule (Cambridge Library Collection - Physical  Sciences) (Volume 2)
Joint Scientific Papers of James Prescott Joule (Cambridge Library Collection - Physical Sciences) (Volume 2)
Energy Equivalent of a Falling Mass

How does one imagine an energy $E_r = 8\times 10^5 J$?  Gravitational potential energy is $E = mgy_0$, where $m$ is the mass of the object, $g= 9.8 m/s^2$ is the gravitational acceleration, and $y_0$ is the initial height from the reference (e.g. ground).  For simplicity, let us set $y_0 = 1 m$, so that the corresponding weight of the object must be
\begin{equation}
mg = 8\times 10^5 N,
\end{equation}
where $N$ is Newtons, the unit of force.  Dividing both sides by the gravitational acceleration $g=9.8 m/s^2$, we get the mass
\begin{equation}
m = 0.8\times 10^5 kg = 80,000 kg.
\end{equation}

ANTIQUE PRINT -ROMAN- BATTERING RAM SYSTEM- 1729
Battering Ram!

How does one imagine a mass $m = 80,000 kg$?.  Steel has a density of
\begin{equation}
\rho = \frac{m}{V} = 7,850 kg/m^3.
\end{equation}
For a mass of $80,000 kg$, the corresponding volume of steel is
\begin{equation}
V = \frac{80,000 kg}{7,850 kg/m^3} = 10 m^3.
\end{equation}
If the steel is is a box with base area of $1 m^2$, then the height of the box must be 10 m or about three building floors.  So we have a pillar of steel: $1 m\times 1 m\times 10 m$.  This is already a battering ram that can destroy the gates of medieval fortresses!


Old Historical Baroque Filipino Church of Loon - 52"W x 35"H - Peel and Stick Wall Decal by Wallmonkeys
Old Historical Baroque Filipino Church of Loon - 52"W x 35"H - Peel and Stick Wall Decal by Wallmonkeys
Thus, Bohol's churches were destroyed because the energy of the quake is equivalent to a battering ram of $1 m\times 1 m\times 10 m$ that is rammed against every square meter of churches foundations with a speed equal to that as if the ram is lifted 1 m from the the point of impact and and then released.  The speed of the impact can be computed from the Law of Conservation of Energy:
\begin{equation}
mgy_0 = \frac{1}{2}mv^2.
\end{equation}
Solving for the final velocity $v$, we get
\begin{equation}
v = \sqrt{2gy_0} = \sqrt{2\times (9.8 m/s^2)\times (1 m)} = 4.43 m/s.
\end{equation}
This speed is equivalent to
\begin{equation}
v = 4.43 m/s = \frac{4.43 m}{s}\times\frac{3600 s}{hr}\times\frac{1 km}{1000 m} =  15.9 = 16 kph.
\end{equation}
Thus, the earthquake of magnitude 7.2 is equivalent to a battering rams of sizes $1 m\times 1 m \times 10 m$ lifted $1 m$ and then released.  The battering rams swing like a pendulum and hit each square meter of the walls at a speed of $4.43 m/s = 16 kph$. Hence, the pile of ruins. (Note: Technically, you still have to compute the moment of inertia of the battering ram as it swings like a pendulum.  But for simplicity, we approximated the ram into a ball of the same mass.  This is not really important; what is more important is the speed of the ram just before impact, and we set this speed to be 4.43 m/s, the same speed if the ram touches the ground as it fell freely from a height 1 m above the ground.)
Medieval Battering Ram
Medieval Battering Ram

Quake Magnitude and Length of Battering Ram

We can repeat the same procedure for 7.0 and 7.1 magnitude quakes.  But I think it is best to derive a formula instead that relates the quake magnitude and the length of the battering ram.

We know that the formula for the quake energy $E$ as function of the Richter magnitude $R$ is
\begin{equation}
E = 10^{1.5 R + 4.8}.
\end{equation}
Dividing this by the time interval $\Delta t$ yields the power
\begin{equation}
P = \frac{E}{\Delta t}.
\end{equation}
The intensity $I_r$ of the quake at a distance $r$ from the epicenter is
\begin{equation}
I_r = \frac{P}{4\pi r^2},
\end{equation}
In terms of energy $E$ and the Richter magnitude $R$, this is
\begin{equation}
I_r =\frac{E}{4\pi r^2\Delta t} = \frac{10^{1.5 R + 4.8}}{4\pi r^2\Delta t}.
\end{equation}
This means that the energy $E_r$ per unit area $A$ at a distance $r$ from the epicenter is
\begin{equation}
\frac{E_r}{A} = \frac{E}{4\pi r^2} = \frac{10^{1.5 R + 4.8}}{4\pi r^2}.
\end{equation}
Replica battering ram at Ch√Ęteau des Baux, France

We define the energy $E_r$ in terms of a mass $m$ falling from a height $h$:
\begin{equation}
E_r = mgy_0.
\end{equation}
For a steel of density $\rho$ which is shaped as solid box of base area $A$ and height $h$, the mass of the steel is
\begin{equation}
m = \rho V = \rho Ah.
\end{equation}
Thus, the energy $E_r$ is
\begin{equation}
E_r = \rho Ahgy_0,
\end{equation}

Using these results, we have
\begin{equation}
\frac{E_r}{A} = \rho hgy_0 = \frac{10^{1.5 R + 4.8}}{4\pi r^2}.
\end{equation}
Solving for the height $h$ of the steel with $1 m^2$ base, we get
\begin{equation}
h = \frac{1}{\rho g y_0} \frac{10^{1.5 R + 4.8}}{4\pi r^2}.
\end{equation}
This height $h$ is the length of the battering ram with $1 m^2$ base area of density $\rho$ raised at a distance $y_0$ from its starting point.  This battering ram is the equivalent of the earthquake of Richter magnitude $R$ originating at a depth of $r$ below the surface.


Illustration of Roman Soldiers Forming Testulas and Using Siege Towers to Attack Fortified Wall - 42"W x 37"H - Peel and Stick Wall Decal by Wallmonkeys
Illustration of Roman Soldiers Forming Testulas and Using Siege Towers to Attack Fortified Wall - 42"W x 37"H - Peel and Stick Wall Decal by Wallmonkeys
Steel Ram vs Wooden Ram

Let us now set the values for a steel ram: $\rho = 7,850 kg/m^3$, $g = 9.8 m/s^2$, $y_0=1m$, $r=20\times 10^3 m$.  These give
\begin{equation}
h = h(R) = \frac{10^{1.5 R + 4.8}}{3.867\times 10^{14}}.
\end{equation}
On the other hand, had we set the values for a wooden ram with $1 m^2$ cross-section, we simply change the density to that of wood $\rho=1\times 10^3 kg/m^3$ (e.g. logwood $\approx 0.9\times 10^3 kg/m^3$).  This would result to
\begin{equation}
h = h(R) = \frac{10^{1.5 R + 4.8}}{4.926\times 10^{13}}.
\end{equation}
As before, the ramming speed is assumed to be $4.43 m/s$ upon impact.

Let us tabulate our results.  Note that this assumes that the structure is immediately above the quake epicenter.  Notice that if the quake epicenter is 20 km below the ground, a 6.5 magnitude quake is approximately equivalent to a wrecking ball less slightly less than 1 m in radius; while a 6.9 magnitude quake is equivalent to 28.7 m (94 ft) long wooden ram hitting the building's foundations, such as that used by the Roman army in their siege:
Roman Siege Weapons - The Aries or Battering Ram. The aries, or battering-ram, consisted of a large beam made of the trunk of a tree, frequently one hundred feet in length, to one end of which was fastened a mace of iron or bronze resembling in form the head of a ram; it was often suspended by ropes from a beam fixed transversely over it, so that the soldiers were relieved from supporting its weight, and were able to give it a rapid and forcible swinging motion backward and forward. (Tribunes and Triumphs)
Games Workshop The Siege of Gondor Lord of the Rings Supplement
Games Workshop The Siege of Gondor Lord of the Rings Supplement
This ram is also similar to the one used by Sauron's armies during the siege of Gondor:
The drums rolled louder. Fires leaped up.  Great engines crawled across the field; and in the midst was a huge ram, great as a forest-tree a hundred feet in length, swinging on mighty chains.  Long had it been forging in the dark smithies of Mordor, and its hideous head founded of black steel, was shaped in the likeness of a ravening wolf; on it spells of ruin lay.  Grond they named it, in memory of the Hammer of the Underworld of old.  Great beasts drew it, orcs surrounded it, and behind walked mountain-trolls to wield it. (The Siege of Gondor, Lord of the Rings, p. 828)
This is only for a 6.9 quake, 20 km deep.  How much more for quakes of magnitudes 7.0, 7.1, or 7.2?



Table 2: Equivalent battering ram lengths for earthquakes of different magnitudes with epicenter depth of 20 km 
Earthquake (R) * Steel Ram (m)** Wooden Ram (m)** 
6.0 0.16 1.3
6.1 0.23 1.8
6.2 0.32 2.6
6.3 0.46 3.6
6.4 0.65 5.1
6.5 0.92 (wrecking ball) 7.2
6.6 1.3 10.2
6.7 1.8 14.4
6.8 2.6 20.3
6.9 3.7 28.7 (Grond in LotR)
7.0 5.2 40.5
7.1 7.3 57.1
7.2 10.3 80.8
7.3 14.5 114.2

* Richter magnitude scale
** Cross-sectional area of 1 square meter and moving at a speed of $4.43 m/s$. This speed is equivalent to the speed of an object as it touches the ground after it was released from a height of 1 m above the ground.



Saturday, October 19, 2013

On the miraculous survival of Virgin Mary's picture amidst the destruction of Bohol's churches: A reply to Filipino Freethinkers

Image of the Blessed Virgin Mary amidst the destruction of a Bohol Church (photo from Megan Young's Facebook page, dated Oct. 15, 2013)
Sonnet: On the destruction of Bohol's Churches

I stand before the broken stones and glass
And gaze at roof beams lying now in dust
An ancient church once stood here tall and strong
Which brown hands built with sand and soft limestone

The brass bells tolled to mark the hours of day
And people stopped to cross themselves and pray
The brass bells tolled to mark the days of feasts
Of harvests, Sundays, Lents, and Christmas Eves

The organ played the old Gregorian chants
As Spanish friars said the Holy Mass
With zeal for souls, with love for Church and Christ
They preached, they teached, they blessed, and they baptized

And through their labors built the Christian lands
Though storms and quakes have passed our Faith still stands

--Monk's Hobbit, 2013.10.18

Freethinkers: A History of American Secularism
Freethinkers: A History of American Secularism
COMMENT BY FILIPINO FREETHINKERS

The Filipino Freethinkers made a video questioning the sudden focus on the miraculous survival of the image of the Blessed Virgin Mary during the 7.2 magnitude earthquake the destroyed Bohol's ancient churches.  Because I am afraid of misquoting them, I tried my best to transcribe (though not perfectly) their thoughts based on their video entitled, "FF Podcast 018: Iglesia ni Cristo’s Medical Mission and the Bohol Earthquake":
12:50 Just a particular thing that has been making the rounds on social media. It was about that one image. it was in that instagram photo that was regrammed by Julius Babao. It was an image of the Virgin Mary and it somehow it managed to survive one of the strong quakes that leveled the church that it was made. You are probably looking at that image right in this very second...What is the meaning of this? What is the significance of sharing and resharing this single image? 
I think people are scrambling for something comforting at least to them in this period of devastation--the tragedy that happened in Bohol. So many people died and many buildings were destroyed. I am sure lots of infrastructure was lost. It is just them thinking that oh there must be reason why this small thing was not destroyed. This is a clear example of selection bias: that you decide to ignore the other bad stuff because it is overwhelming sometimes and you just look it is a good thing. 
As a religious person, what is your take on this? 
Cultures of Disaster: Society and Natural Hazard in the Philippines
Cultures of Disaster: Society and Natural Hazard in the Philippines
14:24 I just find it really sad that suddenly because one easily replaceable picture gets saved vs all of the actual number of people who died. There are some people who need to latch on to that. Again I have been a lot through really terrible things. But at the same time i think that when something bad happens, you need to focus on the people who were hurt and not so much--symbols are important as well--but the tendency can be to conflate the importance. Oh, this one church was saved. Oh, this one picture was saved. This must mean that god doesn't hate us or isn't random or doesn't exist. The immediate response, I think, still needs to be a human response. There are people who are hurt. i think it is obscene to point to one object that may have been saved and how that it is a grand thing and it means that all of this are for a reason, whether there are dead bodies that are never gonna be be replaced or not.
15:35 People just grasp anything to use for hope to keep them from totally sinking in these hard times. It must be terrible what they are going through. But at the same time, I am not saying it is them directly. Perhaps not even the original person said, but a lot of the context in which that picture is being shared has that triumphalist veneer which I find rather disgusting. Maybe it is not even the people who actually went to the tragedy, but it is the people who are perhaps sitting comfortably in their chairs in Metro Manila and they point to this: "Hey, that tragedy happened in Bohol. we were saved. There must be some grand meaning. Checkmate atheists. Checkmate Filipino Freethinkers." That is how petty some people can be. But they will latch on to this in the face of horrible human suffering. Just for one argument. they will Ignore all of that. They will hoist this one symbol up.  It can be that picture. It can be that tsunami in Japan because God is mad at them. All of these things. But that is really the way certain Fundamentalist seem to think. 
Catholic Prophecy: The Coming Chastisement
Catholic Prophecy: The Coming Chastisement
16:58 I do understand there are people who need this kind of help whenever tragedies like this strike, but the skeptic in me still has to ask those questions like what is the meaning of that? Is there even meaning in it? How does it even work? is that image powerful in itself it some how deflected force that was falling on it. Or was there a targeting system from heaven that protected it from everything else. more and more questions could come out of all of this. like why wasn't that targeting system used on the people. why wasn't that force field installed on every human being that was hurt. Is there even a God? This question of course would be very hard to answer. And I guess we will just have to accept that these tragedies are a part of life, a part of nature.  More and more earthquakes will happen. There is nothing special in it. There will be End Times prophets saying the end is near or they hear the voice of God. I like especially that the RH is not a hot topic nowadays, because if it is then you would expect people to relate this to the RH issue. It might as well be the INC mission.



REPLY

I shall focus on five main comments by Filipino Freethinkers:
  1. It is obscene to point to one object that may have been saved and how that it is a grand thing and it means that all of this are for a reason, whether there are dead bodies that are never gonna be be replaced or not.
  2. People just grasp anything to use for hope to keep them from totally sinking in these hard times.
  3. Why was the image of Mary saved from destruction, but not the hundreds who died?
  4. Is there even a God? This question of course would be very hard to answer.
  5. And I guess we will just have to accept that these tragedies are a part of life, a part of nature.  More and more earthquakes will happen. There is nothing special in it. 

Color Persuasion: The Science of using Color to Persuade and Influence Purchasing Decisions (Dynamic Media Series)

Comment 1: It is obscene to point to one object that may have been saved and how that it is a grand thing and it means that all of this are for a reason, whether there are dead bodies that are never gonna be be replaced or not.

In ordinary life in Bohol, people live and and go to mass during Sundays.  So when all of a sudden people die and the churches destroyed, we focus on the destruction and it comes out in the news, in the same way as we focus on the black dot at the center of the white paper.  Now, having expected destruction of old churches everywhere in Bohol and people dying in hundreds, when we see an image of the Blessed Virgin Mary that still stands despite the destruction of the Church that contains it, then we focus more on the image and not on the church or on the number of the dead, in the same way as we focus more on the white dot on a black paper.   This is just a natural human reaction rooted in human vision.  There is nothing  obscene.

Is the survival of Mary's image a miracle?  Maybe.  The word miracle is rooted in the word "wonder":
miracle (n.) mid-12c., "a wondrous work of God," from Old French miracle (11c.) "miracle, story of a miracle, miracle play," from Latin miraculum "object of wonder" (in Church Latin, "marvelous event caused by God"), from mirari "to wonder at, marvel, be astonished," figuratively "to regard, esteem," from mirus "wonderful, astonishing, amazing," earlier *smeiros, from PIE *smei- "to smile, laugh" (cf. Sanskrit smerah "smiling," Greek meidan "to smile," Old Church Slavonic smejo "to laugh;" see smile (v.)). (Online Etymologyical Dictionary)
Since the image of Our Lady aroused wonder among many people, making them praise God for such a wonderful sight, then we can say that the survival of Mary's image is a miracle.  For a more detailed discussion of miracles, please read the Catholic Encyclopedia.

Saved in Hope: Spe Salvi
Comment 2: People just grasp anything to use for hope to keep them from totally sinking in these hard times.

So what do you wish people do? Lose hope and kill themselves, just like the many who committed suicide in concentration camps?  In order to survive the most inhuman conditions, man has to search for meaning and it is only those who found meaning in their life who will survive the ordeal.  And this is what Victor Frankl found in his book, Man's Search For Meaning:
Man's Search For Meaning by Viktor Frankl
Man's Search For Meaning  
Man's Search for Meaning is a 1946 book by Viktor Frankl chronicling his experiences as an Auschwitz concentration camp inmate during World War II, and describing his psychotherapeutic method, which involved identifying a purpose in life to feel positively about, and then immersively imagining that outcome. According to Frankl, the way a prisoner imagined the future affected his longevity. The book intends to answer the question "How was everyday life in a concentration camp reflected in the mind of the average prisoner?" Part One constitutes Frankl's analysis of his experiences in the concentration camps, while Part Two introduces his ideas of meaning and his theory called logotherapy. According to a survey conducted by the Book-of-the-Month Club and the Library of Congress, Man's Search For Meaning belongs to a list of "the ten most influential books in the United States."[1] At the time of the author's death in 1997, the book had sold over 10 million copies and had been translated into 24 languages. (Wikipedia)

If one believes in Darwinian Law of Natural Selection which "the survival of the fittest and the removal of the unfit", then hope is necessary for the survival of the human species, so that we can rephrase Darwin's law as follows: "the survival of the hopeful and the death of the hopeless."

Bartolome Esteban Murillo Immaculate Conception - 18" x 27" Framed Premium Canvas Print
Bartolome Esteban Murillo Immaculate Conception - 18" x 27" Framed Premium Canvas Print
Comment 3: Why was the image of Mary saved from destruction, but not the hundreds who died?

I don't know.  If God exists and we shall face Him during Judgment Day, we can ask Him this question.  Well, we can't even determine the precise reasons why our friends betrayed us or why our loved ones abandoned us.  Why? O, why?  We asked ourselves.  So how much more if we demand from God the reasons for His actions or inactions?

Job, the righteous person, also suffered in a single blow and the persons who survived are not his children but his lowly servants who reported to him:
One day, while his sons and daughters were eating and drinking wine in the house of their eldest brother, 14 a messenger came to Job and said, “The oxen were plowing and the donkeys grazing beside them, 15 and the Sabeans* carried them off in a raid. They put the servants to the sword, and I alone have escaped to tell you.” 16 He was still speaking when another came and said, “God’s fire has fallen from heaven and struck the sheep and the servants and consumed them; I alone have escaped to tell you.”17 He was still speaking when another came and said, “The Chaldeans* formed three columns, seized the camels, carried them off, and put the servants to the sword; I alone have escaped to tell you.” 18 He was still speaking when another came and said, “Your sons and daughters were eating and drinking wine in the house of their eldest brother,19 and suddenly a great wind came from across the desert and smashed the four corners of the house. It fell upon the young people and they are dead; I alone have escaped to tell you.” (Job 1:13-19)
(13x19) Albrecht Durer Job Mocked by His Wife Art Print Poster
What was Job's response?
“Naked I came forth from my mother’s womb,f and naked shall I go back there.* The LORD gave and the LORD has taken away; blessed be the name of the LORD!” (Job 1:21)
And even if the affliction is already on his own body, he still never cursed God:
He took a potsherd to scrape himself, as he sat among the ashes.9 Then his wife said to him,d “Are you still holding to your innocence? Curse God and die!”*10 But he said to her, “You speak as foolish women do. We accept good things from God; should we not accept evil?” Through all this, Job did not sin in what he said. (Job 2:8-10)
But like our friends in the Filipino Freethinkers, Job also would like to ask God why he suffered despite his righteousness:
I will give myself up to complaint; I will speak from the bitterness of my soul. 2 I will say to God: Do not put me in the wrong! Let me know why you oppose me. (Job 10:1-2)  
What are my faults and my sins? My misdeed, my sin make known to me!24 Why do you hide your face and consider me your enemy? (Job 13:23-24)
And God appeared Job. God did not answer Job's question; rather, God only showed Job his wisdom and majesty. Then the Lord answered Job out of the storm and said:
Who is this who darkens counsel with words of ignorance?3 Gird up your loins* now, like a man; I will question you, and you tell me the answers!a 4 Where were you when I founded the earth? Tell me, if you have understanding. (Job 38:1-4)
Hidden Treasures in the Book of Job: How the Oldest Book in the Bible Answers Today's Scientific Questions (Reasons to Believe)
Hidden Treasures in the Book of Job: How the Oldest Book in the Bible Answers Today's Scientific Questions (Reasons to Believe)
And Job replied:
I know that you can do all things, and that no purpose of yours can be hindered.3“Who is this who obscures counsel with ignorance?” I have spoken but did not understand; things too marvelous for me, which I did not know. “Listen, and I will speak; I will question you, and you tell me the answers."5 By hearsay I had heard of you, but now my eye has seen you.* 6 Therefore I disown what I have said, and repent in dust and ashes. (Job 42:2-3)
In the end God restored Job everything that he had and so much more::
 Thus the LORD blessed the later days of Job more than his earlier ones. Now he had fourteen thousand sheep, six thousand camels, a thousand yoke of oxen, and a thousand she-donkeys.13 He also had seven sons and three daughters: 14 the first daughter he called Jemimah, the second Keziah, and the third Keren-happuch.*15 In all the land no other women were as beautiful as the daughters of Job; and their father gave them an inheritance* among their brothers. 16 After this, Job lived a hundred and forty years; and he saw his children, his grandchildren, and even his great-grandchildren.c 17 Then Job died, old and full of years. (Job 42:12-17)
 And like Job we also pray that God may restore our churches not only in Bohol but in whole Philippine archipelago as well, with greater splendor than before.  And we also pray that may God increase the number of the Church's faithful sons and daughter who shall proclaim the Gospel unto the ends of the earth.

New Proofs for the Existence of God: Contributions of Contemporary Physics and Philosophy
New Proofs for the Existence of God: Contributions of Contemporary Physics and Philosophy
Comment 4: Is there even a God? This question of course would be very hard to answer. 

Doubt is different from denial of God's existence.  Here is what Cardinal Newman says:
Ten thousand difficulties do not make one doubt, as I understand the subject; difficulty and doubt are incommensurate. There of course may be difficulties in the evidence; but I am speaking of difficulties intrinsic to the doctrines themselves, or to their relations with each other. A man may be annoyed that he cannot work out a mathematical problem, of which the answer is or is not given to him, without doubting that it admits of an answer, or that a certain particular answer is the true one. Of all points of faith, the being of a God is, to my own apprehension, encompassed with most difficulty, and yet borne in upon our minds with most power.
The easy way out, of course, is just to pretend that the problem of the existence of God does not exist and live on life.  But this question continue to haunt atheists and agnostics, in the same way as a woman who procured abortion would either deny the existence of the baby by calling it a piece of tissue or blood or pretend that nothing happened by trying to live life as normally as possible.  In psychology, there is an explanation for this phenomenon. It is called cognitive dissonance:
The Brain Sell: When Science Meets Shopping; How the new mind sciences and the persuasion industry are reading our thoughts, influencing our emotions, and stimulating us to shop
The Brain Sell: When Science Meets Shopping; How the new mind sciences and the persuasion industry are reading our thoughts, influencing our emotions, and stimulating us to shop
Cognitive dissonance describes the feeling of discomfort we experience when we attempt to hold two conflicting beliefs simultaneously. Imagine you are a smoker who wants to quit but finds it hard to break the habit.  Being exposed to health messages and dire warnings about the medical consequences of failing to give up while continuing to smoke will create cognitive dissonance.  In order to free themselves from these discomforting feelings, smokers have one of two choices: to stop smoking or to rationalize away the risk.  Lifelong smokers will often say: "Of course I understand it's a risky habit, but so is driving a car, riding a bike, or even crossing the street." Alternatively, they may point that their Uncle Charlie smoked 100 cigarettes a day and lived to be a healthy and sprightly 90-year-old.  Both of these approaches will remove the dissonance, although the first actually safeguards health. (Dr. David Lewis, The Brain Sell: When Science Meets Shopping , p. 29)
Here is what St. Aquinas proposes as proofs for God's existence, for he does not shy away from the rational arguments extolled by our atheist and agnostic friends.  These may be difficult to comprehend in the same way as calculus is difficult to comprehend, but not impossible:
The Existence Of God
The Existence Of God by St. Thomas Aquinas
I answer that, The existence of God can be proved in five ways. 
The first and more manifest way is the argument from motion. It is certain, and evident to our senses, that in the world some things are in motion. Now whatever is in motion is put in motion by another, for nothing can be in motion except it is in potentiality to that towards which it is in motion; whereas a thing moves inasmuch as it is in act. For motion is nothing else than the reduction of something from potentiality to actuality. But nothing can be reduced from potentiality to actuality, except by something in a state of actuality. Thus that which is actually hot, as fire, makes wood, which is potentially hot, to be actually hot, and thereby moves and changes it. Now it is not possible that the same thing should be at once in actuality and potentiality in the same respect, but only in different respects. For what is actually hot cannot simultaneously be potentially hot; but it is simultaneously potentially cold. It is therefore impossible that in the same respect and in the same way a thing should be both mover and moved, i.e. that it should move itself. Therefore, whatever is in motion must be put in motion by another. If that by which it is put in motion be itself put in motion, then this also must needs be put in motion by another, and that by another again. But this cannot go on to infinity, because then there would be no first mover, and, consequently, no other mover; seeing that subsequent movers move only inasmuch as they are put in motion by the first mover; as the staff moves only because it is put in motion by the hand. Therefore it is necessary to arrive at a first mover, put in motion by no other; and this everyone understands to be God. 
St. Anselm's Argument for the Existence of God: PROSLOGION The Nature of God Vol. I and II
St. Anselm's Argument for the Existence of God: PROSLOGION The Nature of God Vol. I and II
The second way is from the nature of the efficient cause. In the world of sense we find there is an order of efficient causes. There is no case known (neither is it, indeed, possible) in which a thing is found to be the efficient cause of itself; for so it would be prior to itself, which is impossible. Now in efficient causes it is not possible to go on to infinity, because in all efficient causes following in order, the first is the cause of the intermediate cause, and the intermediate is the cause of the ultimate cause, whether the intermediate cause be several, or only one. Now to take away the cause is to take away the effect. Therefore, if there be no first cause among efficient causes, there will be no ultimate, nor any intermediate cause. But if in efficient causes it is possible to go on to infinity, there will be no first efficient cause, neither will there be an ultimate effect, nor any intermediate efficient causes; all of which is plainly false. Therefore it is necessary to admit a first efficient cause, to which everyone gives the name of God. 
The third way is taken from possibility and necessity, and runs thus. We find in nature things that are possible to be and not to be, since they are found to be generated, and to corrupt, and consequently, they are possible to be and not to be. But it is impossible for these always to exist, for that which is possible not to be at some time is not. Therefore, if everything is possible not to be, then at one time there could have been nothing in existence. Now if this were true, even now there would be nothing in existence, because that which does not exist only begins to exist by something already existing. Therefore, if at one time nothing was in existence, it would have been impossible for anything to have begun to exist; and thus even now nothing would be in existence — which is absurd. Therefore, not all beings are merely possible, but there must exist something the existence of which is necessary. But every necessary thing either has its necessity caused by another, or not. Now it is impossible to go on to infinity in necessary things which have their necessity caused by another, as has been already proved in regard to efficient causes. Therefore we cannot but postulate the existence of some being having of itself its own necessity, and not receiving it from another, but rather causing in others their necessity. This all men speak of as God. 
Metaphysical Demonstration of the Existence of God
Metaphysical Demonstration of the Existence of God
The fourth way is taken from the gradation to be found in things. Among beings there are some more and some less good, true, noble and the like. But "more" and "less" are predicated of different things, according as they resemble in their different ways something which is the maximum, as a thing is said to be hotter according as it more nearly resembles that which is hottest; so that there is something which is truest, something best, something noblest and, consequently, something which is uttermost being; for those things that are greatest in truth are greatest in being, as it is written in Metaph. ii. Now the maximum in any genus is the cause of all in that genus; as fire, which is the maximum heat, is the cause of all hot things. Therefore there must also be something which is to all beings the cause of their being, goodness, and every other perfection; and this we call God. 
The fifth way is taken from the governance of the world. We see that things which lack intelligence, such as natural bodies, act for an end, and this is evident from their acting always, or nearly always, in the same way, so as to obtain the best result. Hence it is plain that not fortuitously, but designedly, do they achieve their end. Now whatever lacks intelligence cannot move towards an end, unless it be directed by some being endowed with knowledge and intelligence; as the arrow is shot to its mark by the archer. Therefore some intelligent being exists by whom all natural things are directed to their end; and this being we call God. (Summa Theologiae, Ques. 2, Art. 3)
Adam and Eve After the Pill: Paradoxes of the Sexual Revolution
Adam and Eve After the Pill: Paradoxes of the Sexual Revolution

Comment 5. And I guess we will just have to accept that these tragedies are a part of life, a part of nature.  More and more earthquakes will happen. There is nothing special in it. 

So in the end, atheists and agnostics cannot provide a meaning to suffering and death, but simply lump these as part of the natural world.  So where their naturalist explanation ends, we propose the good news and the logic of the Catholic Faith:

Man suffered and died because of the disobedience of our First Parents Adam and Eve. They were given a simple rule not to eat a fruit in the middle of garden, and all the preternatural gifts given to them would be theirs and to their descendants.  But since they disobeyed, Adam has to toil to make the ground bear fruit unlike before, and the pains of childbearing of his wife, Eve, increased.  The children of Adam and Eve and all their descendants bore the punishment of suffering and death due to the sin of Adam and Eve.  This is called Original Sin.  And this is why we all suffer and die.

Amazing Love: The Story of Hosea
Amazing Love: The Story of Hosea
The gravity of the sin of Adam and Eve separated them from God.  In order to get a glimpse of the suffering and pain that God suffered because of the rejection of his love by the human race, we turn to the book of Hosea:
Again the LORD said to me: Go, love a woman who is loved by her spouse but commits adultery; just as the LORD loves the Israelites, though they turn to other gods and love raisin cakes. So I acquired her for myself for fifteen pieces of silver and a homer and a lethech of barley. 3Then I said to her: “You will wait for me for many days; you will not prostitute yourself or belong to any man; I in turn will wait for you.” (Hos 3:1)
Here, God's love is likened to a man who married a prostitute (Israel) and made a marriage covenant with her to be his only and no other man's.  But the woman continued in her prostitution (Israel worships other Gods).  The whole Bible is a love story: a love story between God and Man. Since Man spurned God, God took the initiative and became man, subject to suffering and death:
The Crucifixion of Jesus, Completely Revised and Expanded: A Forensic Inquiry
The Crucifixion of Jesus, Completely Revised and Expanded: A Forensic Inquiry

And the Word became flesh*
and made his dwelling among us,
and we saw his glory,
the glory as of the Father’s only Son,
full of grace and truth. (Jn 1:14)
In doing so, God showed Man the way to salvation: not to reject suffering and death, but rather to embrace these and offer these to God, as Christ willingly embraced the Cross and offered to God his spirit.  Thus, the path to salvation is the path of suffering and death, in the same way as Aragorn has to take the Paths of the Dead in order to save Gondor from destruction.  As Christ said:
Whoever wishes to come after me must deny himself,* take up his cross, and follow me.25r For whoever wishes to save his life will lose it, but whoever loses his life for my sake will find it. (Mt 16:24:25)