fourth year in geophysics

things happen before earthquakes

2011-05-26T23:08:00.000-07:00

I read an interesting paper from J. Byerlee on "Model for episodic flow of high-pressure water in fault zones before earthquakes".

This is a part of a dialog between authors on the role of high-pressure water in the fault zones: where the water come from and how it effects fault zones. The flow of high-pressure water differs in their temporal behaviors: no flow, continuos flow and episodic flow. Although this paper is written in 1993, things haven't been clearer since then. Perhaps the discovery of tremor and related phenomena make things more difficult to explain.

Here is today's theme: Things happened before earthquakes. It is an interesting theory. The following story is my own interpretation of the paper and one should trace back to the original paper if interested.

Step 1: Water saturated the fault zone. Water can penetrate into crust down to depth of 20 km. The crust is largely in hydrostatic pressure. The fault zone which consists of fine crushed rocks is highly porous and permeable.

Step 2: Compaction of the fault zone at high pressure and temperature. Silica deposits during the compaction and over-saturated water flow out of the fault zone into country rocks. Seals formed after silica deposition.

Step 3: Seals formed compartments. The seal is impermeable. The 3D compartments developed from deep section of the fault zone and propagated upward. The depth distribution of compartments is from 15 km to 3 km depth.

Step 4: Trigger earthquakes. Within the country rock, in order to prevent hydrofracture, the minimum principle stress has to be greater than the pore pressure. But inside the fault zone, the formation of seal allows a smaller minimum principle stress. The pore pressure can be 85% of lithostatic and the minimum principle stress can be only 60%. Before the formation of seal, however, the minimum principle stress has to increase. This is a key point that has been stated a couple of times in the paper, without any explanations. The seal can still break when further pressed, then the water will flow into country rock from the sealed pores, the effective normal stress would increase and the fault will be further locked. When the shear stress is big enough the lithified seal between compartments will be fail, and there will be a increase in the pore pressure and the fault unclamped. Earthquake (or tremor?) will happen as a result of pore pressure change in the fault zone.

Step 5: The earthquake fractures the fault zone, and everything restart.

To me, this is quite an imagination.

craton formation

2010-12-10T22:48:00.000-08:00

Today, I listened to Dan McKenzie's talk. It's an interesting talk in my opinion though I don't completely understand it.
I learned something:
when considering the heat flow the effect of radiogenic heating in the thickened crust is not negligible.

measuring interseismic deformation using InSAR 1

2010-12-05T17:00:00.000-08:00

Long time no see. I just passed the qualify exam and I am on my second half journey to a PhD.

Today I am going to discuss existing technique and approaches to measure interseismic deformation using InSAR. This is an interesting topic. Currently several groups of people are working on InSAR time-series techniques. In US these groups includes Stanford, Caltech, JPL, Scripps, Berkeley, UCR, etc etc...

Let's start from Persistent Scatterers InSAR (PS). This technique is first developed by [Ferretti et al]. It works like this: align a stack of the SLC images; scale the amplitude image; compute the pixel-wise mean amplitude (m) and standard deviation of the amplitude (σ) for a whole stack; compute the D = σ/m; treat the pixel where D is smaller than a threshold as Permanent Scatters; model the phase of each PS as a mix of linear deformation and DEM error and solve a least-square problem to retrieve both the DEM error and a linear deformation rate.

Instead of using a threshold of amplitude dispersion, Lyons and Sandwell compute s = m/σ and weight the real and imaginary part of the complex image by s^2; apply a non-isotropic filter and form interferogram.

Instead of amplitude dispersion, stanford group [Hooper et al] include the phase information to identify PS. Their method is written in JGR paper. I haven't understood this method yet.

Cracks on San Andreas Fault after Baja California earthquake

2010-05-09T23:48:00.000-07:00

Last weekend, Matt and I drove to Imperial Valley and north shore of Salton Sea to look for cracks after the M7.2 Sierra El Mayor event.
We found evidence to show the earthquake triggered slip on San Andreas Fault system in Southern California.

David told us how to use B4 data to find the fault and it works like a charm. We load the marker into Google Earth after studying the InSAR and B4 data. The accuracy has to be within meters in order to locate the cracks on the ground. It's a surprise when we found them because the cracks are even hardly visible in the real word.

It is an exciting experience to find sub-cm cracks by the means of laser altimetry and InSAR. However, I don't know how much science can come out of it, as it's really tricky to measure the cracks quantitatively.

That's my two cents.

AGU 2009

2009-12-25T10:41:00.000-08:00

Q: What I learned from AGU on Monday?

A: There are two main continental transform fault system: one is San Andreas Fault in California and the other is Alpine fault in New Zealand.

People studied the tectonics processing, but what they're really looking at is the slip rate and strain rate in both geological and geodetic time window. It's mainly focus on the kinematics of the ground motion.

The formation of the Garlock fault is not known.

The effect of the damage zone on the fault property is not known.

The viscosity, plate effective thickness, rigidity is related to the fault deformation.

The fault geometry, topography, crust thickness and heat flow is used to model long-term slip rates.

Geological slip rates, stress direction, GPS velocity and depth of the seismicity are important properties.

Q: What I learned in AGU on Tuesday?

A: For Wenchuan earthquake, the postseismic uplift in mountain side is stronger than the postseismic subsidence in basin side. It is a consistent feature and need explanation. The decay period is 8-14 days in the logarithm decay curve from GPS measurement.

Ionosphere effect is not present if one changed SAR acquisition to another date.

There are two mechanisms for the ductile behavior of the lithosphere: viscous granulus flow and dislocation creep.

Q: What I learned from AGU on Wednesday?

A: Static displacement (near field) decay with the square of the distance. Dynamic displacement (far field) decay with the distance. The r^-1 and r^-2 curve could be useful.

The inelastic and plastic failure is important when the strain is high (> 10^-3). However, it seems such a high strain is only present within a few meters in the fault zone.

Meade and Loveless wrote an interesting paper on crustal motion modeling.

I got too tired to learn in the last two days.

That's for the end of the year.

interesting zombie and plumes

2009-12-05T16:56:00.000-08:00

Now I know what is skepticism.

Recently, PLUME project reports new S wave tomography results supporting the presence of deep plume. In the science paper, the slices of tomography at different depth show a consistent feature of low velocity zone mainly underneath the Hawaii island. The S-wave anomaly is at least 300km wide.

The result is interesting. However, the resolving power of S wave and SKS wave, which vertically penetrate mantle material from deep earth, is not clear to me, especially the vertical variation at very deep (>500km) depth.

The plume is a concept that is in debate. When browsing the website called mantleplumes.org, I learned it has a another nickname called zombie: Zombie cause horrors so people want to nail it into a coffin. But zombie can walk out and sometimes scare people, that's why it's a zombie.

My imagination lead me to agree there should be internal structures in the mantle, just like the clouds in the atmosphere and the waves in the ocean. The plume is a kind of "pioneer" conception of the internal mantle structure. But since it's a pioneer, it is easy to be sacrificed and treated as a zombie.

Reading those website also tell me to let my science to stay on the surface of the earth (i.e. geodesy), otherwise another zombie might be born and scare people, which is not good.

The fantastic ionosphere

2009-11-15T21:46:00.000-08:00

The ionosphere is invisible in the sky most of the time. Sometimes, he does manifest himself in a splendid appearance, in the way called air glow, aurora. He reaches a large range of the sky from 100km to 1000km above ground; most of them concentrate at around 200km to 500km. The ionosphere is gaining his energy from solar radiation, under strong influence of the Earth's magnetic field. The electrons become activated during the day time and goes quiet during the night. Scientists introduce a physical quantity called total electron content to measure the state of ionosphere.

Though human put a much effort on it, the ionosphere is a mysterious subject to study and little is known about its internal 3D structure. It's dynamic, sometimes wild.

Recently, people found L-band radar interferometry has a considerable sensitivity to the electrons in the ionosphere. This maybe a sign of a new stage of probing ionosphere. It should be exciting to watch what will happen.

what is isostasy ?

2009-09-05T16:23:00.000-07:00

In plate tectonics, the lithosphere is rigid overlying the weak asthenosphere in geologic time scales. The high mountain ranges either in the ocean or in the continent can be supported by this rigid lithosphere for millions of years. The presence of the weak layer of asthenosphere is implicated from gravity observations near mountain range. The bougur gravity anomaly indicates negative crustal root underneath the mountains, compensating gravitational force of the high topography. This is called isostasy, meaning gravitationally equilibrium.

There are three isostatic models to achieve compensation:
1 Airy model: The high topography is accommodated by the thickness of the crust.
2 Pratt model: The high topography is accommodated by the density of the crust.

The above two belong to the "local compensation", which means there is no regional effect. One can imagine a picture of "floating iceburg", the vertical load is totally supported by the underlaid "fluid" asthenosphere. The horizontal force between adjacent lithosphere is decoupled.

3 regional compensation (elastic plate model): This model is more realistic and reasonable. Airy model actually belongs to one of its extreme case. Basically, it views the lithosphere as an elastic plate with a distinct parameter called flexure rigidity. The flexure rigidity is equivalent to elastic thickness of the plate.

Isostasy is not universal in the world. In some areas, such as Greenland, the mantle is rebounding to unloading because of the melting of icecap. The violation of isostasy or new isostasy models will certainly arouse new questions to the earth scientists.

Reference system

2009-07-19T11:50:00.000-07:00

In order to understand the Global Positioning System (GPS) in a rigorous way, one need to first learn two scope of knowledge: one is the geometric description of the reference frame, which is used to quantify the related satellite position, velocity and receiver position; the other one is the fundamentals of time measurement, which is necessary to solve for the precise range of the satellite and receiver.

Positioning is intricately linked to a reference system. The reference system is realized by the reference frame which is in turn defined by station positions. The realization of the celestial and terrestrial reference systems are quite involved because of the complexity of the Earth's composition, its interaction with the atmosphere and its mutual gravitational attraction with the Moon and the Sun.

The celestial reference system is realized by a catalogue of celestial coordinates of extragalacitic radio sources determined from astrometric VLBI observations. This coordinate define a celestial reference frame (CRF). On the other hand, the terrestial reference frame (TRF) is determined by a variety of space observations, including satellite laser ranging, VLBI, and GPS. These position define a fundemental polyhedron.

The transformation between the CRF and the TRF can be decribed as a set of transformation. There are three principle rotations involved: r(TRF) = [S][N][P] r(CRF), where r(CRF) is a position vector in the CRF reference system, [S] represents the rotation of the earth along its rotation axis, [N] represents the contribution from nutation and [P] is the contribution from precession, the vector product of these gives the transformed position vector in TRF reference system. Each of these matrix can be further decomposed into three successive rotations along the major axis. The quantitative description of each rotation for a specific location at a specific instant involves complicated definition of time epoch, which has been unified by authoritative society (like IAU).

Two time systems are in use today: atomic and dynamic. Atomic time (UTC or GPS time) is used in timing the carrier phase and pseudorange measurement in satellite device; dynamic time ()is employed in calculating the orbit position of the satellite.

Refer to:
P.J.G. Teunissen, A. Kleusberg, "GPS for geodesy"
Alfred Leick, "GPS satellite surveying"

what is the depth of the moho under SAF

2009-05-17T11:34:00.000-07:00

The San Andreas Fault is a transform fault more than 1000 km long and the plate boundary between North American plate and Pacific plate. an average Moho depth of the oceanic Pacific plate is 6km, whereas of the continental NorthAmerican plate is 35km. It's interesting to ask what the moho depth beneath San Andreas Fault (SAF) where the two plates meet each other ?

The moho depth provide insight into the evolution of the SAF as a long and typical transform fault system, the stress and strain accumulation on the SAF associated with seismicity.

The literature search is the first step to answer this questions:

1. Zhu, LP [2000] used the seismic data in the Los Angeles Region Seismic Experiment and receiver function method to obtain a moho image under San Gabriel mountain, Mojave desert known as East California Shear Zone. The moho is 30km deep under ECSZ and offset by 6-8 km upperward under SAF. This line of seismic profile is limited in 2 dimensional but indicate a shallower Moho depth under mountain range near LA basin. One possible explanation involve the buckling of the elastic plate under compression but I think it's far from satisfaction.

It's fun when you compare the result done by another team.

2. Kohler & Davis [1997] used seismic record from the same experiment as Zhu to study structure variation between the lower crust and upper mantle. It conclude with: "Crustal thickness increases laterally by 12 km over a distance of
less than 50 km into the San Gabriel Mountains." It also suggested the crust thinned under San Gabriel mountain and LA basin by 12 km or so.

I don't think the two results are directly contradictary. However, it's far from satisfactory to learn the moho depth in a clear and 100% consistent way. The two articals both indicate a variation in crust thickness under southern SAF but the numbers are not in exact agreement. In addition, the moho depth under San Gabriel mountain is infered to be deeper than the LA basin. However, the interpretation of the relative moho depth between San Gabriel mountain and Mojave desert (ECSZ) are inconsistent obviously in the two respective result.

That's for today's fair share.

SAR processing

2009-04-21T21:29:00.000-07:00

I would like to review how to make a SAR image from scratch.

The raw SAR data need to be focused to form an image file, which consists the amplitude and phase information. The amplitude is determined by the reflectivity of the ground objects while the phase is related to the range between ground point and radar antenna. The raw data is a binary file that consists of timing information of the orbit and the radar echos. We know from radar design the radar wave is a long frequency-modulated chirp(11 km), as well as the length of the radar echo. Think about the satellite emitting and receiving radar echos while flying over part of the earth, you will see the binary file is nothing but a series of continuous reflected radar echos. The range dimension of the binary file is the length of the radar echos, while the azimuth dimension is total number of the echos. We can convert the binary file into a 2D image by several signal processing techniques.

Generally speaking, we can divide those techniques into 2 steps.

First, range compression. To recover useful signal from the complicatedly reflected radar waves, we convolve it with the original chirp data. This convolution will focus the image in the range direction.

Second, azimuth compression. Range migration is needed to account for the doppler effect. After that, the data is compressed (or say focused) in azimuth direction by convolving another chirp.

This is just a taste of SAR processing.

going to ssa meeting 2009

2009-04-05T22:46:00.000-07:00

I am going to Monterey Bay for the SSA meeting. In the meeting, there are two sessions that attract me: one is great surface rupture, discussing the relationship between historic earthquake from paleoseismology and current great earthquake that had great surface ruptures. The ideal case would be the spatial correlation of the slip area between historic and modern-day earthquakes following a rule. The other one is LiDAR (light detection and ranging), this new technology enable us to measure the topography in a resolution less than one meter over a large area, that will be helpful in improving topographic phase correction to better accuracy for InSAR.

Excerpt from "Ocean of the true"

2009-03-31T22:46:00.000-07:00

Research is not only what counts; it is all that counts. One indication of a false research laboratory is that it closes on weekends. A false scientist takes holidays. A true research scientist does not ever know there is a holiday.

论失败

2009-03-10T20:41:00.000-07:00

校内网上不能发表日志了，所以我要来这里发表一下我的高见。
还是写中文舒服一些。我必须要发牢骚了，这几个月没有写东西，我郁闷。
没有人愿意听的话，就让这些话，印在网络的犄角里吧。

现在的工作正在轨道上，但是最大的问题就是经常失败，有了一个点子，干了两天的活，但是今天发现不管用，也许是我中间过程做错了，也许丫跟儿就不是我想的那个样子。我最大的困难，我想，也可能是我的朋友们每天最大的困难，就是接受每天都可能失败的现实。曾经，每次考试带来的快乐，积累下来，就是我肯定会成功的心理，但是这个是不会再发生的了，因为我这里已经没有考试了，我已经25岁了，19年积累的考试卷子，可以累多高呢？（一张纸1毫米＊52周＊19年），大概有一米高了。现在的转折，对我来说，才是最大的。这是心里上的一个转折。做科研不像别的工作，每天没有那么多的问题，而这些问题最大的特点在于没有答案，我们在找答案。但是没有一个老师知道正确答案。还有一个由此衍生出的问题，就是依赖老板，当然这是我自己的感觉。总是想从他那里要答案，其实和他讨论问题的过程才是最重要的，并且尝试解决问题的过程是最重要的。

失败以后，最大的问题就在于没有地方宣泄，所以我打算以后就常常来这里写一些没有用的文字，权当是牢骚吧。

未完，待续。

Some words

2009-02-26T22:20:00.000-08:00

Recently I am having a hard time to be motivated. A little bit pressure would do good to make me concentrate and stop wandering around. Yet a note for myself would be better to release some of the wasteful thoughts and clear up the thinking process. Moreover, a long day of hiking and regular beer would be even better than that. Alternative is laying myself on the sea but since I lost my wetsuit, I decide go to the swimming pool instead.

So what's the matter? I don't know. It's a feeling that the stuff I am working on is not as significant as others' work. I know I want to insist, and I have to. There surely is a lot of interesting things related to my work, but it's just because I am not aware of that. So I'd better make a change.

There are too many ways to go and I am confused. The solution is to slow down and be more steady, try to go in depth in one problem before switch to another topic. Read more and talk with people.

Amazing satellites

2009-02-26T21:57:00.000-08:00

ALOS is Advanced L-band Observatory Satellite launched by Japanese agency (JAXA). A SAR on board this satellite works in all-weather, day and night give us great opportunity to study geophyiscal surface signal.

ERS-1 and ERS-2 they are SAR satellites launched by European Space Agency. These two satellite orbits the earth consecutively and provide interferograms within a short repeat time, greatly reduce the possibility for temporal-decorrelation.

This is SRTM, Shuttle Radar Topography Mission. Instead of being carried by satellite, antenna is installed on space shuttle to form interferometry. I feel it's amazing and wonderful.

To be continued ...

Coseismic deformation of the earthquakes from InSAR and GPS

2009-01-09T20:43:00.000-08:00

Here is the kind of work I am doing now.

Take a paper " Coseismic deformation of the 2002 Denali fault earthquake: Contributions from synthetic aperture radar range offsets" by Elliott for example.

Let's say an earthquake with magnitude greater than 5 or above happened in some interesting region, we may think about these question when talking about its significance: what's the size, length, depth? How does it influence the neighborhood in the prospective of transportation, habitat, and environment. What is the tectonics in that region and how does this event relate to it ?

To understand the earthquake, one of the key is the development of a robust, detailed slip distribution model. The slip model indicates the locked depth of the fault and the location of major asperities. Spatial variation in slip are caused by preexisting stress heterogeneity and thus provide a fundamental measure of heterogeneity. Postseismic models depend on having a reliable coseismic slip model, especially in terms of fault geometry and how the maximum slip depth compares to the depth where viscous flow is expected to begin. An essential ingredient for an accurate slip model is a set of spatially dense near-field surface displacement measurements, which can be done by InSAR, GPS and geologic mapping. Seismic data, while providing information on how the rupture evolved over time, often apply a poorer constraint on the spatial slip distribution than geodetic measures.

rotation matrix to do basis transformation

2008-11-28T15:33:00.000-08:00

Hi, there is a small matlab code that help you do linear
transformation of basis in 3D. I share it with you.

% Rotation of basis in three-dimensional cartesian coordinate
function [y]=rot3d(x,lon,lat)

% x is a 3*1 vector in old cartesian coordinate: xyz
% y is new 3*1 vector in new coordinate
% the rotation of the new coordinate composite two rotations
% lon is the longitude of the pole and lat is the latitude of it.
% g is the first rotation of xy plane around z axis. xyz -> x'y'z
% b is the second rotation of xz plane around x' axis. x'y'z -> x'y''z'
% each ' denote a change of direction in old coordinate

% lat and lon is in degree
% option: plot the two coordinate systems in 3D
% output the rotation matrix: A 3*3
% y = A*x

% reference: http://mathworld.wolfram.com/RotationMatrix.html
% http://en.wikipedia.org/wiki/Rotation_matrix

% Xiaopeng, Nov 28 2008.

% This code can be used to do coordinate rotation in 3D cartesian.

b=lat-90;
g=lon+90;

Rx=[1 0 0; 0 cosd(b) -sind(b); 0 sind(b) cosd(b)] % around x conterclockwise facing toward x
% Ry=[cosd(lat) 0 -sind(lat); 0 1 0; sind(lat) 0 cosd(lat)]; % around y
% conterclockwise facing toward y
Rz=[cosd(g) sind(g) 0; -sind(g) cosd(g) 0; 0 0 1] % around z conterclockwise facing toward z

A=Rx*Rz

% A*A'

y=A*x

% as a test try to rotate a pole of vector: x=[cosd(32)*cosd(102) ...
% cosd(32)*sind(102) sind(32)] to [0 0 1]

% visualize it
vec = [cosd(lat)*cosd(lon) cosd(lat)*sind(lon) sind(lat)];

figure,quiver3(0,0,0,vec(1),vec(2),vec(3))

axis([-1 1 -1 1 -1 1])
xlabel('x') % greenwich longitude=0
ylabel('y') % longitude = 90E
zlabel('z') % north pole
title('pole of rotation')

view(60,60)

end

Intro to Radar Interferometry

2008-10-12T21:07:00.000-07:00

There is a good paper.

Radar, an acronym for "radio detection and ranging", is installed on the aircraft or satellite to image the earth surface. The first scientific application started from Seasat satellite in 1978, (artist figure to the right) though it only flew for a few months. The physics in radar imaging yield a special coordinate system in two direction: range and azimuth. Range axis is defined by the round-trip travel time of the electromagnetic (EM) echoes, while azimuth axis is defined by the Doppler shift. The satellite transmit and receive EM waves with wavelength in the range of C band (6 cm), X band (3 cm), L band (24 cm). These different frequency give rise to various characteristics in resolution and other effect, such as atmospheric effect, influence on vegetation. The operation on such long-wavelength band leads to all-weather and night time imaging capability. Nowadays, satellites that carried or are carrying geophysical missions include: ERS by European Space Agency, JERS by Japanese Aerospace Exploration Agency, RADARSAT by Canada.

They are elegant with amazing appearance and useful function.

1.1.1 synthesis and geometric properties
The ratio of the EM wavelength to the aperture scale give us the angular resolution, so a radar with 23cm wavelength, 10m aperture gives about 0.01 angular resolution and approximately 10 km on the ground. The resolution is improved by an advanced technique called focusing. The radar transmits and receive thousands of echoes along the track, then synthesize them together, instead of analyzing each signal individually. The synthetic aperture increase to 5km or so rather than 10m. To achieve this long aperture, it must emit signal every 5m along the orbit, consider the flying speed is about 6km/s to the ground, it means thousands pulse repetition frequency is required. This reconstruction of the radar image set up a different coordinate system (range and azimuth) which is defined by the position and velocity vector of the satellite. We can visualize this by imagining taking pictures of the ground from aircraft using a wierd camera, which give us an image similar to ordinary air photo, but in a differet unit. One of the drawbacks worthy to notice is the "layover" effect. The radar distinguish object by echo travel time, hence two objects that have the same travel time but in different location may cause artifact in the image.

1.1.2 Properties of image amplitude
The amplitude of the image relates to the roughness of the surface, EM properties of the material. If the wavelength is far bigger than the scale of the roughness, the situation is similar to seeing somebody from a mirror. If the wavelength is smaller than that, it will like scattering: the radiation energy spread out in all direction. If there is a calm water surface, no much energy will reflect backward, so we have low amplitude, while if there is rough waves swept over by the wind, or a tree standing in the water, acting as corner reflector, then we will have high amplitude. More, the longer wavelength EM waves can penetrate more vegetation, so it's prone to get to the bottom of the ground rather than reflected by the canopy. This kind of property, plus the conductivity of the material influence the amplitude image. In general, this sort of image is just like a black-white phote.

1.1.3 Property of the phase image
The data is a 2D complex array, because the radar echoes carry both the amplitude and the phase information. The phase data is a combination of all kinds of varios effect so it looks like random noise with phase uniform distributed from 0 to 2*Pi. It can become useful if we substract two phase images to remove the random part.

1.2 Principles of radar phase and interferometry
The phase image with a different position, or with a different time can be compared with proper image registration. The phase differece form a interferometric patten with fringes denoting the geophysical signal.

read the following paper if you get interested.

Reference: Radar Interferometry and its Application to Changes in the Earth's Surface
D. Massonnet, et al. Review of Geophy. 1998.

baseline estimate

2008-10-10T13:43:00.000-07:00

Hi, I write a small Matlab code that estimate the baseline between two tracks of the satellite orbit. The two tracks should be selected in advance within common frames and paths. It takes the center of the scenes then calculate the baseline between these two acquisitions, based on simple geometry. It works for the starting point but the hundred-meters errors bound its limit.

function baseline = bl(a,b)
% Xiaopeng Tong 2008 OCT 8th
% This is a baseline calculator
% The input are the center latitude and center longitude of the scenes
% The output is the estimated baseline between the two acquisitions at reference time and repeat time.
% This is a rough estimate from simple sphere geometry and need to test on
% more dataset to make sure it works.

% a and b are the center latitude and center longitude of the scenes respectively.
% a and b are the 2*1 vectors containing the latitude and longitude.
% unit: degree
% longitude range:from -180 to 180 "-" means west.

% ******************************************************************

dlon = abs(b(2)-a(2));
lat = abs((a(1)+b(1))/2);
% radius of the earth in km
R = 6371;
% baseline in meters
baseline = R * cosd(90-lat) * dlon * pi / 180 *1000;

Earthquake prediction

2008-08-15T03:19:00.000-07:00

I am having jet lag now as I just got back from my home.

I have dreamed about writing something for the Wenchuan earthquake for a long time. There are surely a lot of mournful or moving stories to tell, about the goodness of our people. There are also surely critics on the unveiled engineering problems. However, as being a student in geophysics, I want to do something different. Predicting earthquake in short time interval is a bold and unrealistic topic in the actual scientific circle at present, but just like Apollo's mission to the moon or like Wright brother's flying dream, in my opinion, that will come ture some day.

Hiroo Kanamori write an article on earthquake physics and real-time seismology in Nature at the beginning of this year. Simply speaking earthquake (mostly in the crust) happens when a part of the crust break into two parts and slip on the break surface due to outside force. After the earthquake, stress will be released. Study shows the stress drop is pretty low, ranging from 1 to 10 Mpa. This can not be explained from lab experienment as we know the stress change of the fracture of the rocks is about 100 Mpa.

The rupture velocity is variable for different earthquake due to various tectonic environment. People found by the means of broadband seismometers some earthquakes slip fast while some slow. It's necessary to consider this factor because the damaging power of earthquakes depends on it.

Moreover, the displacement at the surface of the rupture is quite mysterious. The point where the earthquake starts is not where it broke most severely.

The new strong motion seismometers, geodetic data obtained using GPS and satellite interferometry reveal more detailed seismic slip below and within the earth surface. Instead of assuming a simplistic uniform model we can investigate the asperities and barriers in the slip field. People found there are silent earthquakes which slip so slowly that it can't be detected by seismometers.

The end.

The productive stupidity

2008-07-13T12:22:00.000-07:00

Now I am doing some research, formally speaking, scientific research after the demanding departmental exam. I thought it should be interesting. I am sitting in front of the computer, parsing the code and run the programs. Debug, debug, dubug......

There is a story that begins like a cliche: the author and the lawyer were both in the same graduate school studying science when they were young. And the lawyer dropped out of it and went to the Harvard law school. Nowadays, the two friends come together and talked about their lives, when the lawyer was asked about why she dropped, she said studying science made her feel stupid. After years of feeling stupid every day, she was ready to do something else.

Perhaps reminded by her, the author start to think about this and finally realized he felt stupid every day too. This feeling hit him and he recognized that he is so used to that feeling, that he didn't care about it even. I must say they are both bright and achieved a lot in subsequent years, no matter dropping out of the science major or not.

We all used to get the right answer in class. To be a Ph.D, doing a research is a whole different thing. There is no right answer and there is even no question. One have to frame his own question and seek out an explanation. In the college, we can almost always go to the professors for a right answer when we dispute about a problem. But nowadays, the most thing I hear is "I don't know". No one knows the answer, more, the question you post may be bad inherently in logic and physics. We had to admit that our ignorance is infinite and the possible course of action is to muddle through as best we can.

Now, we finally come across our title: the productive stupidity. That means if we don't feel stupid, that means we're not really trying. I have to ask myself, am I feel stupid today? though it is a little depressing and self-contradictory. Perhaps after several days, I will forget this story and forget ask myself this question. Or I will enjoy asking this, and even feel more comfortable if my answer is yes! Then I can cite the daunting conclusion from the author: "The more comfortable we become with being stupid, the deeper we will wade into the unknown and the more likely we are to make big discoveries."

Reference:
The importance of stupidity in science research, Marin A. Schwartz, Dept of Microbiology, Univ of Virginal, USA, 2008.

About heat flow

2008-05-22T21:29:00.000-07:00

Now, I want to present some thoughts about heat flow problem. Since it's new topic for me, I'd like to start at very beginning. Heat is transmitted in three forms, generally speaking, conduction, convection and radiation. For solid earth, we are safe to say the crust belongs to conduction, mantle and outer core belong to convection. Some problem, such as unexplainable low temperature in the crust need hydrothermal convection to help.

The conduction problem in the earth crust is the easiest one, so let's start from describing Fourier's law. It goes like this: [heat flow] = - [coefficient of thermal conductivity]*gradient([Temperature]). If we consider in the heat production in the material itself, such as the decay of radioactive elements, and apply energy conservation, we end up with: [ coefficient of thermal conductivity]*laplacian([temperature])+[density]*[heat production rate] = 0
It means the heat flow in the material is balanced by the heat production.

If it is generating energy within itself, the heat flows outward; if it is consuming energy, the heat flow inward. To be even clear in math, I want to think this way: Heat production rate is greater than zero, so it's generating heat. In that case, we would expect laplacian of temperature is less than zero. What will it look like in the plot of the temperature profile, yes, it's just like a parabola. From that you may find the center is hotter and the heat flow does go outward.

There is a little more derivation from the dominating equations above. Knowing that, we can ask how much is the heat flow in the ocean crust, or in the continent? what is the temperature profile along depth looks like? What is the role of the radioactive elements play in oceanic crust, and what in continental?

I state here without proof: the heat flow is due to higher temperature at the bottom of the oceanic crust, rather than the radiogenic isotopes. The typical value of surface heat flow for ocean is 100mW/m^2, and 65mW/m^2 for continent. But for the land, the radiogenic heat production must be investigated as it takes a large fraction of total amount of heat flow.

To be continued ...

P.S. Please forgive me the bad-looking physical formula.

velocity between two points on different plates

2008-02-24T13:30:00.000-08:00

After I read the book, I wrote a small matlab code to deal with the problems in the exercise. Please feel free to use that and give me feedback.

**********************************************************************
function vel=gps(a,b,pole,av)
% this is a program determining the expected relative velocities of two
% points on earth based on the calculation in "Geodynamics"
% The input:
% a and b are the 2*1 vectors containing the latitude and
% longitude.unit: degree longitude range:from -180 to 180 "-" means west.
% pole is 2*1 vector containing the pole postion of a plate on which
% lies b. unit degree.
% the av is angular velocity of the two plates. unit: deg/Myr
% The output:
% vel is the expected relative velocity between these two points
% unit: mm/yr.
% Reference: Donald L. Turcotte and Gerald Schubert "Geodynamics" pp101

% dap is the angle subtended between the lines connecting center of the
% earth to a and p.
colata=90-a(1);
ealona=a(2);
% if a(2)<0
% ealon1=360+a(2);
% else
% ealon1=a(2);
% end
colatp=90-pole(1);
ealonp=pole(2);
dap=subtended(colata,ealona,colatp,ealonp);

% u is the velocity of a relative to the plate in which lies b.
R=6371; % radius of the earth
u=R*sind(dap)*av*pi/180*(1e-6)*(1e6); % mm/yr

% beta is the angle between two great circle path ap and ab.
colatb=90-b(1);
ealonb=b(2);
dbp=subtended(colatb,ealonb,colatp,ealonp);
dab=subtended(colatb,ealonb,colata,ealona);
beta=acosd((cosd(dbp)-cosd(dap)*cosd(dab))/(sind(dap)*sind(dab)));

vel=u*sind(beta);

******************************************************************
function y=subtended(a,b,c,d)
y=acosd(cosd(a)*cosd(c)+sind(a)*sind(c)*cosd(d-b));

Reading Report: bathymetry from space workshop

2008-02-23T16:46:00.000-08:00

After reading report: bathymetry from space workshop

This is a report for novice focusing on the importance of a fine bathymetry. Illustrating a vast potential for its application on climate, geology, and biology research, it calls for new mission features improvement in range precision, cross-track spacing, mission duration, moderate inclination, etc.

Normally, there are two ways in obtaining charts on the sea. One is sonar technique, including single and multiple beams methods. This work is done on the vessels, which is relative expensive and slow but with a resolution of less than one kilometer. In the report, it estimates that to provide a fine bathymetry map using multi-beam echosounders it would take 200 ship-years and billions of dollars. You can achieve the similar thing using by satellite in 5 years with $100M. (of course with a low resolution)

Besides the obvious benefits brought by this mission, such as constructing pipes under the sea, territorial claims under the Law of the Sea, resource exploration , military inspection, I am surprised by its scientific significance on a broad areas.

In the report, it claims that ocean flow, bathymetry and climate are related to each other closely. The mountains and valleys on the land influences the transportation of vapor, temperature and pressure. For example, the Andes in south America stop the water from the Pacific, forming a rainless climate to the east of it. In a similar way, the up and down in the sea also create various circulation in the sea. In a computer simulation, I have a clear sense that how small topographic features cause big difference in the flow model of the currents. The currents carrying heat and salt somehow control the climate as you can think what if a warm current running from equator to polar area change its route or even stop.

Another physics happens in the ocean is called mixing. Yes, you can imagine stirring a cup of milk and chocolate. Mixing rates in the ocean govern the rate at which the ocean absorbs heat and greenhouse gases, moderating climate. Mixing rates in the ocean vary geographically depending on bottom roughness. Low mixing rates were found over the smooth topography and higher mixing rates over the rough topography.

Of course, the sea life in the ocean is very sensitive to even subtle change in temperature or salt. Understanding the mixing and circulation will definite provide biologist with new constraints on the inhabitancy of the sea life.

Plate tectonics thrived in 1960s when only crude bathymetry was available. The evidence mainly came from the geographic pattern of sea floor magnetic anomalies, the global distribution of earthquakes volcanoes and fossils. In the mid-1990s, satellite altimeter measurement confirm and complicate the plate tectonics. In one aspect, it provides us a uniform and detailed view of ocean floor architecture as predicted by the theory. In another aspect, many features remain mysterious such as mid-ocean ridge propagating into old thick oceanic lithosphere; spreading centers that overlapped; complex pattern of volcanic seamounts in the interior of the plate.

Abyssal hills are the most common landform on earth. It appears to depend on spreading rates, crustal thickness and ridge segmentation. In a fast spreading ridge, the abyssal hills get narrower and smaller. The improvement in resolution and coverage will certainly facilitate answering some the questions below: when and where tectonic regimes have changed, whether or not these changes are synchronous along the global spreading system, etc.

The bathymetry from space is also useful in discovering small-scale seamounts, undersea volcanoes, forecasting tsunami with a better knowledge of the seafloor offshore.

All in all, reading this report give me a clear sense about the benefit of a detail charted bathymetry map. It is also worth to note that the resolution is constrained by a physical law called upward continuation. This law states that the shortest wavelength we can resolve is approximately twice the depth of the ocean floor. (8km or so) due to a low pass filter caused by the massive water between the bottom and the surface of the sea. This final resolution can be probably achieved by the current technology. The difficulty is brought by waves typically 2-4m tall. This proposed new mission is aiming at obtaining the final resolution by several improvements in both radar technology and multiple mappings.

Reference:
Sandwell, D.T., Gille, S.T., and W.H.F. Smith, eds., Bathymetry from Space: Oceanography, Geophysics, and Climate, Geoscience Professional Services, Bethesda, Maryland, June 2003, 24pp., www.igpp.ucsd.edu/bathymetry_workshop

An introduction

2008-01-06T23:10:00.000-08:00

Hello, everyone. It's easy to know something yourself, but it's not easy to disseminate it to the public and let others remember what you've said. Nearly everyone I meet will ask the same question when I tell them I study geophysics:What's that? Well, you know, it's Ok that others don't care about your work. I just feel tired of explaining time and time again about what I do and how and why I do it. From now on I can direct them to my blog at ease. That's why I am typing some words here. In addition, I want to review these interesting stuff.

First, the definition from Wiki is as follows: Geophysics, a brance of Earth Science, is the study of the Earth by quantitative physical methods, especially by seismic, electromagnetic, and radioactivity methods.
But it is incomplete. There is a new method called satellite geodesy. I wanna add it to the definition of this rich multi-discipline. Believe me, it is a fast-developing technique.

The theories and techniques of geophysics are employed extensively in the planetary sciences in general. The field of geophysics includes the branches of:
Seismology (earthquakes and elastic waves);
gravity and geodesy (the Earth's gravitational field and the size and form of the Earth);
Atmosphere science,
geomagnetism (study of the Earth's magnetic field)
geothermometry (heating of the Earth, heat flow, volcanology, and hot springs);
hydrology (ground and surface water, sometimes including glaciology);
physical oceanography;
Tectonphysics(geological processes in the Earth);
geodynamics (numerical study of the inner Earth);
Exploration and enginering geophysics(see also Archaeological geophysics);
geophysical engineering;
glaciology;
petrophysics;
applied geophysics;
mineral physics;
engineering geology.

Don't be frightened. I can't and won't go through all of them. I just focus on my interest: Geodynamics. In the Wiki, it has the following definition: is a subfield of geophysics, dealing with dynamics of the Earth masses. Experts in geodynamics commonly use techniques such as geodetic GPS, InSar, seismology to study the evolution of the Earth's lithosphere, mantle and core.

I want to tell you some stories and some people in the stories, what they did and what they thought. Whereas, the world in geophysics is small and the people who made contributions are not well-known. There is no Einstein or Feynman here. Though I don't believe their life and scientific experience is less interesting, it's hard to find their records or episodes. It seems focusing on the theories development is pratical. Later if I still have passion I'd like to talk about what current scientists do and what I am expected to do. It is a serialization. Today is just a beginning. To be continued...

Reference:

Wikipedia

http://en.wikipedia.org/wiki/Geodynamics

http://en.wikipedia.org/wiki/Geophysics

About beach and coast

2007-12-30T17:09:00.000-08:00

Yesterday, as I walked on the La jolla beach, one friend throw a question on us, " there are 2 types of view on the beach, cliffy and sandy. How does it happen? what is the mechanism underlying this pheonomenon? Is it possible that the convergent boundary leads to sandy beach and the divergent lead to cliffy one, or switch the pairs?" Now, I'd like to answer it tentatively.

First thing I am sure is that it is not due to the large-scale movement such as plates movement because it is not in the same scale. We should focus on the type of the rocks, waves in the seashore as well as their interactions. This is confirmed by examing the plate boundaries and the beach of the same area on the map. In La jolla cove, there are some scenaries that features on cliffy and rocky beach. While near SIO pier in La jolla there is sandy beach.

I forget about this problem for a while. Now it's high time to bring it to an end. After reading the books, I come up with a category of the coasts and the beaches. This classification will definitely help us understanding what's going on there.
First, Let's see some pictures of the coasts. We can see the coasts vary on different geometric shapes, rock materials, and elevations. The winds, waves forming an altering force acts on the orginally land-air-shaped landscape. We can divide the coasts into roughly two categories. One is dominated by land-air force with relative little erosion by waves due to either hard rock type or insufficient external force. The other one is cut by strong and constant waves and winds years and years. One should note there is no sharp division in this classification so almost every coast we visit is somewhere in between.
Beach is the sediments spreading all over the shore, a part of the coast that experience the up and down of the waves. The shore is marked by the lowest sea level and highest sea level. The beach is colorful. The black one, like la jolla beach in southern California is from lava. The white beach is derived from coral, the sea organisms. While the pink is made by the shells, green is related to mantle rocks such as olivines.

Well, the coast is dynamic rather than static. Like the sayings in Chinese, " blue sea turn into farm land in one moment". One used to strive to saving several minites really can't feel the time in geology. Maybe this is the difference between us and the nature and is why we can't understand it easily.