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GLOBAL EARTHQUAKE MONITORING PROCESSING ANALYSIS

Moment Tensor Inversion

The focal mechanism of an earthquake de-

scribes the inelastic deformation in the source

region that generates the seismic waves. In

the case of a fault-related event it refers to the

orientation of the fault plane that slipped and

the slip vector and is also known as a fault-

plane solution. Focal mechanisms are derived

from a solution of the moment tensor for the

earthquake, which itself is estimated by an

analysis of observed seismic waveforms.

The moment tensor solution is typically dis-

played graphically using a so-called beachball

diagram. The pattern of energy radiated dur-

ing an earthquake with a single direction of

motion on a single fault plane may be mod-

elled as a double couple, which is described

mathematically as a special case of a second

order tensor (similar to those for stress and

strain) known as the moment tensor. [1]

[1] http://en.wikipedia.org/wiki/Focal_mechanism

Our moment tensor inversion technique uses

a combination of several seismic wave types,

time windows and frequency bands carefully

chosen based on event magnitude and sta-

tion distance. Wave types include body waves,

surface waves, mantle waves as well as the so-

called ’W-Phase’ (Kanamori and Rivera, 2008).

The inversion is currently performed in the

time domain only. An iterative centroid

search can be performed independently both

horizontally and in depth.

Moment tensors can be computed in an auto-

matic fashion within a few seconds of wave-

form data becoming available. Prior to publi-

cation, solutions can be reviewed by an ana-

lyst using the graphical user interfaces.

Waveform review

scmtv (MomentTensorView) is used to cre-

ate and revise moment tensor solutions. It

supports body waves, surface waves, mantle

waves and W-Phase.

Monte Carlo plot visualizes the stability of asolution. The sharper the image the more sta-

ble the solution with respect to the selected

station set.

Moment Tensor Inversiondeveloped by

gempa GmbH and Helmholtz Centre Potsdam, GFZ German Research Centre for Geosciences

Applications

• Local, national and regional networks

• Tsunami early warning

• Fast determination of moment magnitude

and focal mechanism

Features

• Rapid moment tensor inversion in the time

domain

• Real-time module fully integrated into Seis-

ComP3

• Real-time restitution for maximum speed

• Fits body waves, surface waves, mantle

waves and W-phases

• Configurable profiles for magnitude ranges

• Interactive analysis

gempa GmbH · http://www.gempa.de · info@gempa.de

About us

gempa (Global Earthquake Monitoring Pro-

cessing Analysis) GmbH, Potsdam, Germany

is a servicing and software development com-

pany providing installation, training, support

and maintenance for SeisComP3 and other

products based on the SeisComP3 software

framework. With the new automatic and in-

teractive MT and CMT processing modules, de-

veloped in close cooperation with GFZ, gempa

augments its portfolio of tsunami warning

products. The MT/CMT modules have been op-

erative since years at GFZ and others and have

proved their quality and user friendliness in

many situations. The modules proved their

usefulness for tsunami warning systems dur-

ing the April 11, 2012 earthquake in Nothern

Sumatra where they came up with the correct,

but for this region untypical and unexpected

8.6 Mw strike slip solution.

Method

Our method to invert for seismic moment ten-

sors uses the full three-component waveforms

and a set of precomputed Green’s functions

with 8 components (ZSS, ZDS, ZDD, RSS, RDS,

RDD, TSS, TDS) in the time domain. A tensor

is parametrized by a 3× 3 symmetric matrix

M =

xx xy xzxy yy yzxz yz zz

or as a vector m = (xx, yy, zz, xy, yz, xz)containing the six independent moment ten-

sor elements to be determined.

The observed ground displacements are given

as the vector u.

u = G× m̄

whereas G is a n× 6 matrix.

The moment tensor solution of m with given

u and G is retrieved by the least squares in-

version. A goodness-of-fit (GOF) is computed

describing how well the observed data are

represented by the computed moment tensor

with respect to the Green’s functions.

Graphical user interface

Bulletin preview may be sent as e-mail or

copied to a web page.

Fit plot on the waveform review page. It

shows the fits of all contributing stations vs

their distance from epicenter.

Before the actual inversion takes place the al-

gorithm automatically corrects the data for in-

strument response, removes the mean and lin-

ear trends and checks for unclipped data and

a configurable minimum acceptable signal-to-

noise ratio. Furthermore the data are down-

sampled to the sampling rate of the Green’s

functions used.

Modules

scautomt runs in real-time and computes mo-

ment tensor solutions in near real-time fully

automatically triggered by events created by a

SeisComP3 system. It is configured with a set

of magnitude dependent profiles. Each pro-

file defines the phases to invert for and the

corner periods of the band pass filter. When

triggered by an event, solutions for all profiles

matching the SeisComP3 magnitude estimate

are used and the solution with the highest

fit (or lowest misfit) is sent back to the Seis-

ComP3 system as as focal mechanism object

which is in turn considered by scevent to be

selected as preferred solution.

Once an event is received by scautomt itstarts to read waveforms of all enabled sta-

tions up to a configurable epicentral distance

(preferably via SeedLink or any other stream-

ing server) and updates the solution if there is

a significant amount of new data.

scmtv (Moment Tensor View) is the counter-

part to scolv to review automatic or manual

moment tensor solutions. It allows operators

to check observed and synthetic waveforms,

add and remove networks, stations, compo-

nents or even single waveform snippets.

It allows alteration of existing profiles and

switching between them. Several tool and

plots to check the quality and stability of the

solution are provided.

Polar plot on the waveform review window to

check azimuthal coverage and azimuth depen-

dent waveform fits.

Depth search shows the results of all tested

depths and plots selected parameters vs. dis-

tance.