A Two-Step Time-Frequency

Moment Tensor Inversion:

Application to Mining Data

Václav Vavryčuk1, Daniela Kühn2

1 Institute of Geophysics, Prague 2 NORSAR, Kjeller

Motivation

To be able to invert for focal mechanisms and

moment tensors:• accurate• robust and stable

Difficulties:• complex mining environment• complex source-time function• non-double-couple moment tensors

Motivation

Waveform modelling

MTIstrategy

Summary

Synthetic tests

Application to real data

Moment tensor inversions

wave amplitudes (Vavryčuk et al. 2008; Fojtíková et al. 2010; Godano et al. 2011)

amplitude ratios (Miller et al. 1998;

Hardebeck & Shearer 2003; Jechumtálová &

Šílený 2005)

full waveforms

(Šílený et al. 1992 Cesca et al. 2006;

Cesca & Dahm 2008; Sokos & Zahradník

2009)

• applicable to simple media• insensitive to amplifications• non-linear

• applicable to simple media• linear• fast

• applicable to complex media• linear• more time consuming

Motivation

Waveform modelling

MTIstrategy

Summary

Synthetic tests

Application to real data

• microseismic monitoring: since January 2003 safety of the underground

personnel optimisation of mining

process

• network: 12 1-C geophones

+ 6 3-C geophones (ISS)

3-D geometry sampling rate: < 3000 Hz

• events: 1500 events /months

(including blasting) -2 < Mw < 1.5

Pyhäsalmi ore mine, Finland

owned by Inmet Mining Co., installation of seismometer network by the ISS Int. Ltd.

Motivation

Waveform modelling

MTIstrategy

Summary

Synthetic tests

Application to real data

Strongly heterogeneous velocity model • ore body: vp = 6.3 km/s

• host rock: vp = 6.0 km/s

• excavation area: vp = 0.3 km/s

U

D

W E

Velocity model

Motivation

Waveform modelling

MTIstrategy

Summary

Synthetic tests

Application to real data

• E3D: viscoelastic 3-D FD code (Larsen and Grieger, 1998)

• strong interaction with mining cavities: reflection, scattering, conversion

Waveform modelling: 2D

620 mMotivation

Waveform modelling

MTIstrategy

Summary

Synthetic tests

Application to real data

- complex waveforms

- long, strong coda

- complex secondary arrivals

- difficult to interpret P-wave

polarities

- difficult to identify S-wave

arrivals

observed seismograms

Waveform modellingsynthetic seismograms

Motivation

Waveform modelling

MTIstrategy

Summary

Synthetic tests

Application to real data

Moment tensor inversions

wave amplitudes (Vavryčuk et al. 2008; Fojtíková et al. 2010; Godano et al. 2011)

amplitude ratios (Miller et al. 1998;

Hardebeck & Shearer 2003; Jechumtálová &

Šílený 2005)

full waveforms

(Šílený et al. 1992 Cesca et al. 2006;

Cesca & Dahm 2008; Sokos & Zahradník

2009)

• applicable to simple media• insensitive to sensor amplifications• non-linear

• applicable to simple media• linear• fast

• applicable to complex media• linear• more time consuming

Motivation

Waveform modelling

MTIstrategy

Summary

Synthetic tests

Application to real data

Full waveform MT inversions

time-domain inversion

frequency-domain inversion

amplitude spectra(Cesca et al., 2006; Cesca &

Dahm, 2008)

complex spectra(Vavryčuk, 2011a,b)

• polarity of waves is neglected• insensitive to time shifts• non-linear• complex source-time function

• polarity of waves is considered • insensitive to time shifts• linear• simple source-time function

• polarity of waves is considered• sensitive to time shifts• non-linear• complex source-time function

simplified approach(Sokos & Zahradník 2009)

Adamová et al. 2009)

Motivation

Waveform modelling

MTIstrategy

Summary

Synthetic tests

Application to real data

Goal of the study

To develop a moment tensor inversion:

• combination of time and frequency approaches

• keeps advantages of all approaches

(accurate, robust and stable)

Motivation

Waveform modelling

MTIstrategy

Summary

Synthetic tests

Application to real data

Moment tensor inversion: time-frequency approach

Motivation

Waveform modelling

MTIstrategy

Summary

Synthetic tests

Application to real data

Moment tensor inversion scheme

Frequency-domain MTI using complex spectra

Moment tensor

Time-domain MTI

Final moment tensor

Source-time function+

1. step:

2. step:

Motivation

Waveform modelling

MTIstrategy

Summary

Synthetic tests

Application to real data

Full waveform MT inversions

time-domain inversion

• polarity of waves is considered

• insensitive to time shifts

• linear

• simple source-time function

• polarity of waves is considered

• insensitive to time shifts

• linear

• complex source-time function

time-frequency inversion

Motivation

Waveform modelling

MTIstrategy

Summary

Synthetic tests

Application to real data

Tests using synthetic data

Motivation

Waveform modelling

MTIstrategy

Summary

Synthetic tests

Application to real data

Synthetic tests

• source mechanism: DC and explosion

• source time function:

• noise: in amplitudes and in time shifts

− amplitude noise; 0-100% in 5% steps− time shift noise: 0-0.01 s in steps of 0.005 s

• repeating inversions: 100 inversions

0 0.01 0.02 0.03 0.04 0.05

Tim e [s]

two distinctmaxima

Motivation

Waveform modelling

MTIstrategy

Summary

Synthetic tests

Application to real data

Double-couple source: ISO %Mean value Standard deviation

time-domainInversionISO = 3%

frequency-domain InversionISO = 0%

time-frequencyInversionISO = 0%

Motivation

Waveform modelling

MTIstrategy

Summary

Synthetic tests

Application to real data

Explosive source: ISO %Mean value Standard deviation

time-domainInversionISO = 95%

frequency-domain InversionISO = 100%

time-frequencyInversionISO = 100%

Motivation

Waveform modelling

MTIstrategy

Summary

Synthetic tests

Application to real data

Application to real data

Motivation

Waveform modelling

MTIstrategy

Summary

Synthetic tests

Application to real data

Mining blast: ISO %Mean value Standard deviation

time-domainInversionISO = 66%

frequency-domain InversionISO= 71%

time-frequencyInversionISO = 68%

Motivation

Waveform modelling

MTIstrategy

Summary

Synthetic tests

Application to real data

P

T

P

T

P

T

time-domaininversion

frequency-domain inversion

time-frequencyinversion

Mining blast: DC, waveforms

Motivation

Waveform modelling

MTIstrategy

Summary

Synthetic tests

Application to real data

structural model in mines usually is very complex

large and abrupt changes in velocity at cavities

the model varies in time

Summary I

earthquake source is complex (single forces, non-DC components, complex source history)

radiated wave field is complex (reflected, converted, scattered waves, head waves)

Motivation

Waveform modelling

MTIstrategy

Summary

Synthetic tests

Application to real data

Summary II

• the most promising approach: full waveform MTI

• simplified time-domain MTI is robust and stable

• two-step time-frequency MTI improves the performance by considering more complex source-time function

• inversion of blasts reveals some stable DC part

Motivation

Waveform modelling

MTIstrategy

Summary

Synthetic tests

Application to real data

Thank you!