Geophysics Department TU Clausthal

english deutsch Applied Geophysics : Seismics


Huygens' Principle


Applet    ( in separate window, ca. 390 x 275 Pixel )


The applet simulates a simplified demonstration of Huygens' Principle :

A separate frame displays
the vertical cross-section of a 2-dimensional subsurface model,
a spread of 24 equally spaced receivers along the free surface
and
the corresponding traces,

resulting from
a single shot of ( almost ) arbitrary position above the interface ( SHOT RECORD )
or from
shot / receiver pairs at identical surface positions ( ZERO OFFSET ).


Table of Content


Comments
HOWTO
Examples
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Comments


The interface is represented by max. 281 discrete points ( = parallel lines in the 2-d model ), emitting elementary waves when hit by the direct wave.

Each trace is calculated as the superposition of all elemetary waves arriving at the corresponding receiver location.
Trace samples are calculated in constant time steps ( sampling interval Δt ), determined by the min. point distance along the interface ( ALL PNTS = 281 ) and the velocity selected.

A subset ( 71 PNTS ... 1 POINT ) of interface points and corresponding elementary waves can be selected to observe the formation of the final result for ALL PNTS in a series of SHOT RECORDS / ZERO OFFSET sections using an increasing number of interface points.

For compressional waves
the vertical componentVER (P-WAVE) )
or
the horizontal inline componentHOR (P-WAVE) )
of the ground displacement can be calculated,

for horizontally polarized shear waves
the transverse componentS-H (S-WAVE) ).

! Direct wave and elemenary waves are assumed to be of identical type, i.e. no conversion at the interface ! )

The amplitudes of the direct wave are scaled to be of the magnitude of the reflexion amplitudes :
max amp ( DIR ) of all traces = max amp ( RFL ) of all traces.

! The simulation is restricted to primary waves,
i.e. direct waves only can excite elementary waves !
! No velocity contrast at the interface,
i.e. impedance contrast due to density change only => no refraction !
! Boundary conditions at the free surface and at the interface are neglected,
i.e. "reflexioncoefficient" +1 at the interface.

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HOWTO


Dialogue Window
( Screenshot )


SHOW / HIDE
SHOW starts the applet and displays the model + trace frame,
HIDE hides the frame and frees its resources.

INFO
displays informations to the actual cursor postion :
X [m] / Z [m] ( model window ) and X [m] / T [ms] ( trace window ).

HELP
displays possible mouse interactions :

in model window
horizontal zoom,
adjustment of position and geometry of the interface and the receiver spread,
shot position
and
of the "wave length" of the source signal.

in trace window
vertical ( =TWT ) zoom,
adjustment of the AGC window.

The dialogue field INTERFACE refers to the model geometry and scaling :

VELOCITY n.nn [km/s] :

SIGNAL :

TRACES :

SECTION :

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The dialogue field TRACE DISPLAY refers to the display parameters of the seimic section :

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HOR ZOOM  ( model window ) :

The left mouse button sets the horizontal display range of the model ( + traces ),
marked as hor. rectangle ( cyan, starting inside the actual window, may end outside ),

the right button resets the horizontal extend to a value covering the receiver spread ( incl. shot position in SHOT RECORD mode ).

The vertical range of the model window is set automatically ( surface, Z=0 [m], to max. depth of the interface / length of source signal, if shown )

TWT ZOOM  ( trce window ) :

The left mouse button sets the time range of the trace display
( min. start = 0 [ms], max. end = 2 × max. TWT ),

the right button ( or the start of a new recording cycle ) resets the time range to 0 [ms] ... max. TWT.

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Examples


Parameters common to all frames :

Model :
syncline ( 1 - COS ),
hor. -100 [m] ... +100 [m], ver. 50 [m] ... 130 [m],
total hor. extent -280 [m]  ... +280 [m] ( SCAL × ;1.0 )
=> point distance approx. 2 [m] for ALL PNTS, approx. 28 [m] for 21 PNTS.

Velocity :
2.00 [km/s] => Delta-T = 1 [ms]

Source Signal :
Kueppers, Order 2, L-Sig = 20 [ms] = 40 [m], SHOW SOURCE SIG

Traces :
Vertical component, CYL. SPREADING

Trace Display :
Wiggle + Area, D-TRC × 1.0, DEFL × 1.0, SHOW DIRECT WAVE

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ZERO OFFSET section and SHOT RECORD, showing the typical 'tie' reflexion pattern.

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Snapshots of recording cycle at TWT = 60 [ms] and TWT = 80 [ms]
( model represented by 21 points, to reduce number of elementary wave fronts ).

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ZERO OFFSET section and SHOT RECORD,
covering the total horizontal extend of the model,
represented by 3 points and showing the resulting diffraction hyperbola.

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SHOT RECORD ( parmeters identical to the first example ).
AGC scaling applied to the trace display reveals effects of final horizontal extent of the model ( ±280 [m] ).

Below 180 [ms] :
small amplitude diffraction signals from both ends,
though a cosine taper is applied to the impdance contrast of approx. 20 points at both ends of the interface ( ! ALL PNTS mode only ! ).

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Download

Class and html files for a local installation of the applet are available as a zip file and as a tar.gz file.

More applets : the author's Homepage


Rev. 27-jul-2006

Comments to Fritz Keller
( ned gschempfd isch globd gnueg )

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