Applied Geophysics : Seismics

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 ).

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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 component ( VER (P-WAVE) )

or

the horizontal inline component ( HOR (P-WAVE) )

of the ground displacement can be calculated,

for horizontally polarized shear waves

the transverse component ( S-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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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 :

1 - COS / TRIANGLE / PARABOLA / RAMP

selects the general shape of the interface,
to be modified by dragging characteristic points with the mouse.

ALL PNTS / 71 PNTS ... 1 POINT

selects representaion of the interface by all ( 281 ) or a reduced number of discrete points to clarify the superposition of elementary waves.

SCAL x 0.1 ... SCAL x 10.

applies a scaling factor to the subsurface model and the receiver spread

( and to the wave length of the source signal ),

to vary the horizontal extent from approx. 60 [m] to approx. 6 [km].

VELOCITY n.nn [km/s] :

DEC, INC and BY 1.00 .. BY 0.01

increments / decrements the velocity used for calculation

in steps of 1.00 ... 0.01 [km/s].

SIGNAL :

KUEPPERS_2 / KUEPPERS_4 / ZERO PHASE

selects the wave form of the source signal

( Kueppers wavelet of order 2 / 4 or autocorrelation of a sweep ).

SHOW SOURCE SIGNAL

displays the source wavelet in the model window,

scaled identically to the vertical scale of the model

( its wavelength can be adjusted using the mouse ).

TRACES :

VER (P-WAVE) / HOR (P-WAVE) / S-H (S-WAVE)

selects the component to be displayed in the trace window.

NO GEOM. SPREAD. / CYL. SPREADING / SPHER. SPREADING

includes  NO,  1 / SQRT(R)  or  1 / R  scaling in trace calculation.

SECTION :

SHOT RECORD / ZERO OFFSET

selects the type of seimic section to be displayed in the trace window.

DISP WAVE FRONTS

displays direct and elementary wave fronts during trace calulation,

if SHOT RECORD is selected and

the aspect ratio of the model display SCALE VER : HOR = 1.0 : 1

( evtl. adjust the aspect ratio of model + trace window ).

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

AMPLITUDE SCALING

TRUE AMPLITUDE :

const. scaling of all traces, determined by the max. amplitude of all traces,

AMAX PER WIND. :

as above, but max. amplitude taken in actual TWT ( zoom ) window,

AUTOM. GAIN :

AGC scaling of traces,

length of source signal ( blue ) and of AGC window ( red ) shown in the upper left corner of the trace display

( always active during recording cycle, length of AGC window : mouse adjustable ).

DEFLECTION

D-TRC × 0.5 ... D-TRC × 5.0 :

the clip limit for each trace in units of trace distance.

MAX AMPL.

DEFL × 0.1 ... DEFL × 10. :

a const. factor, applied before plotting ( and clipping ) a sample.

SHOW DIRECT WAVE

shows / hides the direct wave in the trace display.

RUN

continuous calculation and display of wave fronts and traces.

STEP

calculation and display of wave fronts and traces in single time step mode.

RESET

resets the trace calculation,

displays the message ! CLICK TO CALC ... ! and

alows adjustment of the AGC window for the next recording cycle.

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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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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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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

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