Traditional practice separates seismic data processing and further interpretation. Traditional practice separates seismic data processing and further interpretation. However the most efficient processing methods utilize a-priori information about However the most efficient processing methods utilize a-priori information about medium to explore.medium to explore. In case of VSP and combined 3D 3C observation systems (2D+VSP, 3D+VSP) In case of VSP and combined 3D 3C observation systems (2D+VSP, 3D+VSP) the usage of the most profound medium model is essential condition for efficient the usage of the most profound medium model is essential condition for efficient processing.processing. The technology of Dynamic Decomposition of wavefields and Reconstruction of The technology of Dynamic Decomposition of wavefields and Reconstruction of the model (DDR) is based on model correction to minimize residues of wavefield the model (DDR) is based on model correction to minimize residues of wavefield after decomposition.after decomposition. The report observes key features of DDR method:The report observes key features of DDR method: 1. Method of raytracing in nonhomogeneous media with sectionally smooth 1. Method of raytracing in nonhomogeneous media with sectionally smooth bounds.bounds. 2. Method of VSP wavefield decomposition using results of raytracing modeling.2. Method of VSP wavefield decomposition using results of raytracing modeling. 3. Approach to build an image of medium near the well.3. Approach to build an image of medium near the well.

Raytracing method application to the wavefiled decompositionRaytracing method application to the wavefiled decompositionand model reconstruction from VSP dataand model reconstruction from VSP data

Medium model definition

GeometryGeometry of the model is defined as a set of points laying on sectionally smooth bounds. of the model is defined as a set of points laying on sectionally smooth bounds.For next calculations smooth bounds are approximated by parametric cubic splines which For next calculations smooth bounds are approximated by parametric cubic splines which

allows to describe ambiguous bounds. The criteria of approximation is a curvature restriction.allows to describe ambiguous bounds. The criteria of approximation is a curvature restriction.The bound is defined as a set of points on the spline between special end points – break The bound is defined as a set of points on the spline between special end points – break

points or another bound intersection. Maximum deviation of the chord between two consequent points or another bound intersection. Maximum deviation of the chord between two consequent points from the spline is limited by preset value.points from the spline is limited by preset value.

Physical parametersPhysical parameters of the model are defined on the bounds. The pressure, shear wave of the model are defined on the bounds. The pressure, shear wave velocity and density are interpolated between bounds producing gradients.velocity and density are interpolated between bounds producing gradients.

Observation system

For a case study the observation system with non-straight well and two shot points For a case study the observation system with non-straight well and two shot points was defined. Distance between receivers in the well is 20 meters. Both shot points are was defined. Distance between receivers in the well is 20 meters. Both shot points are located with offset 2500 meters.located with offset 2500 meters.

Raytracing in gradient medium with sectionally smooth boundsRaytracing in gradient medium with sectionally smooth bounds

The method of raytracing from arbitrary point in arbitrary direction was developed for The method of raytracing from arbitrary point in arbitrary direction was developed for the considered model.the considered model.

In general velocity gradient is not a constant so raytracing is performed step by step. In general velocity gradient is not a constant so raytracing is performed step by step. Direction and length of a step is set according to parameters of the medium in origin point. Direction and length of a step is set according to parameters of the medium in origin point. The step defines chord HThe step defines chord Hi i of a circle which is a true ray trajectory. The first step is made of a circle which is a true ray trajectory. The first step is made

along the chord which has F angle to the ray direction. The F value is a parameter of the along the chord which has F angle to the ray direction. The F value is a parameter of the method and it defines accuracy of a solution. The less F value is the better the chord fits method and it defines accuracy of a solution. The less F value is the better the chord fits the circle.the circle.

A chord value are calculated by given formula:A chord value are calculated by given formula:

,

tgR2H ii

where:where:

iiii

iii sinz,xk

z,xVR

(i=0,1,….N)

-- origin point of the i-th chord origin point of the i-th chord

- pressure wave velocity- pressure wave velocity

- absolute value of velocity gradient- absolute value of velocity gradient

- direction of the tangent to ray trajectory- direction of the tangent to ray trajectory

- direction of the velocity gradient- direction of the velocity gradient

ii z,x

ii z,xV

ii z,xk

iii z,x

iii z,x

From the law of tangential component invariance:From the law of tangential component invariance:it’s easy to represent orthogonal component of refraction vectorit’s easy to represent orthogonal component of refraction vector

of the reflected/refracted ray:of the reflected/refracted ray:

Thus we have complete vector of wave refraction (and the ray direction) just after bound Thus we have complete vector of wave refraction (and the ray direction) just after bound instersection.instersection.

Refraction-reflection effects are considered at a chord intersection with a bound by the Refraction-reflection effects are considered at a chord intersection with a bound by the following algorithm:following algorithm: A tangent to the bound in intersection point is drawn. Then the tangential component of A tangent to the bound in intersection point is drawn. Then the tangential component of refraction vector of incoming ray with defined type is calculated. This component is used refraction vector of incoming ray with defined type is calculated. This component is used for calculation of orthogonal component of refraction vector of outgoing reflected or for calculation of orthogonal component of refraction vector of outgoing reflected or refracted (converted or non-converted) ray.refracted (converted or non-converted) ray.

Refraction vector of incoming ray of wave type and vector of tangentRefraction vector of incoming ray of wave type and vector of tangent

to the bound in intersection point and orthogonal vector of the bound.to the bound in intersection point and orthogonal vector of the bound. Lets separate refraction vector of incoming ray to the orthogonal and tangential Lets separate refraction vector of incoming ray to the orthogonal and tangential components:components:

v

np in

m

N

Npmpp inort

in||

in

out

||in|| pp

v

vp1p

2out||out

ort

Npmpp outort

out||

out

Calculation of model wave fields Model wave field was calculated by the method of finite differences on the grid with 2m Model wave field was calculated by the method of finite differences on the grid with 2m step. The source was calculated analytically in the 100m radius.step. The source was calculated analytically in the 100m radius. High-frequency noise on the grid was no more than 10% in the frequency range High-frequency noise on the grid was no more than 10% in the frequency range 0 - 62.5 – 0 - 62.5 – 125125HzHz. . Inverse wave scattering on model boundaries was no more then Inverse wave scattering on model boundaries was no more then 0.5%.0.5%.

X component of calculated field Z component of calculated field

Calculation of the wave parameters

To calculate parameters of the wave with given type, it’s necessary to determine the To calculate parameters of the wave with given type, it’s necessary to determine the source angle of the ray which hits exact receiver. In case of all such rays are found it’s source angle of the ray which hits exact receiver. In case of all such rays are found it’s possible to calculate travelling time, amplitude and polarization of the wave in the possible to calculate travelling time, amplitude and polarization of the wave in the receiver. Thus the method allows to obtain amplitudes, polarization parameters and receiver. Thus the method allows to obtain amplitudes, polarization parameters and arrival times for every type of the wave.arrival times for every type of the wave.

Example of reflected wave raytracing

Hodographs of the non-converted and converted reflected Hodographs of the non-converted and converted reflected

waves, calculated by the ray methodwaves, calculated by the ray method

To illustrate accuracy of polarization parameters calculation, initial XYZ field was rotated to To illustrate accuracy of polarization parameters calculation, initial XYZ field was rotated to the polarization of converted transferred PS wave from the first bound:the polarization of converted transferred PS wave from the first bound:

R component P component

Amplitudes of the direct wave calculated by the ray-tracing (red) Amplitudes of the direct wave calculated by the ray-tracing (red)

and finite difference (green) methods.and finite difference (green) methods.

Wave detection and subtraction

When hodograph and polarization parameters of the wave are known, it’s possible to When hodograph and polarization parameters of the wave are known, it’s possible to subtract it from initial wave field without influence of the interference effects. Thus, by the subtract it from initial wave field without influence of the interference effects. Thus, by the sequential wave subtraction in the order of amplitudes decreasing, it’s possible to reach full sequential wave subtraction in the order of amplitudes decreasing, it’s possible to reach full wave field analysis up to multiple reflection/refraction ray pathswave field analysis up to multiple reflection/refraction ray paths..

Hodograph of the converted waveHodograph of the converted wave

Wavefield after subtraction of a Wavefield after subtraction of a

converted waveconverted waveSubtracted waveSubtracted wave

DDR methodDDR method

Definition of the a-priori modelDefinition of the a-priori model

Model correctionModel correction by theby the first breaks timesfirst breaks times

Bound selectionBound selection

Calculate the parameters of the waves, scattered by Calculate the parameters of the waves, scattered by the selected boundthe selected bound

Definition and subtraction of the scattered wavesDefinition and subtraction of the scattered waves

Imaging from subtracted waves of different typesImaging from subtracted waves of different types

Test for the model and the image agreementTest for the model and the image agreement

Model correctionModel correction

ExitExit

If all boundaries are correctedIf all boundaries are corrected

Results:Results:

-- model of the mediummodel of the medium

- detected waves of all detected waves of all typestypes

- - image of the medium image of the medium from waves of all typesfrom waves of all types

Wave field with hodographWave field with hodograph Model and raysModel and rays

DDR interface conceptionDDR interface conception

ResultsResults

1.1. New algorithms and programs for fast ray tracing in complicated medium New algorithms and programs for fast ray tracing in complicated medium was developed.was developed.

2.2. Ray-tracing method is proved by comparison with finite difference of the Ray-tracing method is proved by comparison with finite difference of the modeling results.modeling results.

3.3. Demonstrated elements of the combined system of data processing and Demonstrated elements of the combined system of data processing and interpretation, called Dynamic wave fields Decomposition with model interpretation, called Dynamic wave fields Decomposition with model Reconstruction.Reconstruction.

Greetings

The authors express their gratitude to SEPTAR company for the model which The authors express their gratitude to SEPTAR company for the model which was used for comparison of finite difference and ray-tracing method. was used for comparison of finite difference and ray-tracing method.