depth conversion of time interpretations

8/12/2019 Depth Conversion of Time Interpretations

1/58

12.1

Depth Conversion

Depth Conversion

of Time

Interpretations

~

Volume Models

Depth Conversion

Based on the different types of velocity models that can be

derived from well data produce a ranked list of approaches

to depth conversion with the simplest, least accurate at the

top and most accurate at the bottom.


2/58

12.2

Depth Conversion

Long Period Static Anomalies

No LVL Static CorrectionBefore we begin depth conversion

it is necessary to recognise, and

correct, any long wavelength static

anomalies in the time data.

These anomalies will probably be

seen in the times sections, time

map(s) and possibly the stacking

velocity sections or maps. The

problem and solution was first

discussed by Booker et al, 1976,then by Pickard 1992, Musgrove

1994 and Armstrong et al 2001.

After Musgrove, 1994, Time Variant Statics

Corrections During Interpretation, Geophysics v. 59,

no. 3, p. 474.

Depth Conversion


The time delay due to near

surface anomalies is estimated

from the regional residual

separation of time delays on

shallow reflectors. For deep

anomalies it may be estimated

from well depths and velocities.

The width of the time distortion

at the target horizon is derived

from the width of the velocity

anomaly, its depth and the

target horizon depth. Fresnel

zone effects are often ignored.

From Armstrong et al, 2001, Removal of overburden

velocity anomaly effects, Geophysical Prospecting v.49, no. 1, p. 79.


3/58

12.3

Depth Conversion


The technique then simulates

the CMP stack at the target

horizon by modelling the time

delay on each of the traces in

the CMP gather with respect to

distance along the seismic line.

This step requires a knowledge

of the mute pattern at the time

of stacking velocity analysis

(just as the bias correction did).


velocity anomaly effects, Geophysical Prospecting v.

49, no. 1, p. 79.

Tx2 = To

2 + x2 / VRMS2 - x4(VRM4

4 - VRMS4) / 4 To

2 VRMS8

with

VRM44 = VIi

4ti / to.

Depth Conversion

Long Period Static AnomaliesThe time delay on the

stacked traces (the

required correction) is

then found from the

time axis intercept of a

least squares best fit

trend line of the time

delay on the different

traces in the CMP

gather plotted against

the offset squared.


velocity anomaly effects, Geophysical Prospecting v.

49, no. 1, p. 79.


4/58

12.4

Depth Conversion

Ranked Methods for FunctionsThe least accurate methods are at the top and most accurate at the bottom.

1. Constant average velocity.

2. Mapped average velocity.

3. Average velocity function.

4. Instantaneous velocity function.

5. Instantaneous velocity function with mapped parameter.

6. Constant interval velocities.

7. Mapped interval velocities.

8. Interval or instantaneous velocity functions.

9. Interval or instantaneous velocity functions with oneparameter mapped.

10. Interval or instantaneous velocity functions with all

parameters mapped.

Depth Conversion

0

2

4

T(

sec)

5000 Vi (ft/sec) 20,000

1

Depth conversion may use a

single velocity function from

the surface down to the layer

of interest.

Fast

Less accurate

An average velocity functionor an instantaneous velocity

function.

One Function


5/58

12.5

Depth Conversion

One Function

Time

Map

Velocity

Function

Depth

Map

Velocity

Map

Depth conversion process

One Function

Depth Conversion

Time Depth

Apparent closed area depends of choice of contour

interval with respect to spill points in flat areas.

Constant Average Velocity

After Marsden, Layer cake depth conversion, Leading Edge, January 1989.

One Function


6/58

12.6

Depth Conversion

Time Depth

Constant Average Velocity

One Function

The only difference between the maps is in the level of detail

attributable to the different contour interval.

Depth Conversion

The structure in depth

map based on well control

fails to represent the true

structural picture.

The well data is used to

provide a constant average

velocity based on a timedepth plot.

Example after Laurtent Moinard, Application of Kriging to the Mapping of a Reef from Wireline Logs and Seismic Data : a Case

History, in Geostatistical Case Studies, G. Matheron and M. Armstrong (editors) 1987, D. Reidel Publishing Co.

Constant Average Velocity with External Drift

One Function


7/58

12.7

Depth Conversion


Example after Laurtent Moinard, Application of Kriging to the Mapping of a Reef from Wireline Logs and Seismic Data : a CaseHistory, in Geostatistical Case Studies, G. Matheron and M. Armstrong (editors) 1987, D. Reidel Publishing Co.

Structure in time map;

plenty of detail due to

abundant seismic control.

This map is used to derive

the semivariogram. A

plane least squares

surface was used as the

drift so that the

semivariogram is derived

from time residuals.

One Function

Depth Conversion

The depth map produced

from the time surface

using the constant

average velocity and the

semivariogram. This depth

map follows the shape of

the time map but departs

from it in the vicinity of thewell locations where it

matches the measured

depths.

Example after Laurtent Moinard, Application of Kriging to the Mapping of a Reef from Wireline Logs and Seismic Data : a

Case History, in Geostatistical Case Studies, G. Matheron and M. Armstrong (editors) 1987, D. Reidel Publishing Co.


One Function


8/58

12.8

Depth Conversion

Summary - Single Function

Leman field with production platforms

25 km

Depth conversion by

a single function is

well suited to areas

with dense well

control and simple

structure.

One Function

Depth Conversion

Single Function

In the marine environment we may be tempted to use a single layer

for depth conversion when the water layer appears to be relatively

uniform and the depth to the first interface appears to be relatively

deep. There is one anomalous well data point.


9/58

12.9

Depth Conversion

Multiple Functions

In the marine environment if we separate out the water layer from

the underlying Tertiary we will obtain a much better function. The

figure shows the same formation as the previous slide with the

water layer removed. The scatter is reduced to give a better result.

Depth Conversion

0

2

4

T(

sec)

5000 Vi (ft/sec) 20,000

1

A multi-layer approach

should be used in areas

where the overburden

displays lateral velocity

inhomgeneities, i.e. the

velocity structure is not

simple. Each of a number of

layers are then representedby different functions.

Slower

Increased accuracy ?

Multiple Functions

Multiple Functions


10/58

12.10

Depth Conversion

Strategy

How do we decide the layers to be used?

Multiple Functions

Depth Conversion

Strategy

How do we decide the layers to be used?

Consider the main formation boundaries

Where are the major unconformities?

Inspect the velocity/sonic log for changes in slope, or shifts

Next, plot the time-depth charts to each of the possible

boundaries. If the plot shows little scatter the horizon can be

depth converted by a single function. If the plot shows scatter thenthe interval above needs to be subdivided.

Then plot the isochron-isopach charts for each formation or

interval. Select intervals where the plot shows little scatter.

Multiple Functions


11/58

12.11

Depth ConversionMultiple Functions

Strategy

Consider the main formation boundaries

Depth Conversion

Early Jurassic

Triassic

Regression from Early Cretaceous to Early Jurassic

K= 1.49

Strategy


Multiple Functions


12/58

12.12

Depth Conversion

Early Jurassic

Triassic

Regression from Early Jurassic to Triassic

K= 1.2

Multiple Functions

Strategy


Depth Conversion

Early Jurassic

Triassic

Regression from Triassic

K= 0.93

Multiple Functions

Strategy



13/58

12.13

Depth Conversion

target - 5

0

500

1000

1500

2000

2500

3000

3500

4000

0 0.1 0.2 0.3 0.4 0.5

time sec

depthft

target - 2

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

0 0.2 0.4 0.6 0.8 1

time sec

depthft

Multiple Functions

target - 1

0

2000

4000

6000

8000

10000

12000

0 0.2 0.4 0.6 0.8 1 1.2

time sec

depthft

target - 4

0

500

1000

1500

2000

25003000

3500

4000

4500

0 0.1 0.2 0.3 0.4 0.5 0.6

time sec

depthft

Target

8000

8500

9000

9500

10000

10500

11000

11500

12000

0.5 0.7 0.9 1.1 1.3

time sec

depthft

target - 3

0

1000

2000

3000

4000

5000

6000

7000

0 0.2 0.4 0.6 0.8 1

time sec

depthft

Strategy

Next, plot the time-depth charts to each of the possible boundaries.

Depth Conversion

Notice how the scatter decreases as we move up through the

overburden.

Now lets look at the intervals.

When the isopach can be

predicted from the isochron

find the best function using the

RMS depth error to select the

most suitable function.

Multiple Functions

y = 3848.9x2+ 13414x + 109.85

0

1000

2000

3000

4000

5000

6000

7000

8000

0 0.1 0.2 0.3 0.4 0.5 0.6

Isochron

Isopach


14/58

12.14

Depth Conversion

When the isochron-isopach plot shows scatter try an interval

velocity-mid point time function &/or an instantaneous velocityfunction, subdivide the interval or go on to use seismic velocities.

Multiple Functions

y = 12063x + 14.855

RMS error 114 ft

0

500

1000

1500

2000

2500

3000

0 0.05 0.1 0.15 0.2 0.25

isochron sec

isopachft

y = -1842.9x + 13647

RMS error 91 ft

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

0 0.2 0.4 0.6 0.8 1

Mid Point time

IntervalVelocity

Depth Conversion

Multiple FunctionsTime

Maps

Isochrons Velocity

Functions

Isochores Depth

Maps

Average

Velocity

Maps

Layers

Depth conversion process

Multiple Functions


15/58

12.15

Depth Conversion

Time to upper surface

Multi-Layer Example

From a Sattlegger brochure

Multiple Functions

Depth Conversion

Depth to upper surface

Multi-Layer Example


Multiple Functions


16/58

12.16

Depth Conversion

Map of Vo coefficient

from Fausts equation

Vi = Voz1/n (n=3)

Multi-Layer Example


Multiple Functions

Depth Conversion

Map of Vo coefficient

after smoothing with a

16th order polynomial

Multi-Layer Example


Multiple Functions


17/58

12.17

Depth Conversion

Time to lower surface

Multi-Layer Example


Multiple Functions

Depth Conversion

Lower surface depth

converted using

Vi = Voz1/n (n=3)

Multi-Layer Example


Multiple Functions


18/58

12.18

Depth Conversion

Integration

Analytic

functions

Depth

conversion

Interval,

average,

instantaneous

Macro-velocity

modelDepth maps

Seismic

horizontimes

Velocity log

Sonic logCheckshot

or VSP

Z.O. orimage ray

modelling

Compare

Velocity

Maps

Multiple Functions

Depth Conversion

Summary - Multiple Functions

Depth conversion by multiple

functions is well suited to

areas with moderate well

control and moderate

structural complexity.

The functions will account for

vertical gradients and rapidlychanging bed thicknesses.1 km

When we have little well control then we have to make use of

seismic velocities to interpolate the well velocities.

Multiple Functions


19/58

12.19

Depth Conversion

Multi-layer Depth Conversion

5000

6000

7000

8000

9000

10000

0.4 0.5 0.6 0.7 0.8 0.9

Time (sec)

Depth(ft) Observed

Predicted -

multi-layer

Summary - Multiple FunctionsMulti-layer depth conversions essentially predict variations in the

average velocity that cannot be handled by a single function

Multiple Functions

Depth ConversionMultiple Functions

Given a moderately complex macrovelocity model, structures-in-

depth may be revealed where none exist in time


20/58

Depth Conversion

You have to recommend a well on the structure seen at about 1.7 secs., on theaccompanying seismic section. This is a wildcat area with few wells having been

drilled. Make your depth prognosis using the function VA= 5000 + 2500t where t is the

one way time in seconds and the velocity is in ft/sec.

This function comes from good scout information which you trust. Your supervisor is

not so comfortable however and wants you to give an estimate of the error in your

depth conversion.

Make an initial guess at how accurate you think your depth prognosis is.

List the potential sources of error and assign estimates to the magnitude of each.

Exercise 12.1

12.20


21/58

Depth Conversion

12.21

0

1

2

Exercise 12.1


22/58

12.22

Depth Conversion

Average Stacking Velocity

0 4 8 miles

C.I. = 100 m/s

DatacourtesyofAmoco(U.K.)Ex.Co.

Depth Conversion

of Time

Interpretations

~

Grid Models

Velocity Grids

Depth Conversion

How might we use seismically derived velocities for depth

conversion?

Velocity Grids


23/58

Depth Conversion

Now suppose that no well velocity information was available to you. The

only velocity data are stacking velocity functions every 2 km along the line

and they were derived without the benefit of DMO.

What is your depth prognosis now given the two nearest stacking velocityfunctions?

Time

msec

0

152

384

601

859

1401

1756

2151

2621

VS

m/s

1472

1472

1717

1865

2070

2317

2441

2616

3390

VIS

m/s

1472

1861

2102

2483

2662

2879

3283

5725

SP 253

Time

msec

0

165

439

744

968

1438

1713

2045

2572

VS

m/s

1478

1478

1747

1891

2011

2192

2441

2677

3511

VIS

m/s

1478

1891

2081

2367

2525

3463

3661

5688

SP 155

How accurate do you suppose this depth conversion is?

Exercise 12.2

Note:

Dips are relatively gentle so any dip correction will probably do more harm thangood.

The data are relatively old and were probably acquired with a cable short enough

that the bias correction would make no appreciable difference to the results.

12.23


24/58

12.24

Depth Conversion

Sparse Well ControlWhen there is only sparse

well control we usually

generate grid velocity

models from the seismic

data. By calibrating the

grids to the well velocities

we are making use of the

grids to interpolate the well

velocities.

In unexplored basins we

dont always have any wells

to interpolate or extrapolate

from.

Velocity Grids

Depth Conversion

Substitutes

5000 10,0000

2

4

6

8

10

12

14

16 Average

Velocity

RMS

Velocity

Velocity - ft/sec

Depth-x1000feet

Stacking

Velocity

Bias Corrected Models

0

1000

2000

3000

4000

5000

6000

1000 2000 3000 4000 5000 6000

Interval Velocity m/s

Depthm

Original Model

Ray Trace + Semblance AnalysisBias Corrected

Velocity Grids


25/58

12.25

Depth Conversion

Ranked approaches to depth conversion with seismicvelocities.

1. Kriging with seismic velocities and well velocities

* these approaches have constraints

2. Estimate average velocity from interval RMS velocities

* can be done without well control

3. Use seismic velocities to augment well data in deriving

functions

Velocity Grids

Depth Conversion

For Kriging:

From a GX Technology brochure

Cokriging, kriging

with external drift

etc., require a good

linear correlation

between the different

parameters.

Enough data points

are needed to

produce a

reasonable

variogram (a

minimum of 8 or 10).

Histogram of

velocities to be

kriged should show

a normal

distribution.

Velocity Grids


26/58

12.26

Depth Conversion

For Kriging

Stacking,

RMS or

Average

Velocity

Simple or

Common

Kriging

Smoothed

Velocity

Kriging

with

External Drift

Cross Plot

with Well

Velocities

Final

Velocity

Velocity Grids

Depth Conversion

Regional/Residual Calibration

A conventional

horizon oriented

stacking velocity

map. This map

can be smoothed

first by Kriging.

From Francis, Geostatistical Applications in Asset Valuation Uncertainty, PETEX 94.

Velocity Grids


27/58

12.27

Depth Conversion



The variogram from the stacking velocities. The noise

seen in the map produces the large nugget.

RangeSill

Nugget

0 5000 10000 15000 20000 25000

0

250

500

750

1000

Sample Separation (m)

Variance(m2)

Velocity Grids

Depth Conversion



Well velocities co-

kriged with the drift

supplied by the

seismic velocities.

This is an average

velocity map to the

horizon of interest

that ties the wellcontrol and

honours the trends

in the seismic

velocities.

Velocity Grids


28/58

12.28

Depth Conversion

Case History / Example

GOM: Mississippi Canyon

Calibrate Stacking Velocities with VSP Data

Create Depth Map for the 10-5 SequenceTime Horizon

QuantitativeGeosciences, LLP

Depth Conversion

Data:

77,000 seismic stacking velocities

X = Y = 2000 ft CDP spacing

Z (time in ms) = variable (5 15 picks)

2 wells with VSP time-velocity-depths

10-5 Sequence travel times 23,837 travel time values

Grid mesh: 1000 x 1000 ft



29/58

12.29

Depth Conversion

Stacking Velocity and VSP Locations


Depth Conversion

10-5 Sequence Time Structure



30/58

12.30

Depth Conversion

VSP Average Velocity Stacking Velocity

VSPTwo-WayTime

VSPTwo-WayTime

Calibration

VSP Average velocities and Stacking velocity functions at

the well locations.


Depth Conversion

Calibration

VSP Velocity VSP Velocity

Calib

StackingVelocity

UncalibStackingVelocity

Calibrated and uncalibrated stacking velocity functions

Note the linear relationship between the uncalibrated velocities.



31/58

12.31

Depth Conversion

Variograms in three directions


Depth Conversion

Deterministic Velocity Cube from Kriging



32/58

12.32

Depth Conversion

10-5 Sequence Average Velocity


Depth Conversion

10-5 Time Horizon

Calibrated Velocity Cube with Time Horizon



33/58

12.33

Depth Conversion

10-5 Sequence Depth Map


Depth Conversion

Work Flow



34/58

12.34

Depth Conversion

Kriging 1 many wells

Stacking,

RMS or

Average

Velocity

Simple

Kriging

Smoothed

Seismic

Velocity

Cokriging

Cross Plot

Final

Velocity

Well

Average

Velocity

Variogram

Variogram

Time

Map

Deterministic

Depth

Map

This approach is best if the seismic velocities are noisy.

Velocity Grids

Depth Conversion

Kriging 1 few wells

Stacking,

RMS or

Average

Velocity

Simple

Kriging

Smoothed

Seismic

Velocity

Kriging

with

External Drift

Cross Plot

Final

Velocity

Well

Average

Velocity

Variogram

Time

Map

Deterministic

Depth

Map

This approach is best if the seismic velocities are noisy.

Velocity Grids


35/58

12.35

Depth Conversion

Kriging 2 many wells

Stacking,

RMS or

Average

Velocity

Cokriging

Cross Plot

Final

Velocity

Well

Average

Velocity

Variogram

Variogram

Time

Map

Deterministic

Depth

Map

Will produce unreliable results with noisy seismic velocities.

Velocity Grids

Depth Conversion

Kriging 2 few wells

Stacking,

RMS or

Average

Velocity

Kriging

with

External Drift

Cross Plot

Final

Velocity

Well

Average

Velocity

Variogram

Time

Map

Deterministic

Depth

Map

Will produce unreliable results with noisy seismic velocities.

Velocity Grids


36/58

12.36

Depth Conversion

Ranked approaches to depth conversion with seismicvelocities.





3. Use seismic velocities to augment well data in deriving

functions

Velocity Grids

Depth Conversion

For Average Velocity

Stacking,

RMS

Velocity

Robust Filter,

Smooth

Interval RMS

Velocity

Calibrate to

Well Interval

Velocities

Final

Average

Velocity

Robust Filter,

Smooth

Robust Filter,

Smooth

Calibrate to

Average

Velocity

Calibrate to

Well Interval

Velocities

Robust Filter,

Smooth

Interval RMS

Velocity

Calibrate to

Well Interval

Velocities

Velocity Grids


37/58

12.37

Depth Conversion

CalibrationBefore depth conversion it is necessary to calibrate the

seismically derived velocities to the velocities measured in

the wells.

Calibration is the process of using the abundant seismic

estimates, which probably reflect regional geological

variations, to interpolate and extrapolate the sparse well

control which aliases the geological variations.

The result of calibration is that we have velocities in our

model which honour the well measurements and display thespatial sampling of the seismic data.

Velocity Grids

Depth Conversion

Calibration

The calibration is frequently performed in two steps.

The first is a regional calibration which takes care of any shift

between the trends of the two data sets.

The second is a residual calibration which accounts for the

local variations, the residuals, after the first calibration, and

ensures the wells are tied exactly.

Velocity Grids


38/58

12.38

Depth Conversion

Regional CalibrationWe can correlate the VSP

or checkshot data to

stacking velocity (or VRMSor VAS) functions. Linearity

is not required. Correlated

data points must relate to

the same points in the

subsurface, i.e. we need

the VRMS value at the same

travel time as the observedVA.

This approach correlates

the whole velocity volume.

Velocity Grids

Well v. Seismic Average Velocity

y = 3.7050934E-07x3- 6.7773959E-03x2+ 4.1711981E+01x -

8.0315444E+04

4500

5000

5500

6000

6500

7000

4500 5000 5500 6000 6500 7000 7500

seismic

wells

Depth Conversion

Regional Calibration

To calibrate the stacking

velocities (or VRMS or VAS) to

a particular horizon a

percentage calibration

factor is required or used

(93.35% in the example).

A percentage calibrationfactor is equivalent to a

linear trendline being fitted

to the data, which goes

through the origin.

Velocity Grids

Level 8 Interval Velocities

IntVel = 0.9335Vdix

0

1000

2000

3000

4000

5000

6000

7000

8000

0 2000 4000 6000 8000Seismic

Well


39/58

12.39

Depth Conversion

Regional CalibrationFor interval velocity the

interval stacking (or RMS)

velocities are cross plotted

against the corresponding

well velocities.

A good correlation is

usually observed but the

trend does not always go

through the origin.

Velocity Grids

Level 9 Interval Velocities

IntVel = 0.9662Vdix - 329.57

6800

7000

7200

7400

7600

7800

8000

7400 7600 7800 8000 8200 8400 8600Seismic

Well

Depth Conversion

Regional Calibration

After calibration the trend

does go through the origin.

The remaining scatter in

the data means that none

of the wells will be tied

exactly.

As with checkshot functionmisties these misties are a

measure of the overall

accuracy of the method.

Velocity Grids

Calibrated Average Velocities

4500

5000

5500

6000

6500

7000

4500 5000 5500 6000 6500 7000

Well

Seismic


40/58

12.40

Depth Conversion

Misties

Data from a Paradigm Geophysical brochure

After regional calibration the misties at the wells are greatly reduced.

Velocity Grids

Depth Conversion

Ranked approaches to depth conversion with seismic

velocities.





3. Use seismic velocities to augment well data in derivingfunctions a hybrid approach

Velocity Grids


41/58

12.41

Depth Conversion

We now have either a calibrated volume of seismically

derived velocities or a number of calibrated interval velocity

grids associated with different horizons which are used to

derive an average velocity to the horizon of interest.

Velocity functions from the calibrated volume may be treated

as additional checkshot values and used to augment sparse

checkshot data to derive analytical functions.

Velocity Grids

Depth Conversion

Determining K and V0 From SeismicGiven an estimate of the VRMS curve, obtained by the

correction of VS, estimates of analytical function parameters

can be obtained directly from the seismic data and mapped.

From Arnaud et al, K coefficient

determination of an interval velocity

law Vo + Kz from stacking velocityanalyses, EAEG-95 Workshop

Depth Conversion

K

V0

Velocity Grids


42/58

12.42

Depth ConversionVelocity Grids

Determining K and V0 From Seismic

Vrms2 = [VI

2.t] / [t] from our definitions

Vrms2 = [Vi2.dt] / [dt] and Vi = dz / dt

Vrms2 = [(dz / dt)2.dt] / [dt]

Vrms2

= [(dz / dt).dz] / [dt]Substitute any expression for dz/dt and integrate.

Depth Conversion

Determining K and V0 From Seismic

For a single layer model:

For Vi = V0 + Kz, VRMS2 = V0

2(e2Kt - 1)/2Kt

For Faust VRMS2 ={ nK/(n + 1)t}{(n - 1)Kt/n}[(n + 1)/(n - 1)]

ForEvjen VRMS

2 ={ V0

K/(1 + n)t}{[1 + V0

(1 - n)Kt] [(1 + n)/(1 - n)] - 1}

It is therefore possible to use the corrected VRMS data to map

directly the parameters of standard analytic functions.

Velocity Grids


43/58

12.43

Depth Conversion

Pseudo CheckshotsIt is also possible to use the

calibrated interval and

average velocity values as

checkshots thus permitting a

wider range of values to be

used in determining the

analytical function

parameters.

VELOCITY

D

EPTH

After Marsden et al, Leading Edge, 1995

Velocity Grids

Depth Conversion

Summary - Grid Models

Grids of seismically derived RMS velocities can be used when

we have no well control or sparse well control.

We can use kriging to smooth the generally noisy grids and tie

them to the well control. This approach usually yields better

results than the more traditional ways of smoothing the noisy

grids.

The velocities have to be calibrated in some way to well

velocities.

The velocities may also be used to augment well checkshot

data.

Velocity Grids


44/58

12.44

Depth Conversion

Tying

the Well

Control

PGS Reservoir (U.S.) Inc. Doe Contract #DE-AC-22-94-PC 91008

Depth Conversion

Residual Calibration - Tying Well Control

We have our preliminary depth map that does not tie the

well control exactly. We have analysed our misties and

quantified the accuracy of our depth conversion.

How might we make the map tie the well control?

What are the disadvantages of the different methods?

Residual Calibration


45/58

12.45

Depth Conversion

Tying Well ControlHow might we make the map tie the well control? What are the

disadvantages of the method?

For multi-layer depth conversion only tie the target horizons.

Intermediate errors tend to cancel out.

If the errors are random, distribute over an area whose radius

is half the average well spacing. Can produce bulls-eyes at the

wells.

Autocontour the errors. Produces unreasonable gradients and

error values outside the limits of well control.

Kriging. Will separate trend and random components of the

errors.


Depth Conversion

One-Step Calibration - Wells


A popular approach when using checkshot data from

multiple wells:

Fit a simple (linear?) function

Fix all but one of the parameters

Vary the one parameter to effect a tie to each data point

Map the variation of the parameter

Use the parameter grid in depth conversion


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12.46

Depth Conversion



Keep the slope K constant and derive a Vo for each data

point..

0 100 200 300 400 500

One Way Time (msec)

1600

1700

1800

1900

2000

Fit used

Slope (K) = 0.73

IntervalVelocity(m/sec)

Data courtesy of Amoco

Depth Conversion



Map of Vo from previous

plot. The greatest

danger in this approach

to depth conversion is

that this map is

meaningless. The map

should reflect the

geology, variations in V0should reflect thetectonic history.

What are the advantages and disadvantages of this

approach to macrovelocity model building?

10 Miles

1600

1700

1800

1900

CI = 50 m/sec

Data courtesy of Amoco


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12.47

Depth Conversion

One-Step Calibration - Seismic

Average Stacking Velocity

The regionally

calibrated seismic

velocities display

variations of geological

significance even

though they do not tie

points of well control

with the desired

accuracy.

0 4 8 miles

C.I. = 100 m/s



Depth Conversion

0 4 8 miles

C.I. = 100 m/s

Average Velocity from Wells

Velocity maps based

on well control will tie

the wells, more or less

exactly depending on

the contouring

algorithm, but alias the

geological trends.

Datacourtesyof

Amoco(U.K.)Ex.Co.




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12.48

Depth Conversion

0 4 8 miles

C.I. = 2 %

Calibration Factor

The calibration factor or

residual is determined at

each well control point.

These values are then

gridded to determine the

values to be applied to the

seismic grid.

Note that steep gradients

can be introduced whichmay not be geologically

reasonable.

DatacourtesyofAmoco

(U.K.)Ex.Co.



Depth Conversion

0 4 8 miles

C.I. = 100 m/s

Calibrated Average Velocity

The calibrated interval

velocity map ready for

use in depth conversion.

This map ties the well

control and honours the

trends seen in the

seismic data.

Kriging can be used

instead of this traditional

approach.





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12.49

Depth Conversion

Random Errors

When the residuals are small and

random then the errors are

dispersed over an area with a

radius of up to one half the

average inter-well spacing. This

approach is only acceptable when

there is no spatial correlation

between the residuals.


Depth Conversion

Random Errors


Mistie grid.

Mistie values

when flexing

surface over too

small a radius

around wells.


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12.50

Depth Conversion

Random Errors


Tied map.

When the radius

of flexing is too

small then the

circular nature of

the flexing will

show in the final

map.

Depth Conversion

Random Errors


Mistie grid.

Mistie values

when flexing

surface over a

distance of about

half the average

well spacing.


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12.51

Depth Conversion

Random Errors


Tied map.

The circular

nature of the

mistie contour

values does not

show up.

Depth Conversion

Gridding the calibration

factor or residual from

each well control point can

produce undesirable

trends and steep gradients

when dissimilar valuesoccur in closely spaced

wells.

Data from a Paradigm Geophysical brochure


One-Step Calibration


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12.52

Depth Conversion

Random Errors


Mistie grid.

Minimum

curvature gridding

with bicubic

interpolation

of mistie values.

The extrapolation

is geologicallyunreasonable.

Depth Conversion

Random Errors


Mistie grid.

Inverse distance

weighted gridding

with bicubic

interpolation

of mistie values.

Produces almostexactly the same

correction grid as

the previous

example.


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12.53

Depth Conversion

KrigingA semivariogram of the residuals

is a powerful tool that will find

any spatial correlation.

Kriging residuals results in a

calibration grid or error grid that

shows both any remaining -

possibly undetected - trend and

the true random residual error.

The effect is a series of bulls-

eyes in a regional smooth trend.


Depth Conversion

A semivariogram of the residuals

is a powerful tool that will find

any spatial correlation.

Kriging residuals results in a

calibration grid or error grid that

shows both any remaining -

possibly undetected - trend andthe true random residual error.

The effect is a series of bulls-

eyes in a regional smooth trend.


Kriging


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12.54

Depth Conversion

Structure-in-time Map


Examples

Depth Conversion


Depth conversion using five layers and seismic interval

velocities, the one step calibration method was used.

Examples


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12.55

Depth Conversion


Depth conversion by average velocity.

Examples

Depth Conversion


Depth conversion using six analytic functions based on wells.

Examples


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12.56

Depth Conversion

CalibrateAnalytic

functions

Depth

conversion

Interval,Average,

velocity

Macro-

velocity

modelDepth maps

Seismic

horizon

times

Dip correct,Interpolate

WellVelocity

SeismicVelocities

Z.O. orimage ray

modelling

Compare

Velocity

Maps

Invert,

(Dix/Bias)

Edit,

Smooth

Velocity Grids

Depth Conversion

Quality Control

Depth converting the same structure-in-time map by

different methods can result in different depth maps even

though all of the well control is honoured.

So how do we know which depth conversion is the most

accurate?

A final quality control step on our depth conversion, one

that is rarely applied, should be to model our seismic data

by ray tracing through our macrovelocity model.


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12.57

Depth Conversion

Forward Modelling

Data courtesy of Paradigm Geophysical (UK) Ltd.

Normal incidence ray trace

modelling on the velocity /

depth section generates

synthetic event with diffractions

to overlay on the stack section.

Depth Conversion

Summary

When well control is adequate to define the velocity

distribution in the macrovelocity model analytical functions

are used.

When well control is inadequate then seismic velocities may

be used. The seismic velocities have to be calibrated to well

velocities.

The residual misties at the well locations are used to quantifythe accuracy of the depth conversion.

The residual error adjustment of the depth maps is made

when depth maps are required that tie the well control

exactly.


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Depth Conversion

SummaryAccuracy of depth conversion: -

Rank Wildcat (50 km to well control) ~5%

Exploration well (10km to well control) ~2.5%

Appraisal well (2 or 3km to well control) ~1%

Development wells

depth conversion of time interpretations

Documents