Seismic Inversion

Seismic Inversion for

Reservoir Characterization

1. Definition

Up to now, there is no standard definition about Seismic Inversion. The author defines the seismic inversion as :

“Seismic inversion is the technique for creating sub-surface geological model using the seismic data as input and well data as controls”

Figure 1-3 show simple illustration on inversion method compared to the conventional seismic records

Basically, the recovering of seismic record is a forward modeling. In this subject the data input is the AI or reflection coefficient (RC) series of the earth layer itself which then forward modeled into the seismic records. The forward modeling algorithm, basically, is a convolution process between seismic wavelet passing thru the RC series of the earth.

On the other hand, the seismic inversion is basically an inverse modeling, where the input is the seismic record that inverse modeled into the AI section.

This inverse modeling algorithm, basically, is a deconvolution between the seismic records and seismic wave which then produce the AI section.

Figure 4 show various inversion methods. At this moment, the popular issues in reservoir characterization are the post-stack amplitude inversion seismic and pre-stack AVO.

Figure 1. Diagram of forward and inverse modeling. Input Process Output EARTH MODEL MODELING ALGORITHM SEISMIC

RESPONSE EARTH MODEL

MODELING ALGORITHM SEISMIC RESPONSE Model control FORWARD MODELLING INVERSE MODELLING (INVERSION)

BUM

EARTH AI

Seismic Section/ Wavelet = AI

Earth * Wavelet = Seismic Section The Making of Seismic Section Seismic Inversion Process Seismic Inversion For Reservoir Characterization

Figure 3. Types of inversion techniques (Russel, 1988) PRE-STACK INVERSION POST-STACK INVERSION TOMOGRAPHY TIME INVERSION INVERSION AMPLITUDE (AVO) AMPLITUDE INVERSION WAVEFIELD INVERSION BAND-LIMITED SPARSE SPIKE MODEL-BASED SEISMIC INVERSION METHOD

2. AI, RC & Reservoir Characterization

Empirically, the value of seismic amplitude is equal to the reflected energy recorded by the receiver (geophone, hydrophone, etc.). The reflection of seismic wave is caused by the AI change. The ratio between reflected energy and the incidence energy on normal angle is :

E (reflected) / E (incidence) = RC x RC (1)

RC = (AI2-AI1) / (AI1 + AI2) (2)

where E = Energy

RC = reflection coefficient

AI1 = upper layer acoustic impedance AI2 = lower layer acoustic impedance

A RC series is often called as reflectivity series R(t) or just reflectivity.

AI contras can be estimated qualitatively from the amplitude reflection. Larger amplitude associates with stronger reflection and higher AI contras.

AI is rock parameter affected by the type of lithology, porosity, fluids contents, depth, pressure and temperature. Therefore, AI can be used as an indicator of lithology, porosity, hydrocarbon, lithology mapping, flow unit mapping, and reservoir character quantification.

Naturally, the AI section will give sub-surface geology image more detail than the conventional seismic section, because the RC on the conventional seismic section will image the layer boundary while the AI will image the layer itself.

The AI will be controlled mostly by the wave velocity. Figure 5 shows the effect of many factors in velocity. The porosity and gas content effects are the most effecting factors on P-wave velocity value. On clastics rock, the porosity depends mostly to differential pressure which is the difference between overburden and interstitial pressures. The porosity decreases when the differential pressure increases in irreversible process. Therefore, the clastic rock porosity usually depends to the maximum differential pressure occurs.

When the velocity spectrum is plotted for a different type of rocks, overlapping occurs. Therefore, except only for general cases such as associating the low velocity with clastic rocks and high velocity with carbonate or evaporate, the velocity data itself cannot be used to conclude the type of rocks. The high porosity usually related to low velocity and vice versa. The clastic rocks porosity usually decrease to the burial depth due to compaction and cementation (Fig.7).

The seismic inversion technique has been known by the oil-gas industry since 1980’s. But, could not gain popularity well because it was considered to be very complicate and difficult to applied.

In 1990’s, the fast development of computer technology makes the inversion technique become a practical methodology. Currently, it’s not considered as a special method anymore.

Exercise 1. Example of exploration field

Figure 8 shows typical relationship between the AI and porosity values.

Figure 9 and 10 show the conventional seismic section and AI on a same area. Based on the well data, it’s known that the main reservoir position is as shown by the black boxes in these figures. Comparing these two sections, which one is better for delineating reservoir layers and why ?

In Figure 11, for Fm. Bekasap case, which layer is the most porous ? Delineates it’s distribution ?

Figure 12 shows another example of seismic section on exploration field. Give a comment about the exploration well position. What type of trap developed here ?

On each section, show the porous and non porous layer. On each porous layer, analyze further the internal heterogeneity aspect. Discuss the differences between the AI and conventional sections capability for analyzing internal heterogeneity aspect.

Figure 9. The reflectivity section of Line A. The main source-rock interval is shown as box in the well. 2500 2600 2700 2800 2400 2300

sb-x mfs sb-y

sb-x mfs sb-y

13 18

Top Boundary

field to be developed EOR field candidate

Figure 14. The AI section of Figure 15. The bright color shows lower AI value Bottom

13 18

Exercise 2. Development and EOR field examples

Figure 13 shows example of a reservoir layer image on reflectivity and AI sections. Which part of the layer that worth to be developed ? Figure 14 and 15 show a seismic section on the development field (left) and EOR candidate field (right). Give a comment about the layer that worth to be develop in the development filed and also the injection well location for EOR field. Compare the role of AI and conventional sections for the analysis.

Seismic inversion is a technique to get the quantitative AI value from reflectivity.

Conventional seismic data (reflectivity, often called as the “amplitude cube”) “sees” the sub-surface object in the form of boundary plane between the rock layers.

AI ‘sees’ the sub surface object as the layer itself.

Therefore the AI appearance is closer to the reality and more comprehensible.

The conversion from seismic wiggle into AI : a more comprehensive display (specially by the manager !!!). Because the AI section can be converted into reservoir properties section, then seismic inversion can also be used as basis for other reservoir management techniques.

The executives getting more understand the important effectivity of this method for better planning of new well location without significant extra cost and time. The popularity of seismic inversion increased rapidly since the1990’s and now it’s considered as the standard method on reservoir management.

2. Convolutional Seismic Trace Model

Seismic trace is the convolution of earth’s reflectivity with a seismic wavelet with addition of noise component.

S_t = W_t * RC_t + n_t (4)

where S_t = the seismic trace W_t = a seismic wavelet RC _t = earth reflectivity

n_t = additive noise

When the noise component = zero, it can be simplified into :

Seismic data : digital data where the data sampled at a constant interval.

If we consider that the reflectivity consist of a RC at each time sample and the wavelet to be a “smooth” function in time, convolution can be thought of as ‘replacing’ each reflection coefficient with a scaled wavelet and summing the result (Figure 16).

Notice that the convolution with the wavelet tends to ‘smear’ the reflection coefficient. That is there is a total loss of resolution, which is the ability to resolve closely spaced reflector.

An alternative way of looking at the seismic trace is in the frequency domain :

S(f) = W(f) x R(f) (6)

Where S(f) = Fourier transformation of s_t

W(f) = Fourier transformation ofw_t R(f) = Fourier transformation of r_t

It is common to observe the amplitude and phase spectrums from the individual component.

Figure 17 shows the convolutional model in frequency domain. Notice that the time domain problem of resolution loss becomes one of frequency content in the frequency domain. Both the high and low frequencies of the reflectivity have been severely reduced by the effect of the seismic wavelet.

The making of synthetic seismogram, basically, is the convolution process between the RC and wavelet data. Matrix operation is often used to do this convolution process. In physical definition, the convolution describes behavior of how two energy wavelets combined. For example if there are two vectors [A] = [a₀ a₁ a₂ …] and [B] = ]b₀ b₁ b₂…].

Their convolution are indicated by operator *, for example [C] = [A] *[B] which will produce the vector [C] = [c₀ c₁ c₂…]. The [C] element is given by :

∑

=

a

b

c

Synthetic

Figure 16. The convolution model by using closely spaced reflectivity from the well (center). The wavelet is shown

Figure 17. The convolutional model in frequency domain by using three components as on the Figure 16 1.00 0.75 0.50 0.25 0 0 50 100 150 200 250 Hz

(a) Wavelet Spectrum

(c) Trace Seismic Spectrum (b) Reflectivity Spectrum 1.00 0.75 0.50 0.25 0 0 50 100 150 200 250 Hz 1.00 0.75 0.50 0.25 0 0 50 100 150 200 250 Hz

Figure 18. The convolution process in time and frequency domains. Notice how the low frequency component start to be effected by the sampling effect of RC and convolution of wavelet and RC (Jason Geosystem, 1999)

Figure 19. Illustration showing the effect of low and high frequency component losses in inversion ( Latimer, 2000)

For example, if we want to convolute two vectors [A] and [B]. If the [A] = [a₀ a₁] and [B] = [b₀ b₁], so the first, second and third elements of the convolution result are :

c₀ = a₀b₀ , c₁ = a₀b₁ +a₁b₀ , c₂ = a₁b₁ or [A] *[B] = [C] = [a₀b₀ a₀b₁ +a₁b₀ a₁b₁]

Notice that although [A] and [B] each only have two elements, but [C] has three elements. Generally, if the first vector has n element, the second vector m element, then the convolution result vector has n+m-1 element.

Robinson and Treitel (1980) introduced a simple graphic method to do the two vectors convolution. For example if two vectors, each with three elements, are convoluted, both are written in to a row-column product :

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The convolution product is graphically determined as the summing of diagonal elements

and the resulting vector [C] has elements :

[a₀b₀ a₁b₀ + a₀b₁ a₂b₀ + a₁b₁ + a₀b₂ a₂b₁ + a₁b₂ a₂b₂ ]



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For example the vector [A] = [1 2 3 5 7 2], while the vector [B] = [6 2 4], with the graphic way it can be written as :

Thus, [A]*[B] = [C] = [6 20 40 64 46 32 8]                 8 4 12 28 14 42 20 10 30 12 6 18 4 2 6 2 7 5 3 1 4 2 6

Exercise 3. Synthetic seismogram construction

1. The next page shows the log V_p, log ρ, log AI and wavelet

data. The wavelet can be written as the matrix : [W] = [-20 70 -20]

2. By using the Robinson and Treitel (1980) method, construct

the synthetic seismogram (S_t) on the given zone in figure, where S_t = RC_t*W_t

3. Compare your synthetic seismogram with the computer

The Role of Well Control and Seismic Stratigraphy

Figure 1 shows that inversion requires well data control. The required well data are AI and stratigraphy sequence data. The well’s AI value is computed by multiplying the log density and log velocity.

The well’s AI has a quite good vertical resolution (up to 0. 15 m) but a bad lateral resolution. The seismic AI has good lateral resolution and coverage (5-10 m). Integrating both will produce an effective and efficient tools for reservoir characterization.

The AI and stratigraphy sequence data are required to control the low and high frequency that lost when reflectivity is convolved with the wavelet.

Seismic stratigraphy interpretation is required to control the initial model and trap characterization. It is absolutely required since seismic reflector is chronostratigraphy surface not lithostratigraphy

Figure 22. The wavelet used, simplified into a matrix form [W_t] = [-20 70 -20] -40000000 -20000000 0 20000000 40000000 60000000 80000000 0 20 40 60 80 100 ms amplitude

Seismic Synthetic _{Figure 24. The synthetic seismogram created by computer}

Compute RC & AI

4. Type of Inversion Method & The Characteristics

There are three types of the main method of seismic inversion : 1) Recursive inversion, 2)model based inversion, 3) Sparse-spike inversion.

4.1. Recursive Inversion

It is the simplest inversion method. The basic equation :

AI_i+1 = AI_i (1+RC_i) / (1-RC_i) (9)

)

8

(

AI

AI

AI

AI

V

V

V

V

RC

+

−

=

+

−

=

ρ

ρ

ρ

ρ

The seismic data is assumed to be equal to the model on the left of equation (8), and inversed by using the inverse relation on equation (9). For the n-layer case :

Exercise

If we know that the AI₁ = 1, RC₁ = 2/4, RC₂ =1/7, and RC₃ = -3/5. Compute AI₄ using equation 10.

) 10 ( 1 1 1 1 1       − + =

∏

Figure 25 shows the flowchart of this technique. This technique is also known as ‘bandlimited’ inversion because it invert the seismic trace itself, so the AI trace result has the same frequency range as the seismic trace.

The main weakness of this technique is that it doesn’t accommodate the geology control and, therefore, it almost identical to the forward modeling. The correct wavelet is assumed as zero phase wavelet, so it also will effect the resulted geology model.

Low and high frequency components from earth reflectivity which lost when the reflectivity is convoluted with wavelet,

also difficult to be recovered with this technique, so the ability of this technique to laterally predict the AI is not good.

This technique also ignores the seismic wavelet effect and treats the seismic trace as a RC series which filtered by zero phase wavelet. The recursive inversion equation also assumes that the absolute scaling of RC value is correct. Because the equation is applied recursively from top to bottom, the error effect will be accumulated. The noise on seismic trace will be interpreted as a reflection and involved in the inversion.

Figure 25. The recursive inversion technique

SEISMIC SECTION

SCALED TO REFLECTIVITY ENTER LOW FREQ COMPONENT

INVERT TO PSEUDO - IA CONVERT TO PSEUDO - VELOCITY CONVERT TO DEPTH DISPLAY

Exercise 4. Matrix Operation for Recursive Inversion

Robinson and Treitel (1990) give example on how to do the recursive inversion using a simple matrix operation.

If the wavelet and seismic trace data are known, theoretically by using the matrix operation we can compute the RC and AI values.

For example, in Figures 26-27, it is known that [W_t] = [-2 7 -2] and [S_t] = [17 6 3]. the equation W_t* RC_t = S_t can be written in matrix as :

If the number of variable that we want to solve is only a few (for example 3), the equation can be solved using common substitution. However, if the variables is quite many, we need special technique, such as Gauss-Jordan’s elimination method.

Following is the discussion on the application of this Gauss-Jordan’s elimination. For example, the following equation needs to be solved :

In Gauss-Jordan’s elimination technique, the equation can be written as :

2x₁ - 7x₂ + 4x₃ = 9 x₁ + 9x₂ – 6x₃ = 1 -3x₁ + 8x₂ + 5x₃ = 6

The first row is normalized by divide it using pivot element 2; and other elements in the first column is reduced into zero by subtracting the new first row from the old second row, and also by subtracting –3 times the new first row from the old third row. The result is :           − − − 1 0 0 6 5 8 3 0 1 0 1 6 9 1 0 0 1 9 4 7 2

Next, normalized the second row by divide it with pivot element 25/2; then reduce other elements in second column into zero by subtracts -(7/2) times new second row from first row, and –(5/2) times new second row from third row. Notice that the reduction process now involves the sub diagonal and super diagonal elements. The result is :

          − − 1 0 3/2 39/2 11 5/2 -0 0 1 1/2 -7/2 -8 25/2 0 0 0 1/2 9/2 2 7/2 1

Finally, normalize the third row by divide it with pivot element 47/5; then, reduce the rest element in third column into zero by subtract –(6/25) and-(16/25) times the new third row from first and second rows. The resulted matrix is [I] x [B-1_{], where x is}

the solution vector and B-1 _{is the inverse of original matrix}

coefficient :           − 1 1/5 7/5 94/5 47/5 0 0 0 2/25 1/25 -7/25 -25 / 16 1 0 0 7/25 9/25 88/25 6/25 -0 1

Thus, we recover the x₁ = 4, x₂ = 1, x₃ = 2.

Exercise

By using this Gauss-Jordan’s elimination technique, compute

the RC₁, RC₂ and RC₃ , and if known that the AI₀ = 6875,

compute the AI₁, AI₂, and AI₃. Compare your result with the log data.           5/47 1/47 7/47 2 1 0 0 16/235 22/235 13/235 1 0 1 0 6/235 67/235 93/235 4 0 0 1

Figure 26. The wavelet used, simplified into matrix [W_t]= [-2 7 –2] -40000000 -20000000 0 20000000 40000000 60000000 80000000 0 20 40 60 80 100 ms amplitude

Seismic Synthetic

4.2. Model-Based Inversion

On recursive method, the inversion result is affected by noise, bad amplitude recovery, and band limited seismic data. It means, all problems in the data itself will be involved in final inversion result. To solve this problem, model-based inversion technique is developed with task-flow as follows (figure 28): a. Make the initial model and its blocky version by averaging

2. Convert the AI into reflectivity and convolute with the estimated wavelet to recover the synthetic model trace.

3. Subtract the seismic synthetic trace from real seismic trace to get the trace ‘error’.

4. Update the AI model and its thickness iteratively by using the GLI (Generalized Linear Inversion) inversion method, so the error decreases.

In this technique, a direct inversion of seismic data itself is avoided.

To implement the approach in figure 28, we need to answer two main questions :

1. How is the mathematical relation between model data and seismic data ?

Figure 28. The model based inversion technique flow-chart.

SEISMIC

TRACE EXTRACTWAVELET

MODEL

TRACE IMPEDANCEESTIMATE

REVISE IMPEDANCE COMPUTE ERROR ERROR OK? No Yes SOLUTION = ESTIMATE DISPLAY

The application of this technique starts by creating an initial geology model which then updated in several stages.

The geological model is developed into three stages:

1. Add the velocity control (and also density, if necessary) on the inverted seismic line. This velocity control can be added from well data or T-V_RMS. If one control point is added, the velocity is extrapolated on two ways. If more than one control points are added, the velocity is interpolated arround it.

2. Stretch and squeeze the log data in the control points to tie to the seismic data by using reflectivity convoluted with wavelet from seismic data (Figure 29-31).

3. Add the lateral control of main seismic reflector by picking and develop the interpolation of well log in such away, so it match to the reflector. This stage is also known as the initial model development stage (Figure 32).

Seismic stratigraphy concept is accommodated in lateral control development of this initial model.

Figure 33 shows a good well-seismic tie, but a simple extrapolation on lateral directions will produce ‘box’ model.

Figure 34 shows a good initial model after accommodating seismic stratigraphy model in initial model construction.

The discussion above suggests how important is the role of control point and horizon.

For control horizon, the best way is utilizing sharp reflector which related to a certain sequence stratigraphy event as it represents a certain time line (for example sequence boundaries, MCS, etc.).

On the 3D data, one important step to recover a good model control is by gridding and contouring the available points.

(b) Wavelet fasa konstan dengan spektrum amplitudo dari seismik & sumur

Figure 19. Effect of stretch & squeeze to the wavelet : frequency content between synthetic and seismic is to be equalized (Russel, 1997)

Zero-phase wavelet from seismic

Zero-phase wavelet from seismic & well data

After the initial model developed, it can be used for many purposes, depending on the inversion method used. The bandlimited inversion only use the low frequency component model, while on model-based method, the procedure can be summarized as follows :

1. Make the blocky version from the model by averaging the AI along the layer. The layer could be as small as 1 sample (a case where the blocking doesn’t happen), but normally on the range of 3-5 samples.

2. Change the AI into reflectivity and convolute with seismic wavelet to produce synthetic trace.

3. Subtracts the synthetic trace from real trace to produce trace error.

4. Modify the AI and thickness of each layer so the error decrease.

5. Iterate until a satisfying solution obtained.

The mathematical function is applied by minimizing the objective function :

where : T = seismic trace W= wavelet

RC= Final Reflection Coefficient M= Initial AI model estimation

H= integration operator which convolute with the final reflection coefficient to get the final AI

Weight₁ and weight₂ determine how both part is balanced. In

stochastic inversion, the objective function used is exactly as in the equation. But other model-based inversions use only the second weight, or the stochastic input value changed into zero, so the seismic trace role dominate the equation.

If these values is one, the initial model role would be dominated. The total of first and second weight must equal to one. It is called as soft-constraint because the final model can change into any value compared to the initial model.

On the hard-constraint inversion, the algorithm is limited to keep the final AI value on given boundary by the AI maximum change.

Practically, the inversion with constraint usually more preferable than the stochastic inversion because the change of

maximum impedance parameter is more important than the change of constraint model parameter on stochastic method.

The block size affects the final inversion result. Initial estimated model is blocked into a line of blocks in the same size. The final inversion result may change the block size, meanings that some blocks become bigger and other smaller, but the average size is kept constant. Using the smaller block will increase the conformities between input trace and final synthetic trace. Figure 34-37 illustrating these stages.

The number of iteration needed for the solution to converge depends on the block size. A method to determine whether the iteration is already sufficient, is by checking the plot error (Figure 37).

Two main problems of model-based inversion :

1. Sensitive dependency to the wavelet (two different wavelets can produce the same seismic traces).

2. Non-unique solution. Certain wavelet can give appropriate solution with the trace on well location.

Figure 35. The example of inversion result : a) Bandlimited, b) Constrained model-based, c) Stochastic model based, and d) sparse-spike MLH. Analyze the difference of each method and give the explanation. The example is taken from Arief (2001)

Figure 36. Example of trace error display a) constrained model-based, b) Stochastic model-model-based, and c) Sparse-spike MLH. Analyze the difference of each method and give the explanation. The example is taken from Arief (2001)

Thus, the final inversion result depends on two factors : 1. Initial model quality

2. Seismic data quality

In the best scenario, both factors will support each other and give the same result.

In the worst scenario, they will give contradicting information about the sub-surface model, and never give a satisfying solution.

4.3. Sparse-Spike Inversion Method

As discussed previously, the recursive method of seismic inversion is based on the classic deconvolution techniques, which assume a random reflectivity and zero or minimum-phase wavelet. They will produce higher frequency wavelet on the output, but never recover the complete RC series. More recent deconvolution techniques may be grouped under the category of sparse-spike method because these methods assume a certain model of the reflectivity and make a wavelet estimate based on this model assumption.

These techniques includes :

1. Maximum-likelihood inversion and deconvolution 2. Norm L1 inversion and deconvolution

3. Minimum entropy deconvolution

From the point of view of seismic inversion, sparse-spike methods have an advantage over classical methods of deconvolution because the sparse-spike estimate, with extra constraints, can be used as a full bandwith estimate of the reflectivity.

Figure 38 illustrates the fundamental assumption of maximum-likelihood deconvolution, which is that the earth’s reflectivity is composed of a series of large events superimposed on a Gaussian background of smaller events. This contrasts with spiking decon, which assumes a perfectly random distribution of reflection coefficient. The sonic-log reflectivity at the bottom of figure shows that in fact this model is quite logical.

The sparse-spike inversion assumes that only the big spike is important. This method locate the big spike by checking the seismic trace. Reflectivity series reconstruct one spike each at a time. The spike added until the trace modeled accurately. The sparse-spike inversion use the same parameter as the model-based inversion with constraint. The additional parameter which must be added is the parameter to determine how may trace would be determined on each trace. The parameter includes maximum number of spike and threshold of spike detection. Each new spike addition, the trace will be modeled accurately. The new spike is smaller than the previous ones.

Geologically, the large reflectors correspond to the unconformities and major lithologic boundaries.

On the maximum-likelihood method, the main algorithm is SLMA (“single likely most addition”). Figure 39 - 42 illustrate the principle of this method.

The principle of L1 norm method, basically, is the same as the MLH method and illustrated further in Figure 43-56.

Figure 40. Component used for solving both reflectivity and wavelet. Iterate around the loop until converge. Initial Wavelet Estimate Estimate Sparse Reflectivity Improve Wavelet Estimate

Figure 43. The philosophy of sparse spike inversion method using L1 norm which update the reflectivity until small error between real data seismic and the model obtained (Jason Geosystem, 1999)

Figure 45. Filter design for final inversion result. Based on the figure, 0-5 Hz range of low frequency from geology method and 5-50 Hz range from inversion result are taken to get the final acoustic impedance result (the example taken from Kahar, 2000)

Figure 46. The estimation result of wavelet-1 using seismic data and the quality control (Kahar, 2000)

Figure 47. The estimation result of wavelet-2 using seismic data, well data and also the quality control (Kahar, 2000)

Figure 53. Low frequency (0-10 Hz) component from impedance model in Figure 52. This frequency component will be united with the inversion result to the get sub-surface image with complete frequency spectrum (Pendrel & Riel, 2000)

Figure 54. Illustration on how to control the hard constraint. The constraint range determine how far the solution can be varied against the well data (Pendrel & Riel, 2000)

Figure 56. The illustration of final inversion result after combined with low frequency model (Pendrel & Riel, 2000). Determine which layer in the reef potential to be developed

5.Practical Guide for Selecting the Inversion Method

Until now, there are no standard guidance in selecting the best inversion method. The usual practice is try and compare the error on each method.

Sukmono (2000) gave practical guide about this by associating the works with the characteristic of seismic data in each exploration stage.

In the exploration stage, the main target is to detect the target horizon, map it and make initial estimate on the reserve size.

If there is no well data in this stage, the inversion will produce relative AI value. Even the simplest inversion method, that is recursive, will be useful to determine the first exploration well location and predict the drilling problems, such as shallow gas or overpressure zone. If the well data is available, the relative AI relative can be converted into absolute AI.

If the seismic used is quite noisy, the sparse-spike is not recommended, because the noise will be carried into the inversion result. If the seismic data has a good quality and the well data control is sufficient, the selection of model-based method or the sparse-spike method will depend on the reservoir heterogeneity degree.

If the reservoir heterogeneity degree is quite high or it contains many thin beds, the model-based is better than sparse-spike method, because the sparse-spike result will loose subtle reflection detail such as on the model-based method.

On the other hand, if the well data control is relatively rare, the sparse-spike method will give the best solution, because in model-based with few well control, a complete solution may not be recovered (there is no solution convergence) and it’s possible that more than one model match with the control data (non unique solution).

Exercise 5. Inversion Quality Analysis

Figure 57 shows the reflectivity and its AI sections. The AI section recovered by applying the sparse-spike inversion method. The target reservoir is reef.

Show one character of DHI and next exploration well location. Is the inversion result is correct? Give the explanation.

Exercise 6. Reservoir Quality Evaluation

Figure 59 shows the reflectivity and related AI sections. The AI section recovered by applying the sparse-spike inversion method. The interval of target reservoir is also shown. Figure 58 shows the cross-plot between AI, porosity and gamma ray.

How is the inversion result quality? Give the explanation. Based on the cross-plot result, Delineate a reservoir with good-quality, e.g. the one which has high sand/shale ratio and porosity.

Figure 58. The cross-plot of AI vs porosity and gamma-ray 9900 8500 7100 5700 7000 8000 AI

Figure 59. The reflectivity and its AI sections. Give comment about the AI quality and explanation.

8400

7400 9400

Exercise 7

AI for Channels Sandstone Reservoir Mapping-Exploration Field Case

This exercise is taken from Syarif ‘s (2000). Figure 60 is the example of well-seismic tie on Well-1. The reservoir mapped here is sand-1.

Figure 61 shows the correlation between well AI and seismic AI. Figure 62 shows correlation between AI and seismic amplitude, while Figure 63 shows correlation between well AI, depth and type of lithology.

Figure 64 shows reservoir minimum-amplitude map with 20 ms window width (10 ms above and below the sand-1). On the figure also shown the location of where the seismic inversion is run and the result is shown on Figure 65. Notice that the seismic inversion only implemented on the area with good well control and the result is used for mapping the reservoir on other area which has relatively few well data control.

Question

Figure 60. Examole of well-seismic tie in Well-1

Figure 63. Correlation between Well AI vs Depth vs.Lithology type in well-1

sand-1

shale-1 coal-1

Figure 64. Minimum amplitude of sand-1 with 20 ms window. The blue box shows area where the inversion process was held -20000 -17500 -15000 -12500 -10000 -7500 -5000 -2500 0

Exercise 7. AI for identification of Lithology type.

Figure 67 showing the reflectivity and its AI sections. AI section is recovered by applying sparse-spike inversion. The target reservoir interval also shown. Figure 66 showing the cross-plot between AI and density.

How is the inversion result quality? Give explanation. Based on cross-plot result, delineate the good reservoir, e.g, the ones which has high sand/shale ratio and high porosity.

Figure 68. The density section converted from AI section. As a comparison, the AI section is given at background. The black wiggle shows original seismic trace (Verdin, 1999). Show the porous sandstone, tight sands and clay/tuff.

Exercise 8

Seismic Inversion for Delineating Development Well Location Figure 69 shows the AI and the porosity conversion chart. Figure 70 showing porosity, NES and oil-isopach from well data charts.

Delineate development well location based on these figures. Compare if you don’t have the inversion result for this analysis.

Exercise 9

Seismic Inversion for Reservoir Carbonate Characterization-Exploration Field Case

Figure 71. Example of well-seismic tie in Well-1. the target reservoir interval is shown.

Figure 72. Time structure map of top X. Figure 73. Check-shot data.

Figure 74. Depth structure map of top X. Figure 75. Cross-plot of AI vs porosity.

Figure 76. Average AI with 10 ms window width below the top X.

Questions

1. Which part of the X reservoir is best to be developed ?

Åtop X Åbottom X

Figure 77. The AI section through Well-1

Well-1

Bottom X Top X

References

1. Angeleri, G.P. and Carpi, R., 1982, Porosity Prediction

from Seismic Data : Geophysical Prospecting, v.30, 580-607.

2. Brown, A.R., 1991, Interpretation of Three-Dimensional

Seismic Data, AAPG Memoir 42, 3rd _{ed., AAPG.}

3. Galbraith, J.M., and Millington, G.F., 1979, Low

Frequency Recovery in The Inversion of Seismograms : Journal of CSEG, v. 15, p.30-39.

4. Johnston, D.H., 1992, Introduction to Reservoir

Management in Reservoir Geophysics, ed : R.E. Sheriff : SEG

5. Kallweit, R.S. and L.C. Wood, 1982, The Limits of

Resolution of Zero-phase Wavelets : Geophysics, v.47, p. 1035-1046.

6. Kelkar, M., 1982, Applied Geostatistics for Reservoir

Characterization, The University of Tulsa, Oklahoma.

7. Lindseth, R.O., 1979, Synthetic Sonic Logs - a Process for

Stratigraphic Interpretation : Geophysics, v.44, p.3-26. 8. Lines, L.R. and Treitel, S., 1984, A Review of

Least-Squares Inversion and Its Application to Geophysical Problems : Geophysical Prospecting, v.32, p.159-186.

9. Martinez, R., 1985, Expand Abstracts of The SEG

10. Meckel, L.D.Jr. and A.K.Nath, 1977, Geologic

Considerations for Stratigraphic Modelling and Interpretation, in C.E. Payton, ed., Seismic Stratigraphy – Applications to Hydrocarbon Exploration : AAPG Memoir 26, 417-438.

11. Neidell, N.S. and E. Poggiagliolmi, 1977, Stratigraphic

Modelling and Interpretation - Geophysical Principles and Techniques, in C.E. Payton, ed., Seismic Stratigraphy – Application to Hydrocarbon Exploration : AAPG Memoir 417-438.

12. Oldenburg, D.W., Scheuer, T and Levy, S., 1983,

Recovery of The Acoustic Impedance from Reflection Seismograms, Geophysics, v.48, p. 1318-1337.

13. Richardson, J.G., and Sneider, R.M., 1992, Synergism in

Reservoir Management, in Reservoir Geophysics, ed : Sherrif, R.E., SEG.

14. Russel, B.H., 1988, Introduction to Seismic Inversion

Methods (ed : S.N. Domenico), SOC. Of Exploration Geophysicists.

15. Russel, B.H., 1995, Introduction to Seismic Inversion

Methods, STRATA workshop.

16. Russel, B.H. and Lindseth, R.O., The Information

Content of Synthetic Sonic Logs – A Frequency Domain Approach, EAEG, Frances.

18. Sneider, R.M., 1990, The Economic Value of A

Synergistic Organization : presented at the 1990 Archie Conference, Houston.

19. Sukmono, S., 1999a, Interpretasi Seismic Refleksi, Jurusan Teknik Geofisika – ITB.

20. Sukmono, S., 1999b, Seismic Stratigrafi, Jurusan Teknik Geofisika – ITB.

21. Yilmaz, O., 1987, Seismic Data Processing, Society of Exploration Geophysicists.