Unconventional Resources and the Role of Technology
Seismic inversion techniques: choice and benefits
K. Filippova (Fugro-Jason),* A. Kozhenkov (Fugro-Jason) and A. Alabushin (LUKOIL-Komi) provide an overview of the general principles of deterministic and geostatistical inversions of seismic data. They demonstrate with a case study from the Timano-Pechora province that reservoir properties prediction methodology using geostatistical partial stacks inversion can facilitate high resolution 3D distribution of reservoir properties used to plan production well spacing, further verified by drilling.
A dvances in computer technologies in recent years have led to the rapid growth of seismic amplitude interpretation techniques, notably seismic inversion which has spread widely throughout modern work-
flows. Seismic data these days includes not only full stack data but also data stacked in various offset and angle of incidence ranges. Such approaches to seismic amplitude interpretation enable accurate estimation of elastic properties in target res-ervoir intervals.
At the current stage of seismic exploration technology, 2D and 3D seismic surveys have demonstrated their efficiency and reliability. In particular, 2D seismic surveys are used to build structural frameworks of the subsurface with a certain degree of reliability (Omar et al. 2006). However, in complex structural settings this technique has proven to be insufficient and thus should mainly be used at the initial stage of field exploration to reveal promising exploration targets and to provide an initial estimate of their potential as hydrocarbon-bearing reservoirs.
To overcome the limitations of 2D seismic data, the use of 3D seismic data technologies increased and led to the rapid adoption of attribute analysis. Attribute analysis is essentially based on estimating correlations between one or more seismic attributes and reservoir properties of interest (Ampilov, 2008)
As attribute analysis developed, the methods of studying seismic amplitudes evolved to use not only full stack seismic data, but also partial stacks and seismic gathers, particularly to analyze how reflected wave amplitude varies with offset – a method known as AVO analysis (Foster et al., 2010). As the next step in evolution of seismic interpretation techniques, AVO analysis is widely used for exploration of gas reservoirs in young clastic formations, as well as for detection of hydrocarbon saturated reservoirs in oil fields already under development.
In recent years, a number of seismic inversion techniques have been developed, finally making it possible to pass from the analysis of reflection coefficients at acoustic interfaces to the analysis of elastic properties of formations (Avseth et al.,2005). This makes it possible to estimate reservoir proper-
ties based on the relation between petrophysical and elastic rock properties obtained from the interpretation of measured well log data.
At present, several independent methodologies can be distinguished within the spectrum of the 2D and 3D seismic interpretation approaches: multi-dimensional attribute analy-sis, neural networks, AVO analysis, inversion, etc. (Avseth set al. 2005). While each of these approaches has its own advantages and disadvantages, the applicability of any par-ticular technique depends first of all on the available data and geological tasks.
Seismic inversion technologies can be classified as follows:n By the type of seismic data used for inversion (inversion of
full stack seismic data or inversion of partial stack data). With full stack inversion only one elastic property (acoustic impedance) can be estimated. With partial stack inversion, which uses amplitude variation with offset, multiple elastic properties such as P-Impedance, S-Impedance, Vp/Vs ratio, and density can be estimated.
n By the mathematical approach to the solution of the inverse problem. Here we distinguish deterministic and geostatisti-cal approaches that result in a different level of detail of estimated reservoir properties. Deterministic algorithms (Jarvis et al., 2004; Pendrel et al., 2003) can only provide a solution within the seismic bandwidth, while geostatistical algorithms can include fine-scale details beyond the seismic bandwidth (Francis, 2006).
Although a variety of different techniques for seismic data inversion are available in modern software packages, the choice of the appropriate technique should be determined by the complexity of the geological conditions and the range of problems to be solved. Our experience accumulated to date allows us to state that reservoir model construction by means of 3D seismic inversion techniques is controlled by three key points:1. Seismic data quality2. Elastic vs. petrophysical properties relationships from well
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The second area is mainly focused on preparing data for seismic inversion and includes a rock physics approach. Its primary objectives are:
n Continuous reconstruction of formation properties along the wellbore, both for reservoirs and non-reservoirs
n Characterization of rocks in terms of their elastic proper-ties
n Establishment of causal relationships between elastic and petrophysical properties such as porosity, clay content and fluid saturation
A petrophysical bulk model of the target formations is the main prerequisite for reliable discrimination of formations in the elastic properties domain and for the selection of the type of seismic inversion. The model is based on the results of core descriptions and drill cuttings, as well as on the interpretation of well logs. To model elastic properties by rock physics modelling, it is important to maintain a unified approach with the interpretation of log data (petrophysical interpretation) in all wells of a field.
Equations and parameters assumed in log interpretation are subsequently used in elastic properties modelling, which is performed given the volume fractions and properties of minerals composing the solid phase of a rock (clay minerals, quartz, limestone, dolomite, etc.) and fluid saturation.
A bulk model should be built in order to estimate the material composition of the entire rock-fluid matrix. Important information for rock physics modelling is pro-vided by the results of the elastic properties determination
Seismic data qualityAcquisition of seismic data suitable for reliable reservoir modelling starts by designing a proper seismic survey for a particular geological feature of interest. Seismic modelling can be used as an aid to establish acquisition parameters and enable adjustment of the spread layout to achieve an optimum fold and offset distribution at the target interval, thus assuring the best signal-to-noise ratio within the entire range of offsets (Singleton, 2009).
The key element determining reservoir model qual-ity is seismic data processing, which should be focused on preserving seismic amplitudes over the full and partial stack volumes. In the processing special attention should be paid to effectiveness of noise suppression, good static correction, and thorough estimation of stacking velocities. A good method of checking whether the behaviour of amplitudes is preserved at all processing steps is by modelling the seismic gathers at well locations and comparing them to processed data (Figure 1).
Well logs of elastic and petrophysical propertiesWell log data is the next source of information without which it is impossible to reliably predict meaningful reservoir properties. In present-day analysis and interpretation of well log data, two distinct areas can be distinguished.
The first area is traditional, ‘classic’ interpretation for which the primary objectives are:n Detection of reservoirs in target pay formations and deter-
mining their properties;n Estimation of reserves
Figure 1 Comparison of acquired (left panel) and modelled (right panel) gather data in the target interval (cross-correlation shown in colour).
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Let us consider what geological tasks can be solved using different inversion techniques using an example of a complex oilfield located in the Timan-Pechora Basin in northeast European part of Russian Federation. It was already noted previously that specific information is required to perform a successful inversion. In this oilfield a wide range of measure-ments were available:n 3D seismic survey was acquired (250 km2)n Eight wells were drilled - P-sonic and density logs existed in each of the eight wells - S-sonic logs existed in seven of the eight wells - VSP surveys were conducted for four of the eight wells - Core data was available for three of the eight wells
The target formations are Carboniferous shallow water shelf carbonates. Stratigraphically they are confined to the Moscovian (C2m), Bashkirian (C2b), and Upper and Lower Serpukhovian (C1s2 -C1s1b) stages at depths ranging from 2800–3600 m. The seismic and P-impedance sections of the study intervals are presented in Figure 2.
In accordance with the available core data, the Carbon-iferous formations consist of carbonate rocks (limestones, dolomites) and are characterized by significant heterogene-ity in their petrophysical properties. The thickness of an individual reservoir layer varies from 1-12 m. The main geological objective was a detailed reservoir characterization to optimize the production drilling pattern. To do this, it was necessary to build 3D models of the reservoir and its porosity distribution in the target intervals.
from the core data under in-situ conditions (Mavko et al., 2009). Additional information for rock physics modelling of the mineral composition, bulk density, and mineralogical density comes from analyses performed on core samples. A comprehensive suite of well log data and core studies is necessary to do this.
Thus, the quality and completeness of the input suite of well log data and core studies determine the reliability of a petrophysical model and the reliability of the target formation discrimination in the domain of elastic properties. This bulk model should be sufficient for the evaluation of the composition of the formation as well as its structure and properties, not only in the target pay intervals but also in the surrounding strata.
Inversion techniqueAs mentioned above, we can now consider four major inver-sion techniques:n Deterministic inversion of full stack seismic datan Simultaneous deterministic partial stack inversionn Geostatistical inversion of full stack seismic datan Simultaneous geostatistical partial stack inversion
In order to come up with an appropriate inversion and reservoir characterization method that shows a reliable separation of the chosen lithofacies, it is necessary to analyze the geological tasks to define the range of reservoir thickness in the target interval and to perform a feasibility study on well log data.
Figure 2 Comparison of seismic data and inverted P-Impedance for the target interval.
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colour, limestone reservoir in blue, dolomite reservoir in green, and non-reservoir is transparent. We can see that the lithotype distribution obtained from seismic inversion is too blurred and a lower vertical resolution is observed compared to the wells, which is why many reservoir intervals remain ‘undetected’ and are classified as non-reservoirs.
Simultaneous deterministic partial stack inversionWhen performing this simultaneous deterministic inversion, partially stacked (3D / 2D) seismic data are simultaneously inverted into elastic property volumes or sections. The elastic properties are typically acoustic impedance, shear impedance, Vp/Vs, and density. Simultaneous analysis of these properties provides more possibilities to estimate lithology distribution, porosity, and hydrocarbon saturation than is possible from acoustic impedance only. However, this type of inversion requires a more thorough data preparation:n The data should be processed to preserve amplitudes within
the seismic gathers for the entire range of offsetsn During seismic data processing pre-stack migration must be
performed and partial stacks should be obtainedn In addition to P-sonic and density well log data, S-sonic logs
are required at least in some wells
The first step in this case study was the extraction of six partial stacks from the seismic gather data in the offset range from 176–3851 m. This is equivalent to angles from 5–430 in the target interval of the Carboniferous formations. After that a feasibility study was performed. Figure 5 shows the cross-plot of well log data where the colours denote lithology types. In the Vp versus Vs elastic parameter domain, conditions exist allow-ing optimal discrimination between limestone reservoir, dolo-
Let us analyze different inversion techniques and their potential and limitations for solving the posed geological tasks. In doing so, we will adhere to the following sequence:n Cross-plot analysis of the relationship between elastic
properties and petrophysical parameters in the target inter-vals to determine the type of inversion
n Decide what seismic data is necessary for the chosen inver-sion technique
n Comparison of the inversion results to the well log data and analysis of potential of the applied inversion technique
Deterministic full stack inversionIn the inversion process full stack (3D/2D) seismic data are inverted into volumes or sections of acoustic impedance with vertical resolution of about 1/8 of wavelength (Chopra et al., 2006). Measured P-sonic and density logs data at least in one well are required to apply this inversion technique.
The deterministic inversion workflow starts from elastic properties cross-plot analysis aimed to determine the best lithology types separation with respect to different elastic properties. Figure 3 shows P-Impedance histogram for differ-ent lithology types in the target interval. It can be seen that such lithology types as dolomite reservoir, limestone reservoir, and non-reservoir cannot be differentiated reliably using this elastic parameter. When this kind of inversion is used, only the high-porosity limestone reservoir can be detected, corresponding to the lower values of acoustic impedance. Figure 4 shows an example of the spatial reservoir distribution obtained from a deterministic full stack inversion. The blue bodies correspond to limestone reservoir, the wells are plotted in overlay for comparison. In the wells the lithology types from petrophysical interpretation are shown: anhydrite in red
Figure 3 P-Impedance histograms for the target interval in geostatistical scale (limestone reservoir in cyan, dolomite reservoir in green, non-reservoir in dark blue).
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properties. Limitations of the second approach are: low vertical resolution since the properties are accurate only within seismic bandwidth, the inverted properties generally do not coincide precisely with measured well logs, and only one solution exists. On the other hand, the advantage of such models is that they provide independent estimation of reservoir properties from seismic data between the wells and have a much higher lateral resolution.
Geostatistical inversion is a methodological approach that combines the advantages and minimizes the disadvantages of the two approaches of geological modelling mentioned above. It generates stochastic realizations of lithology and elastic properties of a reservoir, which not only reproduce prior lithology probability trends, spatial variograms, and joint probabilistic distributions of elastic properties but also repro-duce the measured well logs and closely match the 3D seismic data within the desired noise levels (Sams et al., 1999).
mite reservoir, and non-reservoir. As such, the parameterization in the Vp, Vs, and density domain was chosen for inversion.
As a result of the simultaneous deterministic partial stack inversion, volumes of the following elastic properties were derived: Vp, Vs, and density. Using the cross-plot shown in Figure 5, a spatial distribution of lithology types was obtained from inverted Vp and Vs volumes. Figure 6 shows the limestone and dolomite reservoir distribution. The lithology types from logs shown at the well locations demonstrate the reliability of the results. It can be seen that the inverted data effectively reflect both known trends: the lateral reservoir distribution and an increase of dolomitization in the lower section. This was verified by the core studies and the results of petrophysical interpretation. These results can be used to delineate reservoir zones but not for quantitative evaluation of, for instance, the net reservoir thickness, because these lithotypes distribution volumes are quite coarse due to seismic data resolution constrains.
Geostatistical inversionThe ultimate objective of the integrated interpretation of well log and 3D seismic data is to build a geological model. Generally speaking, two approaches to geological modelling can be identified. The most widespread approach is to use well data for the stochastic interpolation of properties within the structural framework defined from seismic data (geostatistical reservoir modelling). The advantages of a geological model based on well data include high vertical resolution, precise tie to well data, and multiple realizations enabling probabilistic analysis and risk assessment. However, the accuracy of reser-voir properties generated by such approaches decreases rapidly away from well control since the seismic data is only used as a stratigraphic guide or trend (Sams, 2001).
The second approach consists of using deterministic seismic inversion results to populate a model with reservoir
Figure 4 Reservoir distribution obtained from deter-ministic full stack inversion (reservoir is shown in cyan, the rest is non-reservoir).
Figure 5 Cross-plot of well log data in geostatistical scale, showing P-velocity versus S-velocity with lithology types in colour.
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One of the differences between deterministic and geosta-tistical inversion is the creation of an a priori model. Strictly speaking, deterministic inversion does not use any prior model but instead uses low-frequency trends of elastic properties together with other constraints to define the solution area. In the geostatistical inversion approach, a geostatistical prior model is used to capture various kinds of probabilistic knowl-edge about the reservoir structure, such as spatial property
consistency in the form of 3D variograms and the range and multivariate distributions of elastic properties for each lithol-ogy type and geologic zone as probability density functions. A statistical model example for one of the types of reservoir is shown in Figure 7.
Differences also exist in the output data and in the methods to interpret the results. In deterministic inversion, elastic property cubes or sections are output. Using cross-plots
Figure 6 Limestone and dolomite reservoir distri-bution obtained from simultaneous deterministic partial stack inversion (limestone reservoir in cyan, dolomite reservoir in green, the rest is non-reservoir).
Figure 7 Statistical model created in the elastic property domain from well data for the reservoir (stratigraphic grid scale is 50 m x ¼ ms).
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of elastic versus reservoir properties the elastic properties can then be converted into volumes or sections of reservoir properties such as porosity, reservoir lithology types, and saturation. Geostatistical inversion solves simultaneously for both lithology types and continuous properties, providing a set of equally probable property distributions which enables probabilistic analysis of the results.
Geostatistical inversion, like the deterministic inversion is represented by two algorithms, one of which uses a full stack cube and the other uses partial stacks. As was already shown in Figures 3 and 5, two elastic properties, Vp versus Vs, are needed in our case in order to differentiate between the desired lithology types. The target intervals consist of a bunch of thin reservoir layers where the time thickness (1–1.5 ms in two-way time) is beyond seismic resolution. In order to obtain detailed reservoir distribution geostatistical partial stack inversion was applied.
The key inputs for geostatistical inversion are partial seismic stacks (in this case study six stacks were used) and corresponding estimated wavelets. Prior statistical informa-tion about the elastic properties corresponding to the lithology types is also required. This statistical information was acquired from the available well logs. The statistics with a set of partial stacks were input to this inversion process.
Twenty realizations of high-resolution lithology types distribution with jointly inverted elastic properties were obtained from simultaneous geostatistical partial stack inversion. The sample rate sample rate within the target
interval was 1/2 to 1/8 of sample rate of seismic data, the lithology types were reservoir and non-reservoir, and the elastic properties were Vp, Vs, and density. Reservoir and non-reservoir probability volumes were calculated based on analysis of multiple realizations of lithology types volumes.
Just as is the case in deterministic simultaneous partial stack inversion workflows, it is necessary to perform well ties, estimate individual wavelets for each of the partial stacks, and accurately pick the horizons that define the target interval top and bottom. It is important to compensate misalignment between partial stacks because it strongly affects the accuracy of the elastic property estimation. The next step of the work is the transition from petrophysical lithology type definition to the ‘lithology types’ for inversion. The main criterion for such a translation is the separation in elastic properties between different lithologies (Figure 5). For the target intervals the following ‘lithology types’ were defined: n For the Moscovian (C2m), Bashkirian (C2b), and Upper
n For the Lower Serpukhovian (C1s1): anhydrite and reser-voir
n For the C1s1_b (Lower Part of Lower Serpukhovian stage): reservoir and non-reservoir
For each lithology type in the target interval the statistical model was created using the Vp, Vs, and density data from
Figure 8 Multiple unconstrained realizations of lithology types distribution obtained from geostatictical simultaneous partial stack inversion (anhydrite in red, reservoir in green, non-reservoir is shown in dark blue colour). Vertical scale is ¼ ms.
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Figure 9 A) Reservoir probability from sum of 20 unconstrained geostatictical inversion realizations (yellow = 20 out of 20 realizations delivered reservoir lithol-ogy type, dark blue = 0 out of 20). B) Section of most probable (P50) discrete property type based on 20 unconstrained realization of geostatictical partial stack inversion. C) Section of most probable (P50) discrete property type based on 20 constrained realization of geostatictical partial stack inversion.
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Figure 10 Section of predicted lithology types delivered from geostatictical inversion with lithology log in new drilled well overlaid (limestone reservoir in blue, dolomite reservoir in green, the rest is non-reservoir). A) Well 1; B) Well 2; C) Well 3.
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n Signal-to-noise ratio for each partial seismic stack. This was estimated from the results of deterministic inversion
n Prior probability of lithology types in target interval. This was defined basically from the lithology proportions esti-mated from the well log data and to a lesser degree those estimated from the deterministic inversion model
n 3D variograms for modelling of lithology types and elastic parameters. This was defined from the integrated geological and geophysical analysis of the target forma-tions and from interpretation of deterministic inversion results
the petrophysical interpretation and the rock physics model-ling, (Figure 7).
Geostatistical inversion runs on a stratigraphic grid, so, in order to generate a framework for it, it is necessary to have detailed correlations of stratigraphic boundaries in the target intervals and to define the vertical size of a cell. In this case study, the vertical cell size was set to ¼ ms, as this cor-responded to the expected size of the thin features of interest within the reservoir layers.
After all input data were prepared, the following inver-sion parameters were optimized:
Reservoir properties from drilling
Reservoir properties from geostatictical inversion
Absolute error Relative error (%)
well 1Net Thickness, m 19,2 18,7 0,5 2,6NPV, m 2,4 2,3 0,1 4,6Net Pay, m 7,5 6,9 0,6 8,0HCPV, m 0,9 0,91 0,01 1,1well 2Net Thickness, m 30,8 29,1 1,7 5,5NPV, m 3,5 3,2 0,3 7,4Net Pay, m 6,0 5,0 1,0 16,7HCPV, m 0,9 0,8 0,1 11,5well 3Net Thickness, m 15,5 14,4 1,1 7,1NPV, m 2,2 1,9 0,3 11,5Net Pay, m 6,0 7,0 1,0 16,7HCPV, m 0,9 1,0 0,1 11,0
Table 1 Comparison of reservoir properties obtained from simultaneous geostatistical partial stack inversion with data from newly drilled wells (* NPV - net pore volume; ** HCPV - hydrocarbon pore volume).
Figure 11 Comparison of reservoir distribution obtained from geostatictical partial stack inversion (left) and deterministic partial stack inversion (right) – reservoir in green, the rest is non-reservoir.
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data were used to obtain 3D distributions of petrophysical properties, for example porosity, by means of co-simulation.
The lithology type probability volumes (Figure 9a) enable us to evaluate the reliability of the modelling, as well as making evaluation of, for example, the net thickness within a certain percentile (P10, P50, P90).
QC procedures are very important in the geostatistical inversion workflow. A series of QC procedures were per-formed to check the quality of inversion results:n Analysis of correlation coefficients between the input seis-
mic data and the synthetics obtained during inversion. All partial stacks were involved in this process
n Analysis of signal-to-noise ratio maps for each partial stackn Analysis of residuals, the difference between the seismic
and synthetic data, both in the time and the amplitude-frequency domain
However, data from the newly drilled wells are the best quality and reliability control of 3D reservoir models cre-ated by seismic inversion. In the interval of the Moscovian, Bashkirian, and Upper Serpukhovian formations the verifica-tion of the constructed model was made using three newly drilled wells.
The match between the predicted lithology types dis-tribution and the results of petrophysical interpretation
Next, unconstrained geostatistical inversion was performed without inclusion of wells, i.e., only the statistical model of lithology types, the seismic data, and the wavelets were used. The results obtained from this cross validation approach were analyzed from the following viewpoints (Figures 8, 9a, and 9b)n Stability of the solution: What is the variability of the
details from one realization to another?n Reliability of the tie between the well data and the elastic
properties and lithology types estimated from inversionn Agreement between the statistical reservoir models
described by well log data and those obtained from the results of geostatistical inversion run without being explic-itly constrained to well logs
n Compliance of the posterior property distributions with the prior geological model
The final step in the workflow was the creation of con-strained realizations, where the lithology and continuous property distribution volumes are tied to well data (Figure 9c). As with the unconstrained modelling this means the calculation of 20–30 equally probable realizations, on the basis of which a probabilistic evaluation of the results was later made. The most probable lithology types distribution in the target interval and the minimum, maximum and aver-aged elastic property volumes were produced. Finally, these
Figure 12 Comparison of dolomite and limestone reservoir distribution obtained from geostatictical partial stack inversion and deterministic partial stack inversion (limestone reservoir in blue, dolomite reservoir in green, the rest is non-reservoir).
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properties made by deterministic inversion is often sufficient, as in many cases it can reveal zones with better reservoir. In the case when a more detailed model of a hydrocarbon pool is needed, the geostatistical inversion technique shows excellent results (Figsures 11, 12). The additional detail is critical when building geological and hydrodynamic models or planning a production well pattern, especially in complex carbonate reservoirs with high lateral variability and limited well coverage.
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(lithology type log) at new well locations is illustrated in Figure 10. Table 1 presents quantitative estimates of the precision of reservoir property prediction. To make this comparison the following reservoir parameters were used: net thickness, net pay, and net pore volume. NPV is calcu-lated as net thickness x porosity, and hydrocarbon pore vol-ume (HCPV) is net pay x porosity. For all of the mentioned parameters, absolute and relative errors of prediction were calculated. The average relative error of the predicted net reservoir thickness is not more than 5%. The same for net pay is 14%, for net pore volume 8%, and for hydrocarbon pore volume 8%.
The results shown in this case study demonstrate that the estimation of reservoir properties in carbonate formations based on geostatistical partial stack inversion is confirmed by newly drilled wells and can be successfully used for planning production well locations.
ConclusionAt present, there are several independent techniques of seis-mic data interpretation, and each of them can be beneficial depending on the data available for a given field and the geological tasks to be solved. Seismic inversion proved to be the most advanced, accurate, and reliable method of reser-voir characterization. It is critical that the data involved in the inversion workflow meet certain requirements. The first step to success is seismic survey design, high quality acquisi-tion, and state-of-the-art seismic data processing aimed at preservation of amplitudes. Also, in order to obtain meaning-ful inversion results, well logs describing elastic properties of the rocks (P-sonic, S-sonic and density log) are required. The choice of the necessary number of elastic parameters (P-impedance or Vp, Vs, and density) should be made on the basis of an analysis of the ability to solve the geological tasks by using one or the other set of elastic parameters. Such analysis also determines the type of inversion: full stack or partial stacks.
The choice between deterministic and geostatistical algorithms should be made based on two key points: seismic resolution compared to reservoir thickness and the avail-ability of high quality petrophysical and core data. At the initial stage of field development, estimation of reservoir
