Seismic inversion
Encyclopedia
Seismic inversion, in Geophysics (primarily Oil and Gas exploration/development), is the process of transforming seismic reflection
data into a quantitative rock-property description of a reservoir. Seismic inversion may be pre-or post-stack, deterministic, random or geostatistical, and typically includes other reservoir measurements such as well logs
and cores.
are routinely performed to gather information about the geology
of an oil
or gas
field. These surveys record sound waves which have traveled through the layers of rock and fluid in the earth. The amplitude
and frequency
of these waves can be estimated so that any side-lobe and tuning effects introduced by the wavelet may be removed.
Seismic data may be inspected and interpreted on its own without inversion, but this does not provide the most detailed view of the subsurface and can be misleading under certain conditions. Because of its efficiency and quality, most oil and gas companies now use seismic inversion to increase the resolution and reliability of the data and to improve estimation of rock properties including porosity
and net pay.
There are many different techniques used in seismic inversion. These can be roughly grouped into two categories: pre-stack or post-stack, and seismic resolution or well-log resolution. The combination of these categories yields four technical approaches to the inversion problem, and the selection of a specific technique depends on the desired objective and the characteristics of the subsurface rocks. Although the order presented reflects the advancement in inversion techniques over the past 20 years, each grouping still has valid uses in particular projects or as part of a larger workflow.
estimated from the data. Typically, a reflection coefficient
series from a well within the boundaries of the seismic survey is used to estimate the wavelet phase
and frequency. Accurate wavelet estimation is critical to the success of any seismic inversion. The inferred shape of the seismic wavelet may strongly influence the seismic inversion results and, thus, subsequent assessments of the reservoir quality.
Wavelet amplitude and phase spectra
are estimated statistically
from either the seismic data alone or from a combination of seismic data and well control using wells with available sonic
and density
curves. After the seismic wavelet is estimated, it is used to estimate seismic reflection coefficients in the seismic inversion.
When the estimated (constant) phase of the statistical wavelet is consistent with the final result, the wavelet estimation converges more quickly than when starting with a zero phase
assumption. Minor edits and "stretch and squeeze" may be applied to the well to better align the events. Accurate wavelet estimation requires the accurate tie of the impedance
log to the seismic. Errors in well tie can result in phase or frequency artifacts in the wavelet estimation. Once the wavelet is identified, seismic inversion computes a synthetic log for every seismic trace. To ensure quality, the inversion result is convolved with the wavelet to produce synthetic seismic traces which are compared to the original seismic.
Seismic data is band-limited, reducing resolution and quality. To extend the frequency band available, low-frequency data is derived from log data, pre-stack depth or time migrated velocities and/or a regional gradient. High frequency can be derived from well control or geostatistical analysis.
Initial inversions are often run with relaxed constraints, starting with the seismic and then adding limited-trend data from the wells. This provides a rough overview of the reservoir in an unbiased manner. It is critical at this point to evaluate the accuracy of the tie between the inversion results and the wells, and between the original seismic data and the derived synthetics. It is also important to ensure that the wavelet matches the phase and frequency of seismic data.
Without a wavelet, the solution is not unique. Deterministic inversions address this problem by constraining the answer in some way, usually to well log data. Stochastic
inversions address this problem by generating a range of plausible solutions, which can then be narrowed through testing for best fit against various measurements (including production data).
velocity. Unlike seismic reflection data (which is an interface property) AI is a rock property. The model generated is of higher quality, and does not suffer from tuning and interference caused by the wavelet.
CSSI transforms seismic data to a pseudo-acoustic impedance log at every trace. Acoustic impedance is used to produce more accurate and detailed structural and stratigraphic
interpretations than can be obtained from seismic (or seismic attribute
) interpretation. In many geological environments acoustic impedance has a strong relationship to petrophysical properties such as porosity, lithology
, and fluid saturation.
A good (CSSI) algorithm
will produce four high-quality acoustic impedance volumes from full or post-stack seismic data: full-bandwidth impedance, bandlimited
Impedance, reflectivity model, and low-frequency component. Each of these components can be inspected for its contribution to the solution and to check the results for quality. To further adapt the algorithm mathematics to the behavior of real rocks in the subsurface, some CSSI algorithms use a mixed-norm approach and allow a weighting factor between minimizing the sparsity of the solution and minimizing the misfit of the residual traces.
Simultaneous Inversion (SI) is a pre-stack method that uses multiple offset or angle seismic sub-stacks and their associated wavelets as input; it generates P-impedance, S-impedance and density
as outputs (although the density output resolution is rarely as high as the impedances). This helps improve discrimination between lithology, porosity and fluid effects. For each input partial stack, a unique wavelet is estimated. All models, partial stacks and wavelets are input to a single inversion algorithm —enabling inversion to effectively compensate for offset-dependent phase, bandwidth, tuning and NMO
stretch effects.
The inversion algorithm works by first estimating angle-dependent P-wave reflectivities for the input-partial stacks. Next, these are used with the full Zoeppritz equations
(or approximations, such as Aki-Richards, for some algorithms) to find band-limited elastic reflectivities. These are in turn merged with their low-frequency counterparts from the model and integrated to elastic properties
. This approximate result is then improved in a final inversion for P-impedance, S-impedance and density, subject to various hard and soft constraints. One constraint can control the relation between density and compressional velocity; this is necessary when the range of angles is not great enough to be diagnostic of density.
An important part in the inversion procedure is the estimation of the seismic wavelets. This is accomplished by computing a filter that best shapes the angle-dependent well log reflection coefficients in the region of interest to the corresponding offset stack at the well locations. Reflection coefficients are calculated from P-sonic, S-sonic and density logs using the Zoeppritz equations
. The wavelets, with amplitudes representative of each offset stack, are input directly into the inversion algorithm. Since a different wavelet is computed for each offset volume, compensation is automatically done for offset-dependent bandwidth, scaling and tuning effects. A near-stack wavelet can be used as the starting point for estimating the far-angle (or offset) wavelet.
No prior knowledge of the elastic parameters and density beyond the solution space defined by any hard constraints is provided at the well locations. This makes comparison of the filtered well logs and the inversion outputs at these locations a natural quality control. The lowest frequencies from the inversion are replaced with information from the geologic model since they are poorly constrained by the seismic data. When applied in global mode a spatial control term is added to the objective function and large subsets of traces are inverted simultaneously. The simultaneous inversion algorithm takes multiple angle-stacked seismic data sets and generates three elastic parameter volumes as output.
The resulting elastic parameters are real-rock properties that can be directly related to reservoir properties. The more advanced algorithms use the full Knott-Zoeppritz equations and there is full allowance for amplitude and phase variations with offset. This is done by deriving unique wavelets for each input-partial stack. The elastic parameters themselves can be directly constrained during the seismic inversion and rock-physics relationships can be applied, constraining pairs of elastic parameters to each other. Final elastic-parameter models optimally reproduce the input seismic, as this is part of the seismic inversion optimization.
to assess risk. Highly-detailed petrophysical models are generated, ready for input to reservoir-flow simulation.
Geostatistics
differs from statistics in that it recognizes that only certain outcomes are geologically plausible. Geostatistical inversion integrates data from many sources and creates models that have greater resolution than the original seismic, match known geological patterns, and can be used for risk assessment
and reduction.
Seismic, well logs and other input data are each represented as a probability density function
(PDF), which provides a geostatistical description based on histogram
s and variogram
s. Together these define the chances of a particular value at a particular location, and the expected geological scale and composition throughout the modeled area.
Unlike conventional inversion and geomodeling algorithms, geostatistical inversion takes a one-step approach, solving for impedance and discrete property types or lithofacies at the same time. Taking this approach speeds the process and improves accuracy.
Individual PDFs are merged using bayesian inference
techniques, resulting in a posterior PDF conditioned to the whole data set. The algorithm determines the weighting of each data source, eliminating potential bias. The posterior PDF is then input to a Markov Chain Monte Carlo
algorithm to generate realistic models of impedance and lithofacies, which are then used to co-simulate rock properties such as porosity. These processes are typically iterated until a model emerges that matches all information. Even with the best model, some uncertainty remains. Uncertainty can be estimated using random seeds to generate a range of realizations. This is especially useful when dealing with parameters that are sensitive to change; an analysis of this sort enables greater understanding of development risk.
(AVO) (AVA) geostatistical inversion incorporates simultaneous AVO (AVA) inversion into the geostatistical inversion algorithm so high resolution, geostatistics, and AVO may be attained in a single method. The output model (realizations
) are consistent with well log information, AVO seismic data, and honor rock property relationships found in the wells. The algorithm also simultaneously produces elastic properties (P-impedance, S-impedance and density) and lithology volumes, instead of sequentially solving for lithology first and then populating the cell with impedance and density values. Because all output models match all input data, uncertainty can be quantitatively assessed to determine the range of reservoir possibilities within the constraining data.
AVA geostatistical inversion software uses leading-edge geostatistical techniques, including Markov Chain Monte Carlo (MCMC) sampling and pluri-Gaussian lithology modeling. It is thus possible to exploit "informational synergies" to retrieve details that deterministic inversion techniques blur out or omit. As a result, geoscientists are more successful in reconstructing both the overall structure and the fine details of the reservoir. The use of multiple-angle-stack seismic volumes in AVA geostatistical inversion enables further evaluation of elastic rock properties and probable lithology or seismic facies and fluid distributions with greater accuracy.
The process begins with a detailed petrophysical analysis and well log calibration. The calibration process replaces unreliable and missing sonic and density measurements with synthesized values from calibrated petrophysical and rock-physics models. Well log information is used in the inversion process to derive wavelets, supply the low frequency component not present in the seismic data, and to verify and analyze the final results. Next, horizon and log data are used to construct the stratigraphic framework for the statistical information to build the models. In this way, the log data is only used for generating statistics within similar rock types within the stratigraphic layers of the earth.
Wavelet analysis is conducted by extracting a filter from each of the seismic volumes using the well elastic (angle or offset) impedance as the desired output. The quality of the inversion result is dependent upon the extracted seismic wavelets. This requires accurate p-sonic, s-sonic and density logs tied to the appropriate events on the seismic data. Wavelets are extracted individually for each well. A final "multi-well" wavelet is then extracted for each volume using the best individual well ties and used as input to the inversion.
Histograms and variograms are generated for each stratigraphic layer and lithology, and preliminary simulations are run on small areas. The AVA geostatistical inversion is then run to generate the desired number of realizations, which match all the input data. The results are quality control
led by direct comparison of the inverted rock property volumes against the well logs. Further QC involves review by a multidisciplinary team of all input parameters and the results of the simulation. Analysis of multiple realizations produces mean (P50) property cubes or maps. Most often these are lithology or seismic facies
cubes and predicted lithology or facies probabilities
, but other outputs are also possible. Selected lithology and facies cubes are also generated for P15 and P85 probabilities (for example). Reservoir 3-D bodies of hydrocarbon
-bearing units are captured with their corresponding rock properties, and the uncertainty in reservoir size and properties is quantified.
Reflection seismology
Reflection seismology is a method of exploration geophysics that uses the principles of seismology to estimate the properties of the Earth's subsurface from reflected seismic waves. The method requires a controlled seismic source of energy, such as dynamite/Tovex, a specialized air gun or a...
data into a quantitative rock-property description of a reservoir. Seismic inversion may be pre-or post-stack, deterministic, random or geostatistical, and typically includes other reservoir measurements such as well logs
Well logging
Well logging, also known as borehole logging is the practice of making a detailed record of the geologic formations penetrated by a borehole. The log may be based either on visual inspection of samples brought to the surface or on physical measurements made by instruments lowered into the hole...
and cores.
Introduction
Seismic surveysReflection seismology
Reflection seismology is a method of exploration geophysics that uses the principles of seismology to estimate the properties of the Earth's subsurface from reflected seismic waves. The method requires a controlled seismic source of energy, such as dynamite/Tovex, a specialized air gun or a...
are routinely performed to gather information about the geology
Geology
Geology is the science comprising the study of solid Earth, the rocks of which it is composed, and the processes by which it evolves. Geology gives insight into the history of the Earth, as it provides the primary evidence for plate tectonics, the evolutionary history of life, and past climates...
of an oil
Petroleum
Petroleum or crude oil is a naturally occurring, flammable liquid consisting of a complex mixture of hydrocarbons of various molecular weights and other liquid organic compounds, that are found in geologic formations beneath the Earth's surface. Petroleum is recovered mostly through oil drilling...
or gas
Natural gas
Natural gas is a naturally occurring gas mixture consisting primarily of methane, typically with 0–20% higher hydrocarbons . It is found associated with other hydrocarbon fuel, in coal beds, as methane clathrates, and is an important fuel source and a major feedstock for fertilizers.Most natural...
field. These surveys record sound waves which have traveled through the layers of rock and fluid in the earth. The amplitude
Amplitude
Amplitude is the magnitude of change in the oscillating variable with each oscillation within an oscillating system. For example, sound waves in air are oscillations in atmospheric pressure and their amplitudes are proportional to the change in pressure during one oscillation...
and frequency
Frequency
Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency...
of these waves can be estimated so that any side-lobe and tuning effects introduced by the wavelet may be removed.
Seismic data may be inspected and interpreted on its own without inversion, but this does not provide the most detailed view of the subsurface and can be misleading under certain conditions. Because of its efficiency and quality, most oil and gas companies now use seismic inversion to increase the resolution and reliability of the data and to improve estimation of rock properties including porosity
Porosity
Porosity or void fraction is a measure of the void spaces in a material, and is a fraction of the volume of voids over the total volume, between 0–1, or as a percentage between 0–100%...
and net pay.
There are many different techniques used in seismic inversion. These can be roughly grouped into two categories: pre-stack or post-stack, and seismic resolution or well-log resolution. The combination of these categories yields four technical approaches to the inversion problem, and the selection of a specific technique depends on the desired objective and the characteristics of the subsurface rocks. Although the order presented reflects the advancement in inversion techniques over the past 20 years, each grouping still has valid uses in particular projects or as part of a larger workflow.
Wavelet estimation
All modern seismic inversion methods require seismic data and a waveletWavelet
A wavelet is a wave-like oscillation with an amplitude that starts out at zero, increases, and then decreases back to zero. It can typically be visualized as a "brief oscillation" like one might see recorded by a seismograph or heart monitor. Generally, wavelets are purposefully crafted to have...
estimated from the data. Typically, a reflection coefficient
Reflection coefficient
The reflection coefficient is used in physics and electrical engineering when wave propagation in a medium containing discontinuities is considered. A reflection coefficient describes either the amplitude or the intensity of a reflected wave relative to an incident wave...
series from a well within the boundaries of the seismic survey is used to estimate the wavelet phase
Phase (waves)
Phase in waves is the fraction of a wave cycle which has elapsed relative to an arbitrary point.-Formula:The phase of an oscillation or wave refers to a sinusoidal function such as the following:...
and frequency. Accurate wavelet estimation is critical to the success of any seismic inversion. The inferred shape of the seismic wavelet may strongly influence the seismic inversion results and, thus, subsequent assessments of the reservoir quality.
Wavelet amplitude and phase spectra
Bandwidth-limited pulse
A bandwidth-limited pulse is a pulse of a wave that has the minimum possible duration for a given spectral bandwidth. Optical pulses of this type can be generated by mode-locked lasers...
are estimated statistically
Statistics
Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....
from either the seismic data alone or from a combination of seismic data and well control using wells with available sonic
Sonic logging
Sonic logging shows a formation’s interval transit time, designated Dt. It is a measure of a formation’s capacity to transmit sound waves. Geologically, this capacity varies with lithology and rock textures, notably porosity....
and density
Density logging
Density logging is a well logging tool determining rock bulk density along a wellbore. This is the overall density of a rock including solid matrix and the fluid enclosed in pores. Geologically, bulk density is a function of the density of the minerals forming a rock Density logging is a well...
curves. After the seismic wavelet is estimated, it is used to estimate seismic reflection coefficients in the seismic inversion.
When the estimated (constant) phase of the statistical wavelet is consistent with the final result, the wavelet estimation converges more quickly than when starting with a zero phase
Deconvolution
In mathematics, deconvolution is an algorithm-based process used to reverse the effects of convolution on recorded data. The concept of deconvolution is widely used in the techniques of signal processing and image processing...
assumption. Minor edits and "stretch and squeeze" may be applied to the well to better align the events. Accurate wavelet estimation requires the accurate tie of the impedance
Acoustic impedance
The acoustic impedance at a particular frequency indicates how much sound pressure is generated by a given air vibration at that frequency. The acoustic impedance Z is frequency dependent and is very useful, for example, for describing the behaviour of musical wind instruments...
log to the seismic. Errors in well tie can result in phase or frequency artifacts in the wavelet estimation. Once the wavelet is identified, seismic inversion computes a synthetic log for every seismic trace. To ensure quality, the inversion result is convolved with the wavelet to produce synthetic seismic traces which are compared to the original seismic.
Components of inversion
Inversion includes both seismic data and well data, where well data serves to add the low frequency below the seismic band and to constrain the inversion. Well logs are first conditioned and edited to ensure there is a suitable relationship between impedance logs and the desired properties. The logs are then converted to time, filtered to approximate the seismic bandwidth and edited for borehole effects, balanced and classified by quality.Seismic data is band-limited, reducing resolution and quality. To extend the frequency band available, low-frequency data is derived from log data, pre-stack depth or time migrated velocities and/or a regional gradient. High frequency can be derived from well control or geostatistical analysis.
Initial inversions are often run with relaxed constraints, starting with the seismic and then adding limited-trend data from the wells. This provides a rough overview of the reservoir in an unbiased manner. It is critical at this point to evaluate the accuracy of the tie between the inversion results and the wells, and between the original seismic data and the derived synthetics. It is also important to ensure that the wavelet matches the phase and frequency of seismic data.
Without a wavelet, the solution is not unique. Deterministic inversions address this problem by constraining the answer in some way, usually to well log data. Stochastic
Stochastic
Stochastic refers to systems whose behaviour is intrinsically non-deterministic. A stochastic process is one whose behavior is non-deterministic, in that a system's subsequent state is determined both by the process's predictable actions and by a random element. However, according to M. Kac and E...
inversions address this problem by generating a range of plausible solutions, which can then be narrowed through testing for best fit against various measurements (including production data).
Post-stack seismic resolution inversion
An example of a post-stack seismic resolution inversion technique is the Constrained Sparse-Spike Inversion (CSSI). This assumes a limited number of reflection coefficients, with larger amplitude. The inversion results in acoustic impedance (AI), which is the product of rock density and p-waveP-wave
P-waves are a type of elastic wave, also called seismic waves, that can travel through gases , solids and liquids, including the Earth. P-waves are produced by earthquakes and recorded by seismographs...
velocity. Unlike seismic reflection data (which is an interface property) AI is a rock property. The model generated is of higher quality, and does not suffer from tuning and interference caused by the wavelet.
CSSI transforms seismic data to a pseudo-acoustic impedance log at every trace. Acoustic impedance is used to produce more accurate and detailed structural and stratigraphic
Stratigraphy
Stratigraphy, a branch of geology, studies rock layers and layering . It is primarily used in the study of sedimentary and layered volcanic rocks....
interpretations than can be obtained from seismic (or seismic attribute
Seismic attribute
In reflection seismology, a seismic attribute is any quantity derived from seismic data using measured time, amplitude, frequency, attenuation or any combination of these. It intends to output a subset of the data that quantifies rock and fluid properties and/or allows the recognition of geological...
) interpretation. In many geological environments acoustic impedance has a strong relationship to petrophysical properties such as porosity, lithology
Lithology
The lithology of a rock unit is a description of its physical characteristics visible at outcrop, in hand or core samples or with low magnification microscopy, such as colour, texture, grain size, or composition. It may be either a detailed description of these characteristics or be a summary of...
, and fluid saturation.
A good (CSSI) algorithm
Algorithm
In mathematics and computer science, an algorithm is an effective method expressed as a finite list of well-defined instructions for calculating a function. Algorithms are used for calculation, data processing, and automated reasoning...
will produce four high-quality acoustic impedance volumes from full or post-stack seismic data: full-bandwidth impedance, bandlimited
Bandlimited
Bandlimiting is the limiting of a deterministic or stochastic signal's Fourier transform or power spectral density to zero above a certain finite frequency...
Impedance, reflectivity model, and low-frequency component. Each of these components can be inspected for its contribution to the solution and to check the results for quality. To further adapt the algorithm mathematics to the behavior of real rocks in the subsurface, some CSSI algorithms use a mixed-norm approach and allow a weighting factor between minimizing the sparsity of the solution and minimizing the misfit of the residual traces.
Pre-stack seismic resolution inversion
Pre-stack inversion is often used when post-stack inversion fails to sufficiently differentiate geologic features with similar P-impedance signatures. Simultaneous inversion solves for S-impedance and density, in addition to P-impedance. While many geologic features can express similar P-impedance characteristics, few will share combined P-impedance and S-impedance traits (allowing improved separation and clarity). Often a feasibility study using the wells logs will indicate whether separation of the desired lithotype can be achieved with P-impedance alone or whether S-impedance is also required. This will dictate whether a pre- or post-stack inversion is needed.Simultaneous Inversion (SI) is a pre-stack method that uses multiple offset or angle seismic sub-stacks and their associated wavelets as input; it generates P-impedance, S-impedance and density
Density
The mass density or density of a material is defined as its mass per unit volume. The symbol most often used for density is ρ . In some cases , density is also defined as its weight per unit volume; although, this quantity is more properly called specific weight...
as outputs (although the density output resolution is rarely as high as the impedances). This helps improve discrimination between lithology, porosity and fluid effects. For each input partial stack, a unique wavelet is estimated. All models, partial stacks and wavelets are input to a single inversion algorithm —enabling inversion to effectively compensate for offset-dependent phase, bandwidth, tuning and NMO
Normal Move Out
Normal Move Out is a term used in seismics and geophysics to describe the effect of the separation between receiver and source on the arrival time of a reflection that does not dip, abbreviated NMO...
stretch effects.
The inversion algorithm works by first estimating angle-dependent P-wave reflectivities for the input-partial stacks. Next, these are used with the full Zoeppritz equations
Zoeppritz equations
In seismology, the Zoeppritz equations describe how seismic waves are transmitted and reflected at media boundaries, which are boundaries between two different layers of earth....
(or approximations, such as Aki-Richards, for some algorithms) to find band-limited elastic reflectivities. These are in turn merged with their low-frequency counterparts from the model and integrated to elastic properties
Elastic modulus
An elastic modulus, or modulus of elasticity, is the mathematical description of an object or substance's tendency to be deformed elastically when a force is applied to it...
. This approximate result is then improved in a final inversion for P-impedance, S-impedance and density, subject to various hard and soft constraints. One constraint can control the relation between density and compressional velocity; this is necessary when the range of angles is not great enough to be diagnostic of density.
An important part in the inversion procedure is the estimation of the seismic wavelets. This is accomplished by computing a filter that best shapes the angle-dependent well log reflection coefficients in the region of interest to the corresponding offset stack at the well locations. Reflection coefficients are calculated from P-sonic, S-sonic and density logs using the Zoeppritz equations
Zoeppritz equations
In seismology, the Zoeppritz equations describe how seismic waves are transmitted and reflected at media boundaries, which are boundaries between two different layers of earth....
. The wavelets, with amplitudes representative of each offset stack, are input directly into the inversion algorithm. Since a different wavelet is computed for each offset volume, compensation is automatically done for offset-dependent bandwidth, scaling and tuning effects. A near-stack wavelet can be used as the starting point for estimating the far-angle (or offset) wavelet.
No prior knowledge of the elastic parameters and density beyond the solution space defined by any hard constraints is provided at the well locations. This makes comparison of the filtered well logs and the inversion outputs at these locations a natural quality control. The lowest frequencies from the inversion are replaced with information from the geologic model since they are poorly constrained by the seismic data. When applied in global mode a spatial control term is added to the objective function and large subsets of traces are inverted simultaneously. The simultaneous inversion algorithm takes multiple angle-stacked seismic data sets and generates three elastic parameter volumes as output.
The resulting elastic parameters are real-rock properties that can be directly related to reservoir properties. The more advanced algorithms use the full Knott-Zoeppritz equations and there is full allowance for amplitude and phase variations with offset. This is done by deriving unique wavelets for each input-partial stack. The elastic parameters themselves can be directly constrained during the seismic inversion and rock-physics relationships can be applied, constraining pairs of elastic parameters to each other. Final elastic-parameter models optimally reproduce the input seismic, as this is part of the seismic inversion optimization.
Post-stack log detail inversion
Geostatistical inversion integrates high resolution well data with low resolution 3-D seismic, and provides a model with high vertical detail near and away from well control. This generates reservoir models with geologically-plausible shapes, and provides a clear quantification of uncertaintyUncertainty
Uncertainty is a term used in subtly different ways in a number of fields, including physics, philosophy, statistics, economics, finance, insurance, psychology, sociology, engineering, and information science...
to assess risk. Highly-detailed petrophysical models are generated, ready for input to reservoir-flow simulation.
Geostatistics
Geostatistics
Geostatistics is a branch of statistics focusing on spatial or spatiotemporal datasets. Developed originally to predict probability distributions of ore grades for mining operations, it is currently applied in diverse disciplines including petroleum geology, hydrogeology, hydrology, meteorology,...
differs from statistics in that it recognizes that only certain outcomes are geologically plausible. Geostatistical inversion integrates data from many sources and creates models that have greater resolution than the original seismic, match known geological patterns, and can be used for risk assessment
Risk assessment
Risk assessment is a step in a risk management procedure. Risk assessment is the determination of quantitative or qualitative value of risk related to a concrete situation and a recognized threat...
and reduction.
Seismic, well logs and other input data are each represented as a probability density function
Probability density function
In probability theory, a probability density function , or density of a continuous random variable is a function that describes the relative likelihood for this random variable to occur at a given point. The probability for the random variable to fall within a particular region is given by the...
(PDF), which provides a geostatistical description based on histogram
Histogram
In statistics, a histogram is a graphical representation showing a visual impression of the distribution of data. It is an estimate of the probability distribution of a continuous variable and was first introduced by Karl Pearson...
s and variogram
Variogram
In spatial statistics the theoretical variogram 2\gamma is a function describing the degree of spatial dependence of a spatial random field or stochastic process Z...
s. Together these define the chances of a particular value at a particular location, and the expected geological scale and composition throughout the modeled area.
Unlike conventional inversion and geomodeling algorithms, geostatistical inversion takes a one-step approach, solving for impedance and discrete property types or lithofacies at the same time. Taking this approach speeds the process and improves accuracy.
Individual PDFs are merged using bayesian inference
Bayesian inference
In statistics, Bayesian inference is a method of statistical inference. It is often used in science and engineering to determine model parameters, make predictions about unknown variables, and to perform model selection...
techniques, resulting in a posterior PDF conditioned to the whole data set. The algorithm determines the weighting of each data source, eliminating potential bias. The posterior PDF is then input to a Markov Chain Monte Carlo
Markov chain Monte Carlo
Markov chain Monte Carlo methods are a class of algorithms for sampling from probability distributions based on constructing a Markov chain that has the desired distribution as its equilibrium distribution. The state of the chain after a large number of steps is then used as a sample of the...
algorithm to generate realistic models of impedance and lithofacies, which are then used to co-simulate rock properties such as porosity. These processes are typically iterated until a model emerges that matches all information. Even with the best model, some uncertainty remains. Uncertainty can be estimated using random seeds to generate a range of realizations. This is especially useful when dealing with parameters that are sensitive to change; an analysis of this sort enables greater understanding of development risk.
Pre-stack log-detail inversion
Amplitude versus offsetAmplitude Versus Offset
In geophysics, amplitude versus offset or amplitude variation with offset is a variation in seismic reflection amplitude with change in distance between shotpoint and receiver. It is also referred as AVA...
(AVO) (AVA) geostatistical inversion incorporates simultaneous AVO (AVA) inversion into the geostatistical inversion algorithm so high resolution, geostatistics, and AVO may be attained in a single method. The output model (realizations
Realization (probability)
In probability and statistics, a realization, or observed value, of a random variable is the value that is actually observed . The random variable itself should be thought of as the process how the observation comes about...
) are consistent with well log information, AVO seismic data, and honor rock property relationships found in the wells. The algorithm also simultaneously produces elastic properties (P-impedance, S-impedance and density) and lithology volumes, instead of sequentially solving for lithology first and then populating the cell with impedance and density values. Because all output models match all input data, uncertainty can be quantitatively assessed to determine the range of reservoir possibilities within the constraining data.
AVA geostatistical inversion software uses leading-edge geostatistical techniques, including Markov Chain Monte Carlo (MCMC) sampling and pluri-Gaussian lithology modeling. It is thus possible to exploit "informational synergies" to retrieve details that deterministic inversion techniques blur out or omit. As a result, geoscientists are more successful in reconstructing both the overall structure and the fine details of the reservoir. The use of multiple-angle-stack seismic volumes in AVA geostatistical inversion enables further evaluation of elastic rock properties and probable lithology or seismic facies and fluid distributions with greater accuracy.
The process begins with a detailed petrophysical analysis and well log calibration. The calibration process replaces unreliable and missing sonic and density measurements with synthesized values from calibrated petrophysical and rock-physics models. Well log information is used in the inversion process to derive wavelets, supply the low frequency component not present in the seismic data, and to verify and analyze the final results. Next, horizon and log data are used to construct the stratigraphic framework for the statistical information to build the models. In this way, the log data is only used for generating statistics within similar rock types within the stratigraphic layers of the earth.
Wavelet analysis is conducted by extracting a filter from each of the seismic volumes using the well elastic (angle or offset) impedance as the desired output. The quality of the inversion result is dependent upon the extracted seismic wavelets. This requires accurate p-sonic, s-sonic and density logs tied to the appropriate events on the seismic data. Wavelets are extracted individually for each well. A final "multi-well" wavelet is then extracted for each volume using the best individual well ties and used as input to the inversion.
Histograms and variograms are generated for each stratigraphic layer and lithology, and preliminary simulations are run on small areas. The AVA geostatistical inversion is then run to generate the desired number of realizations, which match all the input data. The results are quality control
Quality control
Quality control, or QC for short, is a process by which entities review the quality of all factors involved in production. This approach places an emphasis on three aspects:...
led by direct comparison of the inverted rock property volumes against the well logs. Further QC involves review by a multidisciplinary team of all input parameters and the results of the simulation. Analysis of multiple realizations produces mean (P50) property cubes or maps. Most often these are lithology or seismic facies
Facies
In geology, facies are a body of rock with specified characteristics. Ideally, a facies is a distinctive rock unit that forms under certain conditions of sedimentation, reflecting a particular process or environment....
cubes and predicted lithology or facies probabilities
Probability
Probability is ordinarily used to describe an attitude of mind towards some proposition of whose truth we arenot certain. The proposition of interest is usually of the form "Will a specific event occur?" The attitude of mind is of the form "How certain are we that the event will occur?" The...
, but other outputs are also possible. Selected lithology and facies cubes are also generated for P15 and P85 probabilities (for example). Reservoir 3-D bodies of hydrocarbon
Hydrocarbon
In organic chemistry, a hydrocarbon is an organic compound consisting entirely of hydrogen and carbon. Hydrocarbons from which one hydrogen atom has been removed are functional groups, called hydrocarbyls....
-bearing units are captured with their corresponding rock properties, and the uncertainty in reservoir size and properties is quantified.
Further reading
- Caulfield, C., Feroci, M., Yakiwchuk, K. "Seismic Inversion for Horizontal Well Planning in Western Saskatchewan", Evolving Geophysics Through Innovation, p. 213-214.
- Chakrabarty, C., Fossey, J., Renard, G., Gadelle, C. "SAGD Process in the East Senlac Field: From Reservoir Characterization to Field Application", No. 1998.192.
- Contreras, A., Torres-Verdin, C., Chesters, W., Kvien, K., Globe, M., "Joint Stochastic Inversion of Petrophysical Logs and 3D Pre-Stack Seismic Data to Assess the Spatial Continuity of Fluid Units Away from Wells: Application to a Gulf-of-Mexico Deepwater Hydrocarbon Reservoir", SPWLA 46th Annual Logging Symposium, June 26–29, 2005.
- De Barros, Dietrich, M., "Full Waveform Inversion of Shot Gathers in Terms of Poro-elastic Parameters", EAGE, London, June 2007.
- Deutsch, C., Geostatistical Reservoir Modeling, New York: Oxford University Press, 2002, 376 pages.
- Francis, A., "Limitations of Deterministic and Advantages of Stochastic Seismic Inversion", CSEG Recorder, February 2005, p. 5-11.
- Hasanusi, D., Adhitiawan, E., Baasir, A., Lisapaly, L., van Eykenhof, R., "Seismic Inversion as an Exciting Tool to Delineate Facies Distribution in Tiaka Carbonate Reservoirs, Sulawesi – Indonesia", Proceedings, Indonesian Petroleum Association, Thirty-First Annual Convention and Exhibition, May 2007.
- Russell, B., Hampson, D., "The Old and the New in Seismic Inversion", CSEG Recorder, December 2006, p. 5-11.
- Stephen, K., MacBeth, C., "Reducing Reservoir Prediction Uncertainty by Updating a Stochastic Model Using Seismic History Matching", SPE Reservoir Evaluation & Engineering, December 2008.
- Vargas-Meleza, L., Megchun, J., Vazquez, G., "Petrophysical Properties Estimation by Integrating AVO, Seismic Inversion and Multiattribute Analysis in a 3-D Volume of Playuela, Veracruz", AAPG International Conference: October 24–27, 2004, Cancun, Mexico.
- Wang, X., Wu, S., Xu, N., Zhang, G., "Estimation of Gas Hydrate Saturation Using Constrained Sparse Spike Inversion: Case Study from the Northern South China Sea", Terr. Atmos. Ocean. Sci., Vol. 17, No. 4, 799-813, December 2006.
- Watson, I., Lines, L., "Seismic Inversion at Pike’s Peak, Saskatchewan", CREWES Research Report, Volume 12, 2000.
- Zou, Y., Bentley, L., Lines, L., "Integration of Reservoir Simulation with Time-Lapse Seismic Modeling", 2004 CSEG National Convention.
External links
- American Association of Petroleum Geologists
- Australian Society of Exploration Geophysicists (ASEG)
- Earthworks Seismic Inversion company
- Understanding Stochastic Inversion
- Fugro-Jason, Jason Geoscience Workbench (JGW)
- CGGVERITAS, Simultaneous Elastic Inversion
- European Association of Geoscientists and Engineers
- Petroleum Exploration Society of Australia (PESA)
- Society of Exploration Geophysicists
- Society of Petroleum Engineers
- Society of Petrophysicists and Well Log Analysts (SPWLA)
- The University of Texas at Austin Petroleum and Geoscience Engineering Reading Room
- Geological Survey Publications Warehouse