AVO, Seismic Inversion, Machine Learning and Predictive Modelling and the Economics of the Play – New Age for Oil and Gas Exploration

BRIAN WM. SCHULTE

SPROTT SCHOOL OF BUSINESS – CARLETON UNIVERSITY / SCHIEFER RESERVOIR CONSULTING, BRIAN.SCHULTE@GMAIL488.COM

DAVID GRAY

GEOMODELING TECHNOLOGY CORP. SENIOR VICE PRESIDENT INTEGRATED SOLUTIONS, DAVID.GRAY@GEOMODELING.COM

RENJUN WEN

GEOMODELING TECHNOLOGY CORP. CEO, RENJUN.WEN@GEOMODELING.COM

Abstract

Proxy modelling using seismic attributes significantly speeds up our understanding of what is going on between wells, adding substantially to the value that geoscience brings to our businesses. One of the most valuable uses of seismic data is to extract fluid and lithological information for reservoir characterization. Amplitude versus Offset (AVO) analysis and seismic inversion (deterministic or stochastic) are valuable tools for doing this. To do reservoir characterization with AVO and seismic inversion, we need to calibrate the AVO attributes and inversion products to geological, petrophysical and production data with the producing and non-producing wells in an area. To accomplish this, it generally takes large amounts of time and effort to confirm anomalies. It has been found in the past with AVO and seismic inversion that the interpretations were inconsistent and not repeatable from user to user. However, it is now possible to encapsulate a lot of this work using multivariate techniques.

Today’s reservoir characterization involves a multi-disciplinary approach using cross plots, multiple seismic attributes, multivariate analysis through colour blending, etc., to integrate geology, geophysics, petrophysics, and engineering to understand porosity, water saturation, lithofacies, permeability and barriers to resolve fluid flow.

Geostatistical, multi-linear regression or NN (neural network) analysis can be used to estimate any elastic constant or well log, such as Young’s Modulus, Density, Stress, Porosity, Gamma Ray, Facies, etc., from the seismic attributes. These attributes volumes can then be incorporated into the geomodel to help interpolate rock properties across it by, e.g., using co-kriging. These volumes bridged the issue of relating seismic data quantitatively to reservoir properties.

Then we began to develop predictive modelling or what they call proxy modelling in the oil and gas industry, which is the development of models that can forecast future events, trends, or patterns based on historical well data, production data, Distributed Fibre Optical Sensing (DFOS or DOFS), microseismic, seismic, AVO attributes, seismic inversion, spectral decomposition, velocities, etc. Using the seismic in these models helps us understand what is happening away from the well locations.

Businesses have been using these models to make informed decisions for future endeavours, and we can use them to make predictions especially about production, which can help with economical issues such as:

1. Which leases to bid on
2. Assess mergers and acquisitions
3. Pad locations, well direction and spacing
4. Infrastructure
5. Acquiring funding.

These are all important aspects of the business where seismic data can add substantial value.

Introduction

In the 20th century ability to store copious amounts of data was developed. Now, in the 21st century, we are moving towards learning how to analyze this data to find trends that will allow us to do better business planning and reduce costs in many industries. What we see in other businesses is that aggressive analytic competitors are becoming leaders in their industry, and that success is due to the exploitation of the data (Davenport, 2006).

Many feel that these are not technologies that businesses can afford to adopt later (Ali, 2022), so some in the oil and gas industry are examining how to use predictive modelling, or what they call proxy modelling. By implementing predictive modelling, oil and gas operators want to improve the production of their fields (increase product) and reduce their operating expenses (lower costs), which reduces their break-even prices for that field and allows oil and gas operators to be still profitable if the price of natural gas or oil falls.

Predictive modelling uses historical data, so it is ideal as many oil and gas companies continue to practise capital discipline, focusing on developing their current producing fields rather than drilling frontier exploratory wells, which can cost millions to drill and years to develop to their maximum production. Oil and gas operators are staying away from exploration wells because many investors are concerned about a drop in demand for oil and gas as countries implement policies against selling internal combustion engine (ICE) vehicles.

Development of this technology began with AVO analysis and seismic inversion, where we were able to map fairways for prospects from these seismic attributes and de-risk the play using multiple properties from different disciplines. This was the beginning of geomodelling.

Geomodels are a 3D representation of the current distribution of petrophysical and geomechanical properties in the context of the present-day structural framework, built using data from different disciplines. Their goal is to integrate and bridge the gap across the subsurface disciplines, which (Garner, 2020):

1. Improves the effectiveness of the integrated teams
2. Increases the Net Present Value (NPV)
3. Builds efficiencies (timelines, production, carbon emissions, etc.).

It is the teamwork among the asset team that empowers the successful geomodelling project. The following data tends to be used in the geomodel:

1. Well log curves
2. Well tops
3. Completion information
4. Pressure data
5. Production data
6. Seismic data
7. Seismic inversion products
8. Spectral decomposition
9. Geometrical attributes (structural) which enhance the visibility of the geometrical characteristics within seismic data. Examples include dip, azimuth, continuity, etc.
10. Physical attributes (stratigraphical) which enhance the lithological properties inherited in seismic data. Examples include frequency, amplitude, phase, porosity, etc.
11. Seismic horizons.

Within the geomodel, all this data must follow standards for consistency. When geomodelling first began, only a few geomodels were created because these geomodels took months to build because of the need to clean up the data and apply standards.

Today, with quality control (QC) tools, we can help identify outliers in the input data through their inconsistency with other forms of data in the geomodel. The geomodel itself provides consistency, which in turn allows for the clean-up of the data.

Geomodels also utilize geostatistics methods such as kriging, kriging with external drift and co-kriging, which all use variograms (Brown, 2022) to interpolate properties. The strength of using geostatistics for interpolation is it can capture the anisotropy of the underlying geologic variables through the spatial covariance model. This will yield maps that are more geologically plausible (Wikipedia contributors, 2022).

Geomodels are used to create reservoir simulations that predict fluid flow through porous media or reservoir rock. Reservoir simulations are quality controlled using:

1. Production history, where historical field production and pressures are compared to those calculated in the simulation.
2. Time-lapse (4D) seismic, where we predict the changes in the 4D using the Reservoir Simulation and then update the reservoir simulation with what we see in the 4D.

The reservoir simulation is used to calculate the economics of the play by figuring out the distinct types of reserves (Schulte and Felton, 2020):

• Proved Developed Producing (PDP), which is the current oil and gas production and reservoir analysis of ultimate recovery (type curves) from existing wells.
• Proved Developed Non-Producing (PDNP), which is the oil and gas that has been verified in existing wells but is not yet produced.
• Proved Undeveloped (PUD) – oil and gas that may be recovered from new development wells on undrilled acreage, which are completed in the same geological formation as the existing direct offset wells yet still require substantial capital expenditures to drill these new wells. This information can come from the geomodel and reservoir simulation.

The Geomodel is driven by the well data due to the resolution issues between the seismic and well log data, and because the seismic inversion products tend to be average impedances across an interval.

Stochastic inversion was then developed, which produces property models at the same vertical scale of resolution as the well logs. Still, it uses the seismic information between wells and produces a distribution of impedances similar to those seen in logs so cut-offs can be used (Shrestha and Boeckmann, 2009).

Stochastic inversion uses a background model (usually derived from wells, but it could be from seismic velocities or other methods) for the low frequencies, seismic frequencies for the mid frequencies and variograms for the high frequencies (Figure 1).

Figure 1. Frequency spectrum of a stochastic inversion showing the low frequencies come from the low-frequency well model, the mid frequencies from the seismic and the high frequencies from the variogram (geostatistics), taken from Schulte (2022).

Stochastic inversion integrates the fine vertical sampling of the log data with the dense areal sampling of the seismic data to create detailed, high-resolution models of rock properties such as acoustic impedance, density or velocity utilizing geostatistical algorithms (Shrestha and Boeckmann, 2009; Haas and Dubrule, 1994).

Stochastic inversion, geomodelling and reservoir simulation all take considerable amounts of time.

Due to the time element, some are looking at predictive modelling, which is used in many industries. In the oil industry, some have referred to predictive modelling as proxy modelling, which tends to be created using historical data for brown fields. The main reason they are looking at predictive modelling is the run-times of seconds for the proxy models rather than weeks for a geomodel or stochastic inversion and hours or days for a reservoir simulation (Mohaghegh, 2011).

The advantages of using proxy modelling are (Mohaghegh, 2011):

1. Short development time
2. Low development cost
3. Fast track analysis
4. Practical capability to quantify the uncertainties associated with the static model.

Figure 2 looks at the progression of the different methodologies to do reservoir characterization to understand fluid flow and production.

Figure 2. Review of the progression of the different methodologies to do reservoir characterization over the last 20 years. The goal of reservoir characterization is to understand fluid flow and production with each technique illuminate fluids and fluid flow in their own way, adopted from Schulte (2022).

AVO Attributes

We began developing fairway maps with AVO and AVO attributes from the seismic integrated with data from other disciplines (Figure 3), which showed the most favourable areas of hydrocarbon accumulation with minimal geologic risks. This helped operators to decide the most valuable lease blocks or packages of land by using (Schulte, 2019):

1. Observation of direct hydrocarbon indicators (DHIs) such as flat spots
2. Identification of hydrocarbon traps in the geological structure
3. Understanding of the regional structure that will aid in constraining the geological history and identifying potential hydrocarbon sources
4. Identification of lithology and fluids within the rock using AVO cross plots, AVO attributes, and offset stacks.

This was the beginning of geomodelling.

Figure 3. Integration of different data into the interpretation software taken from Schulte (2014).

Geomodel

Geomodels are being used by many operators in the industry. Part of this is due to many utilizing Paradigm or Petrel software for their interpretation. Most companies in the early days of geomodelling hired geomodellers to build the geomodel. These tended to be specialists in Petrel but were seated in a technology group and were contracted by the asset to build this model.

We found that part of the issue with building the geomodel was that the data was not standardized. Operators began to develop standards that should be applied to the data in the geomodels so that the geomodel can be repeated in a short time. The goal of the geomodel is to build a reservoir simulation so reserves (Proved Developed Production) can be booked and fluid movements can be predicted to understand where to drill the next well or place the next injection well.

With the geomodel we want to deliver for each facies: water saturation (Sw), shale volume, permeabilities (horizontal [Kh] and vertical (Kv]) (Figure 4), and porosity.

Figure 4. Horizon showing the distribution of Kh and KV and the heteorgeneity. Image courtesy of Geomodeling Technologies Corp.

When we started using geomodels in unconventional plays, we began to recognize the heterogeneity within the shales and other lithologies within unconventional plays.

When we first started to develop shale and other unconventionals, many considered plays like the Montney as being homogeneous shales, and the emphasis was on reducing costs by implementing “factory drilling,” where there is a succession of laterally drilled wells from a common pad with common completions (Yarus and Yarus, 2014). With this type of drilling, we were not as successful as we wanted. Even in the best of these wells, only about 40% of the completions produce >90% of the production. Therefore, there is a significant opportunity to improve the economics of these plays.

There were issues with parent-child wells and interference due to poor understanding of the spacing of the horizontal laterals, staying in zone while drilling, short laterals, not understanding where the fractures were going, etc., that affected the economics of the plays.

Well Data

Well data was initially used in the geomodel due to:

1. Difference of sampling between wells and seismic
2. Difficulty in properly modelling the petro-elastic relationships
3. Products from deterministic inversion are average impedances over larger intervals than the vertical spacing in the geomodel
4. Deterministic inversions exaggerate reservoir connectivity and underestimate net reservoir volumes.

Well logs are utilized by the different disciplines (Figure 5). They are used commonly to:

1. Identify lithology
2. Differentiate between porous and non-porous zones
3. Identify fluids in the rock and their contacts.
4. Map temperature
5. Map pore fluids pressure and tectonic stresses
6. Map the distribution of oil, gas, and water saturation.

Figure 5. How the different disciplines use well logs, taken from Schulte (2019).

In a study, there can be 100’s well logs from different vintages, and they have different mnemonics, may be calibrated differently, may be mislabelled, have artifacts created by borehole conditions, come from different logging tools, water or oil-based mud systems, and different processing parameters.

Well logs are also acquired in “runs”, so many runs may make up a continuous well log. To make a continuous well log, we may have to splice the different runs together. At times we may even have to select which is the better run to be used to be spliced together.

Many just assume well logs are perfect; they are not. There can be many issues with well logs.

One of the easiest things we can do is normalize the well logs (Figure 6).

Figure 6. These are gamma ray logs for 3 wells. The curve on the right is before normalization and the curve on the left is after normalization. On the third well, notice how the gamma ray has changed after normalization. The problem with well logs is that they may not have been calibrated properly. Image courtesy of Geomodeling Technology Corp.

The quality control for machine learning can be used to identify well logs that are outliers. We can see in 200 wells, with the QC for the machine learning, that we may have 10 to 20 outliers. These 10 to 20 outliers are more manageable than trying to work with 200 wells.

It is important that we fix or condition the well logs for our work since well logs are the basis for a lot of what we do. If we do not do this work before a seismic inversion, the seismic inversion will be affected.

Some companies are selling conditioned well logs that have been edited for well conditions, which includes inferior quality or incomplete curves being replaced with the best curves available, multiple runs spliced into a complete well log, generic mnemonics used, etc. to provide better well logs for the geomodel work.

With the geological tops, each formation has distinctive characteristics that appear similar from one well to the next. This is how formations are identified in the subsurface. Machine learning can be used to pick these tops, so again, we produce geological tops that are more accurate and consistent for the geomodel. It also reduces the time spent picking geological tops.

With seismic, most use it to build the structural framework in the geomodel to define the major formation boundaries, which include faulting, folding, and unconformities. A Discrete Fracture Network (DFN) can be easily built using artificial intelligence, producing attributes such as Fault Likelihood, to identify faults within the seismic data (Figure 7). The Fault Likelihood can notice faults that can be easily missed by a human interpreter and provides a more complete set of faults and fractures than picking by hand.

Figure 7. Fault likelihood. Geomodeling Technology Corp.

A geomodel is a multidisciplinary, interoperable, and updatable database about the subsurface. It is the numerical equivalent of a three-dimensional geological map complemented by a description of physical quantities in the domain of interest. An integrated multidisciplinary team builds the geomodel bringing together data from various sources such as: well data, well tops, completion information, pressure data, seismic data, seismic inversion products, seismic horizons, etc. All this data needs to follow standards. The workflow for the geomodel is in Figure 8.

Figure 8. Geomodelling workflow, taken from Schulte (2022).

We have excellent rock properties information from the well data, but it is only a single point in space. We want to interpolate what is happening between the wells, and to do that, we need to incorporate the seismic data as a guide. Unfortunately, seismic data does not directly transform to some of the rock properties we want for our geomodel, such as porosity, permeability, lithology, saturation, etc.

The rock properties that seismic directly transform to, to name a few, are:

1. P-wave velocity (seismic velocities, P-wave inversion product)
2. Shear velocity (shear velocity inversion product)
3. Density (density inversion product)
4. Acoustic Impedance
5. Shear Impedance
6. Poisson Ratio
7. Young’s Modulus
8. Lambda-rho
9. Mu-rho
10. Stresses (the seismic itself is a stress measurement).

Many assume that an elastic property, often Acoustic Impedance, represents some reservoir property such as:

1. Porosity
2. Bitumen
3. Hydrocarbons

There may be linear relationships proved in cross plotting of the well data where acoustic impedance or one of the other elastic properties does correspond to these reservoir properties, but it is not a direct transformation. In this case, that seismic attribute can be used as a guide for interpolating the corresponding well log.

When using deterministic inversion products, we need to be aware that they are average impedances over intervals, and they will exaggerate reservoir connectivity and underestimate net reservoir volumes. When these matter, use stochastic inversions.

For the facies modelling, we can use seismic facies, defined as a group of seismic amplitude variations with characteristics that distinctly differ from those of other facies (Lake et al., 2005).

We can determine seismic facies using cross plots. Cross plots enable the simultaneous and meaningful evaluation of multiple attributes, most often by a standard 2D cross plot, or more attributes can be evaluated using a 3D cross plot and colour with well data (Chopra et al., 2003). The goal of using cross plots is to isolate specific rock properties such as lithology or fluid type. Cross plots also help illuminate subtle information that may not be seen if we just look at the attributes separately.

For reflection data, we can use the Intercept versus Gradient cross plot (Figure 9). Notice that the Intercept versus Gradient cross plot represents lithology, fluid content and porosity at the same time. We also have a mirror where we have the top of the sands and the base of the sands. After we have defined the polygons, we can output the facies model. With the facies model, we can use the polygons to identify the top and base of the rocks, or we can design the polygons to eliminate the top and base of the sands. It depends upon what the interpreter wishes.

Figure 9. Cross plot of Intercept versus Gradient, taken from Schulte (2022).

With seismic inverted products, we have transformed the seismic reflection data into quantitative rock properties so we can look inside the sand instead of at the top or base of the sand (Figure 10).

Figure 10. Cross plot of Lambda-rho versus Mu-rho, taken from Schulte (2022).

With seismic inversion cross plots, many are using rock physics templates (RPT) instead of polygons. RPTs are becoming the basis for reservoir characterization, and they are charts and graphs generated using rock physics models constrained by the local geology. RPTs are lithology and fluid differentiation tools that are powerful in validating hydrocarbon anomalies in undrilled areas and aid in seismic interpretation and prospect evaluation (Datta Gupta et al., 2012).

One of the cross plots that we can use with RPTs is Vp/Vs versus acoustic impedance (AI). Different RPTs e.g., constant-cement model using contact theory, constant-cement and patchy cemented sandstone can be superimposed on this cross plot, and a seismic facies volume can be created (Kabanda, 2017).

There are two ways to include seismic such as the seismic facies volume into the kriging of the data in the geomodel by using:

1. Cokriging, which takes advantage of the covariance between two or more regionalized variables that are related when the main attribute of interest (well data) is sparse, and the related secondary information (seismic) is abundant.
2. Kriging with external drift, which has an assumption that the primary variable is linearly related to the secondary variable.

Neural Network

As mentioned, the prediction of petrophysical parameters for the geomodel utilizing seismic data is a common challenge due to the lack of linear relationships with seismic elastic attributes.

Using neural networks (NN), we have the possibility to estimate any elastic constant or well log, such as Vp, Vs, Density, Vp/Vs, Porosity, Saturation, etc., using multiple seismic attributes with various weights (Figure 11). The neural network finds the best transform, which relates multiple seismic attributes to any well property. Using multiple samples from a multitude of attributes with various weights removes the wavelet, like what happens in the inversion, and the neural network can be computed at sub-seismic rates, which increases the resolution beyond what is achieved with the seismic inversion (Ross, 2016).

Figure 11. Workflow of the neural network taken from Schulte (2022).

The NN can also be utilized to QC the various seismic attributes because it uses correlation-based attribute selection, which ranks the features according to the highest correlation. If we are looking at porosity, and our well modelling shows there is a linear relationship between acoustic impedance and porosity, acoustic impedance should be one of the highest ranked attributes.

There is this ongoing discussion around whether NNs are affected by multicollinearity (two or more features are highly correlated/dependent). The issue with multicollinearity is that it leads to the creation of redundant information, which skews the results in the regression model. What happens is that a change in one variable causes a change in another, causing the model to fluctuate a lot, and results to become unstable, varying a lot given a minor change in the data (Wu, 2020).

One argument is that NNs are black boxes, so if it performs to a given expectation, we will never know the impact of multicollinearity, so most think NNs are not affected by multicollinearity.

One of the ways to look at multicollinearity is the correlation matrix (Figure 12), and we can then choose which attribute we wish to get rid of and which one to keep. We can also use Principal Component Analysis which reduces the dimension of data by decomposing data into a number of independent factors (Wu, 2020).

Figure 12. Correlation matrix showing how different variables are correlated. Warm colours indicate strong correlation between variables, while cool tones represent low correlations. Geomodeling Technology Corp.

Staying in zone

Prestack depth migration is being used by many operators to stay in zone because it handles lateral velocity variations between wells, which allows for the zone of interest to be better positioned in the seismic and reduces the risk of getting out of zone.

The velocities used in prestack depth migration are constrained by the geology and are interval velocities which reflect the velocities of the rock (sonic velocities), and anisotropy can be incorporated.

Staying in the sweet spot or zone of interest will increase production. The sweet spots tend to be high porosity zones which causes the rate of penetration to increase, and the well will be drilled faster, reducing the cost of the well (Rauch-Davies et al., 2018; Schulte, 2018).

Prestack depth imaging is also used to achieve better resolution due to the use of:

1. Tomography, which uses raypaths to correct for the residual velocity that accommodates ray-bending effects. The interval velocities are not derived by Dix but by globally solving a linear system of equations (Zhou et al., 2003; Schulte, 2012)
2. Automatic High Density, High Resolution Continuous (AHDHRC) velocities and etas to represent anisotropy which utilizes the higher-order moveout equation (Alkhalifah and Tsvankin, 1995)
3. Velocity variation with offset
4. Spectral enhancement.

If we have prestack time migration, the seismic interval velocities are used to convert the time data to depth.

The biggest challenge comes back to dealing with the overburden velocities, which can create velocity pull-up because it takes a shorter time for the rays to travel through the rock or push-down because it takes a longer time for the rays to travel through the rock. Figure 13 is a diagram of an overthrust in the near-surface, which can cause velocity push-down in the zone of interest, which are the channel sands. If not corrected, these effects could affect the planning of the horizontal lateral. Staying in zone is a Key Performing Indicator (KPI) for many operators. KPIs are derived from the most critical constraints in our value chain, and staying in zone directly affects our production and the success of the well. Comparisons of key KPIs help in comparing the performance of other operators in an area. Some operators have tied the percentage of staying in zone back to yearly bonuses.

Another issue is some may just use the well data, which is sparse (Figure 14, left side) for velocities, or they may use the seismic stacking velocities (Figure 14, right side), which are denser. The well velocities and seismic stack velocities can be Kriged with External Drift to create a better velocity field. To do this, the well velocities need to be compared to the seismic stacking velocities, and a scalar correction needs to be applied that corrects for anisotropy. Anisotropy is the difference between vertical (well logs) and horizontal (seismic stacking) velocities. The scalar should be in the range of 10% to 20%.

Figure 13. Diagram of a reverse or thrust fault in the near surface over the target channel sand.

Figure 14. Left is the well map distribution, and on the right are the well and seismic velocity points showing the difference in density of velocity points between the two. These velocities could never be properly estimated with just the well information. Image courtesy of Geomodeling Technology Corp.

There is also automatic high density, high resolution continuous velocities or full waveform inversion (FWI) velocities, which are velocities at every sample on every CDP or crossline and inline; others use the P-wave velocity from the inversion.

The neural network can use multiple attributes to build the velocity field with the depth-stretched sonic logs as the target. This may be a better solution because it will produce a high-density, high-resolution volume that converts seismic data from time to depth quickly and as accurately as possible away from well control (Zhang et al., 2023).

We can use this volume to do a better depth stretch, especially to improve the results in the overburden. Seismic interval velocities overlaid on the seismic can indicate compartments in the data, especially for reservoir engineering, pore pressure zones, or hydrocarbons. With Rose and Associates DHI consortium, one of the attributes to verify an AVO play is a drop of interval velocity across the zone, and so high-resolution velocities are a useful corroboration of AVO anomalies.

Seismic Facies

At the wells, we have an understanding of the facies, but we want to gain an understanding of the facies away from the wells, and it can be done utilizing cross plots or neutral network to create the facies volume (Figure 15).

Figure 15. Facies volume. Facies 1 – 3 are all reservoir sands in this figure, with increasing amounts of mud in each, with Facies 1 yellow, Facies 2 blue, and Facies 3 orange. Facies 1 is the best reservoir sand and Facies 3 is the worst reservoir sand. Geomodeling Technology Corp.

Seismic Inversion

One of the reasons why Lancaster & Whitcombe (2000) and Connolly (2010) developed the coloured inversion was to do inversion without the use of a low-frequency model that could leak through. The coloured inversion also does not require a wavelet that can change with travel time or can contain errors because of how the wavelet was calculated (Schulte et al., 2019). Coloured inversion is used by many interpreters and is in a lot of the seismic interpretation software packages because it is quick and easy to use to invert seismic data and can be implemented by anyone.

NN can be used to create inversion products such as Vp, Vs, Density, Vp/Vs, Poisson Ratio, Lambda-Rho, Mu-Rho, etc. (Figure 16). As mentioned before, using multiple attributes with various weights removes the wavelet, which is like what happens in the deterministic inversion, and the neural network can be computed at sub-seismic rates, which increases the resolution (Ross, 2016), creating a higher resolution seismic inversion which would allow thinner beds to be resolved.

Figure 16. Lambda-rho inversion from the neural network. Faults are visibly present in the data and form possible compartments. There is also channelling present in the data. Image courtesy of Geomodeling Technology Corp.

The inversion created by the NN may not suffer from the exaggeration of reservoir connectivity that the deterministic inversion products suffer from.

With the NN higher resolution data, we will be able to see subtle faults within the data, which will help with the planning of the horizontal lateral to stay in zone (Figure 16 and Figure 17). It will also help us find any critically stressed faults that may cause induced seismicity, especially if we are near the basement, like where we are currently developing the Duvernay.

Figure 17. A subtle fault within the subsurface can cause us to get out of zone and miss out on production.

Stochastic Inversion

The purpose of stochastic seismic inversion is to produce the property models at the same vertical scale of resolution as the well control but use the seismic information between wells (Shrestha and Boeckmann, 2009). It integrates the fine vertical sampling of the log data with the dense areal sampling of the seismic data to create detailed, high-resolution rock properties such as acoustic impedance, density or velocity models using geostatistical algorithms, as shown in Figure 18 (Shrestha and Boeckmann, 2009; Haas and Dubrule, 1994).

Figure 18. Diagram showing that stochastic inversion integrates the reservoir model from well data for the fine vertical sampling with the dense areal sampling of the reservoir model from the seismic data (taken from Schulte, 2022).

With stochastic inversion, the lower frequencies, below the minimum seismic frequency, tend to come from the well model; the middle frequencies come from the seismic; and the frequencies above the seismic frequencies come from the variograms (Figure 1).

The vertical variogram is typically easy to derive from well logs, while the horizontal variogram tends to be defined more empirically and can be derived from secondary information such as the seismic when well control is sparse (Delbecq and Moyen, 2010).

Stochastic inversion is a statistical process in which several realizations are possible. There is not just a single realization that is the solution, and we need to analyze the stochastic results to translate the uncertainties from the elastic attributes into the geological / engineering properties needed, such as the P10, P50 and P90 cases (Delbecq and Moyen, 2010).

The workflow for the stochastic inversion is illustrated in Figure 19.

Figure 19. Workflow for the stochastic inversion, taken from Schulte (2022).

Predictive Modelling

Predictive modelling is the development of models that can forecast future events, trends, or patterns based on historical data. It has been used by businesses, manufacturing, marketing, insurance, banking, finance, healthcare, retail, and weather forecasts to detect future risks and promising opportunities. It has been successfully used to make informed decisions for future endeavours such as mergers and acquisitions, in a shortened timeframe and at a lower cost. In a survey done by Merit Mile, it was found that 37% of companies said the CEO and COO are typically the primary drivers for the adoption of predictive modelling, so we see the Board of Directors talking about this (Sternal, 2020).

Benefits of Predictive Modelling

Geomodels, deterministic and stochastic inversions and reservoir simulations take time to build. Predictive modelling or proxy modelling can be done in short periods of time. Most of the time is spent on selecting the attributes to build the predictive model. The attributes chosen for the prediction model help us identify which attributes we wish to use in interpretation.

Predictive modelling can help us to figure out key factors that affect the outcome of the success of the play, such as:

1. Which leases to acquire
2. Assess mergers and acquisitions
3. Well locations
4. Infrastructure
5. Acquiring funding.

To decide which leases to bid on, assess mergers and acquisitions, or where to place the horizontal lateral well locations, we can look at production prediction in an area. This will give us a lot of information (Figure 20).

Figure 20. Production prediction utilizing fairway mapping, where red is no production, yellow is higher risk production, and green is the best production in the area. This example shows two blocks up in a lease sale, and it allows us to choose which one we will bid higher for.

Reserves evaluation

With the production prediction, we can also figure out our distinct types of reserves:

• Proved Developed Producing (PDP)
• Proved Developed Non-Producing (PDNP)
• Proved Undeveloped (PUD).

If we know the amount of production possible, we can decide on the lease infrastructure, which affects our lease operating expenses (LOE) and the takeaway capacity. Knowing the takeaway capacity allows us to put in storage tanks or a pipeline, especially if we have gas as this will reduce flaring and reducing flaring will reduce greenhouse gas emissions.

In many areas, we are seeing anti-flaring policies, which means if we cannot pipe the gas out, we may have to shut the well in. This is a problem in basins like the Eagle Ford and Permian when they are producing both oil and natural gas. It also puts stress on the available pipeline, and in some areas, it has become hard for us to build new pipelines due to environmental pushback.

Issues with pipeline capacity at hubs also cause the price of natural gas at the hub to fall. Understanding the amounts of natural gas we may produce can help us plan better.

We also see this offshore where planning offshore infrastructure is so important – for example, meticulously designing the Floating Production Storage and Offloading (FPSO). If the FPSO is too big, it is a waste of equipment, and if it is too small, it will hinder production.

Understanding Fractures

We can also utilize microseismic to predict where the microseismic events will occur to help mediate induced seismicity issues, help us to predict the hydraulic fracturing and, most importantly, help to determine the spacing between the horizontal laterals to avoid interference which will affect the production between them (Figure 21).

With new wells in plays like the Bakken, Permian, and Eagle Ford having less barrels of oil per lateral foot, it shows we are getting out of the Tier 1 rocks we have been drilling in and are moving into Tier 2 and 3 rocks.

Understanding the fractures distribution will help us decide how to improve our production in the lesser quality rock.

Figure 21. Microseismic density prediction shotgun barrel plot, where warm colours indicate high event density.

Financing with PDP

There is a push towards divesting away from oil and gas due to climate change and ESG investing, which has made it hard for oil & gas operators to obtain funding through traditional sources of financing such as equity investment and issuance of high-yield bonds or reserve-based lending (RBL) (Paraskova, 2022).

This has caused oil and gas to use PDP securitization, which is when oil & gas operators use cash from their oil and/or gas production as collateral for the notes placed with investors.

In 2022, private firms have sold to investors $3.9 billion in PDP securitizations, up from just $1.2 billion in 2021 (Paraskova, 2022).

Understanding our Proved Developed Producing earlier allows us to obtain Proved Developed Producing securitizations to further develop the field, especially the Proved Developed Non-Producing (PDNP) and Proved Undeveloped (PUD) reserves.

Obstacles to Predictive Modelling

There are obstacles to predictive modelling, such as:

1. Obstacles in management – there needs to be support from management to make predictive modelling and its required software an operational solution.
2. Obstacles in data – we need access to substantial relevant data from a range of disciplines, and, as mentioned before, the data needs to be conditioned to be used in the predictive model.
3. Obstacles with modelling – the biggest issues are time, which proxy modelling solves, and overfitting, which is when the model has too many inputs, and therefore it is memorizing the training data. Effects of overfitting are:
   
   1. Model performs poorly on new data, and the interpretation of the model is unreliable.
   2. The project is too ambitious in the kind of model that can be built.

Selection and QC of data for predictive modelling

Considerable amounts of data are being generated during the development and operation of unconventional reservoirs. Statistical methods such as predictive modelling use this plethora of data to supply data-driven insights into production performance and are currently gaining popularity in the industry.

Just like geomodels, they integrate and bridge the technical disciplines, and teamwork is necessary for prediction modelling to be successful (Figure 22).

Figure 22. Diagram showing how we take all the data from all the disciplines and use QC tools to reduce these attributes to create a better combination of attributes for the predictive model. Geomodeling Technology Corp.

Correlated attributes in predictive modelling

Many see the implementation of machine learning and predictive modelling as a means to replace jobs but to be successful, we need to bridge computer and data science with domain expertise, so machine learning and predictive modelling should augment what geoscientists and engineers do. Like the geomodel, this needs to be an integrated team effort. Realistically, engineers and geoscientists who know how to create value from our data will replace engineers and geoscientists who don’t.

To be able to select the right data for the predictive modelling, we need to use:

1. Correlation matrix to identify correlated attributes
2. Cross Entropy
3. Cross plots of prediction & original data points, in terms of training, validation, testing
4. SHAP plots (Lundberg and Lee, 2017) that quantify the magnitude and direction of a feature’s effect on a prediction.
5. Partial Dependence Plots (PDP) and Individual Conditional Expectation (ICE) plots.
6. Histograms.

As mentioned with NN, there are issues with multicollinearity, which reduces the power of your model to find independent variables that are statistically significant. For predictive models, it does not influence predictions, the precision of the predictions, forecasts, and the goodness-of-fit statistics (Khanna, 2020). The issue really comes back to correlated variables supplying redundant information and removing one does not affect R² that much.

Training, Validation, and Testing

Why do we need to look at training and validation, and testing sets is because (Shah, 2021):

• Training set is necessary to train the model and learn the parameters.
• Validation supplies an unbiased evaluation of the model fit during hyperparameter tuning of the model.
• Testing set determines whether the model can generalize correctly on unseen data.

With training, validation, and testing data, we are looking for indications of overfitting where the training data has a low error rate and the test data has a high error rate. To avoid overfitting, we can pause the training process earlier, known as “early stopping”, or we can reduce the complexity of the model by eliminating less relevant inputs.

Another issue, which we call underfitting, occurs when you pause too early, or we exclude too many key features, the model has not trained for enough time, or the input variables are not significant enough to decide a meaningful relationship between the input and output variables.

What we are looking for is the sweet spot between overfitting and underfitting so that we can show a dominant trend and apply it broadly to new datasets (Figure 23).

Figure 23. Diagram showing Prediction and R or slope of the best-fit line for one attribute. The horizontal axis is the measured data and the vertical axis is the prediction. The line is a 1:1 line around which the data points should fall. It appears that the data is not underpredicted because if a range of lines were fitted to this data, the 1:1 line would fall within it. Image courtesy of Geomodeling Technology Corp.

Cross entropy

Deep learning requires a loss/cost function to optimize the model during training. Cross entropy is a loss function, and the goal is to minimize the loss function to optimize the model (Koech, 2020). It is also used with predictive models as an error metric that compares the actual results with the predicted results. In Figure 24, we see that the best validation is obtained at 170 iterations.

Figure 24. Diagram showing a cross plot of Cross Entropy versus Iterations which shows the best validation occurs around 170 iterations. Image courtesy of Geomodeling Technology Corp.

SHAP plots

With predictive modelling, there is an issue with a higher number of features because the error increases with the increase in the number of features in the dataset (Tetera, 2020). We want to reduce the dimensionality while maintaining as much information as possible (Marcílio and Eler, 2020).

To reduce problems like these, we can use SHAP plots (Lundberg and Lee, 2017) which tell us how much each factor in a model contributed to the prediction and explains the predictions of a model to select features. With a SHAP waterfall plot (Figure 25), we see how much each factor contributed to the model’s prediction when compared to the mean prediction. With the SHAP values, the positive SHAP value means a positive impact on the prediction, leading the model to predict 1, and the negative SHAP value means there is a negative impact, leading the model to predict 0 (Wang, 2022). Large positive/negative SHAP values show that the feature had a significant impact on the model’s prediction.

Figure 25. SHAP waterfall plot to visualize the feature importance. Distance to Well has the largest influence, and Eigenstructure coherence has the least influence of these attributes on the NN result. The SHAP values are all positive which indicate all the attributes have a positive impact on the prediction. Diagram courtesy of Geomodeling Technology Corp.

The benefits of using SHAP values over other techniques are (Wang, 2022):

1. SHAP values not only show feature importance but show whether the feature has a positive or negative impact on predictions.
2. Calculate SHAP values for each individual prediction and know how the features contribute to that single prediction.
3. SHAP values are used to explain a large variety of models, including linear regression, tree-based models and NNs. In contrast, other techniques can only be used to explain limited model types.

There are also SHAP scatter plots that plot the value of the feature on the x-axis and the SHAP value of the same feature on the y-axis, and we can colour the points using a chosen feature which interacts the most with the feature so we can understand the relationships. SHAP scatter plots show how the model depends on the given feature. In Figure 26, we see the SHAP values contribute for distances that are proximal to the well and get lesser as distance increases away from the well.

Figure 26. SHAP scatter plot showing the Distance to Well on the x-axis, and the SHAP value of the same feature on the y-axis, coloured by Most Positive Curvature. Vertical dispersion of the data points represents interaction effects. Diagram courtesy of Geomodeling Technology Corp.

Partial dependence plots (PDPs)

Partial dependence plots are based on the idea of visualizing the relationship between a subset of the features and the response while accounting for the average effect of the other predictors in the model. To do this, we vary the value for one of the features and record the resulting predictions and then take the average. We are isolating the relationship of the feature (O’Sullivan, 2022; Greenwell, 2017).

Partial Dependence plots are misleading in the presence of substantial interactions because they are averaged predictions, and any strong heterogeneity can conceal the complexity of the modelled relationship between the response and predictors of interest (Goldstein et al., 2015; Greenwell, 2017). To overcome this issue, Goldstein, Kapelner, Bleich, and Pitkin developed the concept of individual conditional expectation (ICE) plots.

Individual Conditional Expectation (ICE) plots

ICE plots are useful when there are interactions in your model. That is, if the relationship of a feature with the target variable depends on the value of another feature (O’Sullivan, 2022). ICE plots provide insights into heterogeneous relationships created by interactions (Figure 27).

Figure 27. Example of a PD plot and ICE plot for gamma ray by mean frequency. The red line is the PD plot. The recommendation is to display the PD plot and ICE plot together so the average relationship as well as the heterogenenous relationship between the attribute and prediction can be displayed. Diagram courtesy of Geomodeling Technology Corp.

Histogram of Importance

It shows the importance of the variable in building the model (Figure 28).

Figure 28. Histogram of importance. Notice the top attributes in order are: Density, Depth, Distance to well, Acoustic Impedance, Poststack Amplitude, Mu, Relative Acoustic Impedance, Poisson Ratio and Most Positive Curvature. Diagram courtesy of Geomodeling Technology Corp.

Selection of Data / Conclusion

The various tests we produce to analyze the deep learning NN allow us to determine the attributes we should use to build the predictive model. Using seismic data and attributes allows us to understand and predict what is occurring between the wells.

In the past, with some of the NNs, there was no analysis of the attributes, which allows for the data selection, and a plethora of attributes was used. It became an exercise of inputting multiple attributes and looking at the results, so these NNs became a black box (Figure 29).

Figure 29. Selection of data for the NN to produce a lithology volume using the Gamma Ray as the training data. The Acoustic Impedance and Near Offset Stack are correlated, Vp/Vs and Poisson Ratio are correlated, Mid stack and Full stack are correlated, and Far stack and Fluid Factor are correlated. Out of 11 attributes, we have 8 correlated, so this is redundant data going into the NN.

The tools to look at a correlated matrix allow us to decide which data is correlated, and we can reduce the number of attributes used, so we do not overfit the model. With overfitting of the model, it will perform well on the training data but will likely perform very poorly on unseen data.

When doing machine learning, we can think of the underlying pattern we wish to learn from the data and call this the signal.

While noise is the irrelevant data or randomness in the dataset and with overfitting, we can not separate the signal from the noise. Therefore, we want to remove redundant data, but we need to choose the right datasets to keep and which ones to remove based on domain expertise (Figure 30).

One of the goals of using machine learning is to build a model that will be trained to predict production, microseismic, or other valuable information. We typically use multiple seismic attributes to build this predictive model, but well or geomodel attributes could also be used.

Like the NN, we need to be selective of the attributes we choose so that we can pick up on the information that is the signal and separate out the noise, which is the randomness.

Lots of predictive models fail due to not picking the right attributes. Using various techniques such as NN validation, testing, SHAP values, Partial Dependence Plots, ICE plots, geology constraints, and domain knowledge improves the selection of attributes. We also want to make sense of the prediction by understanding the relationship between the target and input features, impact, exceptions, etc.

Figure 30. Selection of data for the NN to produce a lithology volume using the Gamma-Ray as the training data. The data is better selected after removing correlated attributes, examining SHAP values, visual inspection, domain knowledge and talking to other disciplines.

We want to use these predictive or proxy models to make decisions quicker to affect our bottom-line on a play. Sometimes the faster we can decide, the better, especially if we beat our competition in placing wells in an area or in lease sales. The timing of drilling a well is important due to operators and contractors having to work together, especially in terms of fracking.

Building a geomodel or creating a stochastic inversion and then doing a reservoir simulation takes time. With upcoming lease sales or opportunities to buy a company, a decision needs to be made quickly with the data we have.

It is better to use the predictive or proxy model to be able to make these decisions than to participate in a lease sale blindly and acquire the wrong lease blocks or acquire a company and realize too much was paid or miss out on a good asset by bidding too low. We can also look at other factors with the predictive model, such as the length of the horizontal laterals or water and sand tonnage for the well. Being able to lower these costs can reduce our costs of drilling yet still yield optimal production.

It is these decisions and the timing of making these decisions that affect how competitive we can be in a play which will ultimately affect our stock price.

About the Authors

Brian Wm. Schulte attended The University of Calgary, graduating in 1989 with a Bachelor of Science in Geology and a minor in Geophysics. Brian has worked in seismic processing, acquisition, interpretation, rock physics, and petrophysics. Some of the companies he worked for are Gale-Horizon, Schlumberger, Vastar (a division of Arco), BP, Explora Seismic Processing (ESP), Geokinetics, Talisman Energy Inc., and Repsol. Brian also served as an Instructor of Petroleum Engineering Technology at Houston Community College-NE Energy Institute. He made outstanding contributions as a member of the Program Industry Advisory Committee that led to several program recognitions and students’ successes. Brian is working at his own consulting company Schiefer Reservoir and is now attending Sprott School of Business – Carleton University obtaining an MBA in Business Analytics. Brian has served as the Chief Editor of the Recorder since 2018.

David Gray frequently lectures on geophysics and has presented over 100 papers at various technical conferences and luncheons. His career has included positions at Geomodeling, Nexen, Veritas, CGG, Subsurface Dynamics, Ikon, and CNOOC, and he has made notable contributions to quantitative seismic interpretation, seismic geomechanics, and seismic fracture characterization. He holds several patents. David received a Bachelor of Science degree in Honors Geophysics from the University of Western Ontario (1984) and a Master of Mathematics degree in Statistics from the University of Waterloo (1989). David is Senior Vice President Integrated Solutions at Geomodeling, and currently a member of SPE, SEG, CSEG, EAGE, and APEGA.

Renjun Wen is the founder and CEO of Geomodeling Technology Corp, an international geosciences software company with headquarters in Calgary, Canada. Renjun holds a Ph.D. in Petroleum Geology from the Norwegian University of Science and Technology, Norway (1995). He worked for Statoil Research Center in later 1995 and founded Geomodeling in later 1996 in Calgary. He has published papers in the fields of reservoir modelling, sub-seismic fault modelling, geostatistical application in image processing, and seismic attribute analysis. Dr. Wen has collaborated with and consulted for major international oil companies to develop innovative reservoir modelling software in the SBED consortium. Dr. Wen is an editorial board member of Petroleum Geoscience (EAGE), and a registered Professional Geologist in Alberta (APEGGA).