An Introduction to Velocity Modelling and Depth Conversion in Hydrocarbon Exploration

Note – this is an introductory guide and some concepts have been simplified for a general audience in order to enable dialogue between geophysicists and other specialists

Why Depth Convert?

Seismic data consists of images of the sub-surface geology which is interpreted by geophysicists to provide an understanding of potential geological features where oil and gas may be found. Reflection seismic works by sending a sound wave from a source (e.g. air gun, dynamite or vibroseis) into the earth and recording the resultant reflections using a receiver (a geophone or a hydrophone). Following some mathematical processing the reflections are transferred into an image which may be a 2D section or a 3D volume. All seismic data is initially in the time domain, that is the time taken for the wave to travel to the reflecting event and return to the receiver sensor. The time is therefore two way or TWT.

But, we need to have interpretations in depth relative to an elevation datum. The volumes in potential prospects are calculated using depth maps. Well drillers need the prognoses for the planned well in metres (or feet if you work in America) rather than milliseconds. In order to do this we use sound velocities from the formula; Distance = time x velocity. 

Building the required velocity model can be relatively simple or quiet complicated, depending on the level of detail, availability of velocity data, and the type of desired final product. What must also be borne in mind is that any velocity model has significant uncertainties which need to be evaluated and quantified. Just because the map has metres or feet in the scale does not mean that it is the sole representation of reality

Velocity of Sound in Different Media

First let us look at what the velocities actually represent.

Sound velocity is dependent on the medium that the wave travels through. P wave Velocities vary from 1480 m/s for water to about 6000 m/s for hard rocks such as marble. Velocity is dependent on the following variables

1.      Mineralogy – Some minerals have distinctive velocities, for example halite (rock salt) is around 4500 m/s, Quartz is around 6000 m/s and coal is around 2500 m/s

2.      Porosity – the Wylie equation where 1 / velocity = ((1-porosity) / velocity matrix ) + 1 ((1-porosity) / Velocity fluid , gives the relationship between velocity and porosity. Basically the more porous the rock the slower the velocity of sound through it. Sedimentary rocks compact as they are buried deeper, losing porosity and increasing in velocity

3.      Fluid content. Water has a velocity of about 1480 to 1500 m/s depending on salinity, oil has a velocity of about 1200 m/s and gas (methane) has a velocity of 446 m/s. This velocity difference leads to seismic anomalies formed by some gas bearing rocks.

For more detail please go to the Stanford University course at https://pangea.stanford.edu/courses/gp262/Notes/8.SeismicVelocity.pdf

Velocity Definitions

·        Instantaneous Velocity – the speed of sound measured at a specific point in time

·        Average Velocity – the velocity from the seismic datum to a point in depth or time - Vave = Depth / Time (one way)

·        Interval Velocity – The mean velocity within a defined layer or interval – Vint = Depth thickness ( or isochore) / time thickness (or isochron)

·        V0 or velocity at time or depth zero is the velocity of the rock at the datum, as if it had been decompacted (i.e. before compaction due to burial had reduced the porosity and increased the velocity). Time zero can be sea level, ground level or in the case of relatively deep water the seabed

·        Velocity Gradient – the rate of change of velocity with depth or time due to compaction, also known as k

·        Processing velocities – velocities used in seismic data processing including

o  V Rms – root mean square velocity – an automatically calculated velocity used to correct the droop on seismic gathers due to the offsets on the receiver cable ( Normal move out – NMO)

o  Migration velocities – the velocity model used in seismic migration – a technique to correctly positon reflectors which are mis-located due to ray path refraction – for more explanation of this topic please go to this EAGE talk by Claudio Strobbia (25 minutes NO EQUATIONS - https://www.youtube.com/watch?v=re_nAZ88uSs

·        Velocity Anisotropy – velocities vary dependent on the direction that the sound wave travels. This is due to the structure of the rocks. Layered rocks such as shales have high anisotropy while homogenous rocks such as halite have lower anisotropy. This is why seismic velocities are about 10 to 15 % faster than the vertical velocities we need for depth conversion. For more about anisotropy please go to this EAGE talk by Etienne Robein ( 23 minutes - https://www.youtube.com/watch?v=gjuKMx6uzHM&t=578s) 

Figure 1. Velocity Definitions

Sources of Velocity information

There are several sources of velocity information

·        Sonic Logs – a sonic log is a device which is lowered down a borehole which measures the instantaneous velocity by sending a soundwave into the formation and picking up the refracted wave at a sensor. The measurement is the travel time between the source and receiver and is measured in microseconds per foot. This can be converted into metres per second. ( for more information please see (2 minutes) - https://www.youtube.com/watch?v=e1ISSNcyWMw) The sonic log may be integrated to form a complete velocity profile although this is not very accurate due to frequency differences between the sonic log and seismic data.

·        Vertical Seismic Profiling (VSP) and Checkshots. This process involves a seismic source at surface (usually an airgun) and a sensor located down the well. The seismic wave travels through the rock and is detected at the receiver giving a one way travel time, enabling time to depth calibration.

o  a checkshot refers to the first arrival at the receiver giving the travel time and is used to scale an integrated sonic log. The VSP includes subsequently recorded data that can be used to produce a fine resolution seismic image local to the well or a corridor stack which is a seismic trace along the well path which can be used to calibrate the surface seismic data.

o  Seismic while drilling uses a either a seismic source located on the surface and a receiver located in the drilling assembly, or a surface receiver and the drill bit as a source. This technique is used to monitor drilling on the seismic data in real time and helps predict hazards ahead of the drilling bit. 

Figure 2 – VSP surveying

·        Seismic Processing Velocities  - as defined above – for more about seismic processing please see this video - https://www.youtube.com/watch?v=Ta_3jv80M_g&t=523s 55 minutes

Figure 3. Explanation of seismic velocities

Figure 4 – Checkshots and Sonic logs

Depth Conversion Methods

Now that we have defined velocities we can look at methods of depth conversion.

Before depth converting we must consider the following:

·        What is the objective? Is it producing a map, planning a well or building a complex earth model?

·        How much data do I have? Do I have wells? Do the wells have any sonic logs or checkshots / VSP? Do I have seismic processing velocities and what spatial interval are they sampled at? Do I have a seismic migration velocity model? When and how was it built?

·        How reliable is my data? Well locations accurate? What about seismic data locations? How do different seismic surveys’ velocities compare? Were the seismic velocities picked on a Monday morning after the Houston Texans lost a game?

·        How complex is my geology? Where are the interfaces between layers of significantly different velocity? Is here a presence of a high velocity layer such as halite (salt) or limestone? How do the velocities vary laterally?

Layering – dividing the earth model into layers with similar velocity behaviour

In very simple geology we can use a single layer going directly from the seismic datum to the target horizon. This can happen if there is a near constant velocity or if the velocity varies with depth in a predictable manner which can be modelled using a function (see below for functions). In reality the earth is complex, but can normally be subdivided into stacked layers of relatively constant rock 

Figure 5. Example of a velocity layering scheme from the Southern North Sea, Permian Salt Basin. An area with a complex geological history. Some layers can be merged for simplicity and most areas are nowhere near this complex.

Depth conversion Methods

What we need to bear in mind is that all depth converted maps are estimates. There is always some uncertainty and there is a need to quantify and understand these uncertainties. It is necessary to use an appropriate method or set of methods for the task and available data at hand.

Figure 6. Depth conversion methods in terms of complexity, which means cost, time, detail and relative difficulty in implementing. Some methods can be done easily by the seismic interpreter, more complex methods may need specialist support.

Table 1. Using appropriate depth conversion methods for different project stages in the E&P cycle.

The Simplest Method – Using Average Velocities

This method involves compiling time and depth pairs from well data to your target horizon using a single layer. The time depth pairs are converted into average velocity values and then interpolated (gridded) to produce a velocity map. The velocity map is then multiplied by the time map to produce a depth map.

Depth = TWT/2 * (Average velocity)

Pros – a very simple and quick method.

Cons – not very accurate if there is any complexity

Interval Velocities

This is a method that uses constant velocities for each layer. The interval velocity is the depth thickness (isochore) divided by the time thickness (isochron). The interval velocities calculated at the wells are then interpolated (gridded) to produce a map, alternatively a single value may be used for example for the water layer in marine data

Depth = sum of thicknesses for the individual layers

Thickness = ((TWT base – TWT top)/2) * Interval velocity; Interval velocity = (depth base – depth top of layer) / 9(TWT base-TWT top)/2)

Pros – simple to do, no need for specialist software, takes some geological complexity into account, can incorporate wells without check shots

Cons – Layers need to be relatively homogenous, breaks down if there are significant lateral velocity variations

Velocity Functions

A velocity function is a mathematical formula which relates velocity (or depth directly) to travel time. In sediments velocity tends to increase with depth due to compaction of the sediment which is caused by burial. Functions can be used as a single layer or as part of a layering scheme. There are two basic ways to use a velocity function:

a.      A function with non-variable parameters. Since a uniform value is used which would not fit all of the wells, any wells would need to be fitted with a correction surface to produce a final map. – this is most useful in frontier areas with limited well control

b.      A function with a variable parameter which is interpolated based on well data. This method automatically fits the wells and is best in areas with a fair amount of well control.

Functions can be linear, exponential or polynomial

Figure 7. The V0/K function. V0 is the velocity at the surface datum (for example seabed in marine data), K is the rate at which velocity increases with compaction due to burial.

Figure 8. Polynomial Velocity function – suitable for areas with simple overburden

Other functions such as midpoint depth, midpoint time, isochore / isochron etc. are also used.

Using Seismic Velocities in Depth Conversion

Seismic processing velocities have the advantage of being a regularly sampled grid (with no spatial bias) with a 3D survey and a regularly sampled set of lines in a 2D survey. Typical intervals are 1 km. While a 3D survey should be consistent it will still probably require some smoothing. Two 2D lines would have less consistency and a multi survey dataset will have even less consistency. Seismic processing velocities are converted into interval velocities using the Dix formula:

Vint = [(t2 VRMS22 ? t1 VRMS12) / (t2 ? t1)]1/2,

Where:

Vint = interval velocity

t1 = trave ltime to the first reflector

t2 = travel lime to the second reflector

VRMS1 = root-mean-square velocity to the first reflector

VRMS2 = root-mean-square velocity to the second reflector.

Several things need to be borne in mind when using seismic velocities for depth conversion

1.      The Dix formula breaks down for thin intervals, it should not be used for intervals under 500 ms TWT thickness, and should really be avoided in intervals under 1000 ms thickness

2.      Seismic velocities show significant anisotropy (due to having to travel diagonally rather than vertically) and need to be corrected to produce vertical velocities needed for depth conversion. The correction factors rang from 0.95 to 0.85. Generally, if we have well data the well velocities are used to correct seismic velocities.

3.      Seismic velocities are designed to give the optimum seismic image, not for depth estimation. This can lead to inconsistencies which would need to be smoothed out during the depth conversion process

Using Depth Domain Seismic Directly

Some seismic is available in depth domain, that is the Z scale is in metres or feet rather than milliseconds. This has some advantages: What you see is close to what you will get, most velocity distortions (such as pull ups or push downs) should be eliminated and structures should be in roughly the right place. A depth section is also easier to work with while explaining concepts to non- geoscientists including the drillers who are planning wells together with you. Depth domain data is also good for rapid screening to identify potential features which you will want to look at in more detail.

However, just because it is labelled metres in the Z domain does not mean that this is true! There is still uncertainty due to velocity modelling and this can get lost when people work only in the depth domain. Depth migrated data is normally also available stretched back into the time domain using the migration velocity model in order to be able to be compared with other time domain data and for depth conversion sensitivities to be possible. Depth domain data comes in a variety of forms. It is essential for the interpreter to know how it originated:

1.      Depth stretch – this is time domain data that has been stretched into depth domain – how was the velocity model built? , By whom and where?, how good is the fit to any wells?

2.      Isotropic depth migrated data. Prior to new algorithms being developed between 2000 and 2005. Depth migrated data was produced using algorithms that dis not take velocity anisotropy into account very well. The volumes produced using these methods had good imaging resolution and horizontal geometry but were not quite correct vertically, with poor fit to wells. They could be supplied unstretched or with a 90% stretch that had the wells in roughly the right place. Most interpreters were aware of this and generally worked in time domain with this data

3.      Anisotropic depth migrated data. Algorithms which fully took anisotropy into account are now standard and any post 2010 data has probably used them (you really need to check by reading the processing reports, yes, I know it is 300 pages but please just do it). Anisotropic data is more accurate in terms of imaging and depth placement and this data can be safely shown to management. Having said that I would still interpret in time domain for depth sensitivities.

Building a velocity model for depth migration is a complex task. The nest models are made by an interpreter working closely with the processor and running several tomographic iterations. These models can be loaded into interpretation software and visualised to give a greater understanding of the geology. However we must bear in mind that these models are made to create an optimum image rather than for depth conversion purposes.

The worst models are made by a processor working alone on speculative, non-exclusive data in an area where they don’t know the geology with tight deadlines. I am aware of an instance where some false structures were generated by poor contractor processing which went away after interpretation.

Stochastic Depth Conversion.

Deterministic depth migration is aimed at producing a single answer. This may be OK for a specific task such as initial interpretation to identify a prospect but gives us no information about the range of volumes that the prospect or field may contain. Several different deterministic cases can give you some alternatives but we still do not know what the possible range of outcomes is. More deterministic cases will increase our knowledge (or opinions) but don’t really get there in terms of giving a full distribution of uncertainty.

Stochastic depth conversion relies on modelling a parameter within the depth conversion model in a stochastic manner to produce a set of realisations. Typically, this would involve a model for V0 in a velocity function model or the anisotropy correction factor in a processing velocity based model.

The program will produce many (up to 500) realisations. Each realisation will fit any constraints such as wells and may be bounded by common sense ranges in order to avoid ridiculous looking realisations. These realisations can then be ranked and statistically analysed to produce a volumetric range with average, low case and high case values. In a producing field we can build reservoir models for high mid and low cases, and then history match these models against production data in order to determine how likely they are to be close to reality.

Additional products will include a range map showing areas of maximum uncertainty and iso-probability maps which show the likelihood of any point on the map being above any hydrocarbon water contact. These maps can be used to plan the location of any appraisal well which would be focussed on reducing uncertainty.

Figure 9. Fictional example of a histogram showing the volumetric distribution from a stochastic depth conversion study

Figure 10. Examples of depth realisations from a fictional depth conversion study shown as a depth cross section. Note all realisations fit the horizon markers at the two wells but have different shapes.

Figure 11. Idealised QC maps produced during stochastic depth conversion studies. The iso-probability map shows the probability of being above the hydrocarbon water contact at any point. The uncertainty map shows the range between different realisations at any point. The range is zero at the wells and increases with distance away from the wells.

Conclusions

Velocity modelling and depth conversion is a bit of a Cinderella in geophysics. This can be because depth conversion is done at the back end of the interpretation project and is pressed for time, we may have limited data in terms of wells and seismic velocities, limited interpreter knowledge (and skill in using more complex velocity modelling software packages) and limited management understanding of the impact of uncertainties in this area.

However, modelling velocity and its associated uncertainties is essential to safe and successful exploration and development of hydrocarbon assets. This includes producing depth maps for input to geological models and well prognoses.

·        Evaluate – need to properly frame the velocity modelling

What data do we have? (wells, seismic processing velocities, depth migration velocity models) , What do we need to deliver? (prospect map, field reservoir model, well prognosis, uncertainty) , what is the geology like? (any complex layers)

·        Create – producing velocity models and depth maps

Delivering appropriate maps and models. Deterministic, multi deterministic or stochastic? Done by the interpreter or by a specialist adviser in partnership with the interpreter?

·        Explain – QC tools and explanatory displays to understand what is happening

Backed out average velocity maps, iso-probability maps, uncertainty maps, spill point maps and depth section views can be used to show and explain the uncertainties that exist to fellow members of your sub-surface development team.