In
geophysics
Geophysics () is a subject of natural science concerned with the physical processes and Physical property, properties of Earth and its surrounding space environment, and the use of quantitative methods for their analysis. Geophysicists conduct i ...
and
reflection seismology
Reflection seismology (or seismic reflection) is a method of exploration geophysics that uses the principles of seismology to estimate the properties of the Earth's subsurface from reflection (physics), reflected seismic waves. The method requir ...
, amplitude versus offset (AVO) or amplitude variation with offset is the general term for referring to the dependency of the
seismic attribute
In reflection seismology, a seismic attribute is a quantity extracted or derived from seismic data that can be analysed in order to enhance information that might be more subtle in a traditional seismic image, leading to a better geological or geo ...
,
amplitude
The amplitude of a periodic variable is a measure of its change in a single period (such as time or spatial period). The amplitude of a non-periodic signal is its magnitude compared with a reference value. There are various definitions of am ...
, with the distance between the source and receiver (the offset). AVO analysis is a technique that
geophysicists can execute on seismic data to determine a rock's
fluid content,
porosity
Porosity or void fraction is a measure of the void (i.e. "empty") spaces in a material, and is a fraction of the volume of voids over the total volume, between 0 and 1, or as a percentage between 0% and 100%. Strictly speaking, some tests measure ...
,
density
Density (volumetric mass density or specific mass) is the ratio of a substance's mass to its volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' (or ''d'') can also be u ...
or
seismic velocity
A seismic wave is a mechanical wave of acoustic energy that travels through the Earth or another planetary body. It can result from an earthquake (or generally, a quake), volcanic eruption, magma movement, a large landslide and a large man ...
, shear wave information, fluid indicators (hydrocarbon indications).
The phenomenon is based on the relationship between the
reflection coefficient
In physics and electrical engineering the reflection coefficient is a parameter that describes how much of a wave is reflected by an impedance discontinuity in the transmission medium. It is equal to the ratio of the amplitude of the reflected ...
and the
angle of incidence and has been understood since the early 20th century when
Karl Zoeppritz wrote down the
Zoeppritz equations. Due to its physical origin, AVO can also be known as amplitude versus angle (AVA), but AVO is the more commonly used term because the offset is what a geophysicist can vary in order to change the angle of incidence. (See diagram)
Background and theory

For a seismic wave reflecting off an interface between two media at
normal incidence, the expression for the reflection coefficient is relatively simple:
:
,
where
and
are the
acoustic impedance
Acoustic impedance and specific acoustic impedance are measures of the opposition that a system presents to the acoustic flow resulting from an acoustic pressure applied to the system. The International System of Units, SI unit of acoustic impeda ...
s of the first and second medium, respectively.
The situation becomes much more complicated in the case of non-normal incidence, due to mode conversion between
P-waves
A P wave (primary wave or pressure wave) is one of the two main types of elastic body waves, called seismic waves in seismology. P waves travel faster than other seismic waves and hence are the first signal from an earthquake to arrive at an ...
and
S-waves
__NOTOC__
In seismology and other areas involving elastic waves, S waves, secondary waves, or shear waves (sometimes called elastic S waves) are a type of elastic wave and are one of the two main types of elastic body waves, so named because t ...
, and is described by the Zoeppritz equations.
Zoeppritz equations
In 1919,
Karl Bernhard Zoeppritz derived four equations that determine the amplitudes of
reflected
Reflection is the change in direction of a wavefront at an interface between two different media so that the wavefront returns into the medium from which it originated. Common examples include the reflection of light, sound and water waves. The ...
and
refracted
In physics, refraction is the redirection of a wave as it passes from one medium to another. The redirection can be caused by the wave's change in speed or by a change in the medium. Refraction of light is the most commonly observed phenome ...
waves at a planar interface for an incident P-wave as a function of the angle of incidence and six independent elastic parameters. These equations have 4 unknowns and can be solved but they do not give an intuitive understanding for how the reflection amplitudes vary with the rock properties involved.
[Shuey, R. T. ]985
Year 985 ( CMLXXXV) was a common year starting on Thursday of the Julian calendar.
Events
By place
Europe
* Summer – Henry II (the Wrangler) is restored as duke of Bavaria by Empress Theophanu and her mother-in-law Adelaide at an ...
A simplification of the Zoeppritz equations. Geophysics, 50:609–614
Richards and Frasier (1976), Aki and Richards (1980)
P. Richards and C. Frasier expanded the terms for the reflection and transmission coefficients for a P-wave incident upon a solid-solid interface and simplified the result by assuming only small changes in elastic properties across the interface. Therefore, the squares and differential products are small enough to tend to zero and be removed. This form of the equations allows one to see the effects of density and P- or S- wave velocity variations on the reflection amplitudes. This approximation was popularized in the 1980 book ''Quantitative Seismology'' by K. Aki and P. Richards and has since been commonly referred to as the Aki and Richards approximation.
Ostrander (1980)
Ostrander was the first to introduce a practical application of the AVO effect, showing that a gas sand underlying a shale exhibited amplitude variation with offset.
Shuey (1985)
Shuey further modified the equations by assuming – as Ostrander had – that
Poisson's ratio
In materials science and solid mechanics, Poisson's ratio (symbol: ( nu)) is a measure of the Poisson effect, the deformation (expansion or contraction) of a material in directions perpendicular to the specific direction of loading. The value ...
was the elastic property most directly related to the angular dependence of the reflection coefficient.
This gives the 3-term Shuey Equation:
[Avseth, P, T Mukerji and G Mavko (2005). Quantitative seismic interpretation. Cambridge University Press, Cambridge, UK]
:
where
:
and
:
;
where
=angle of incidence;
= P-wave velocity in medium;
= P-wave velocity contrast across interface;
= S-wave velocity in medium;
= S-wave velocity contrast across interface;
= density in medium;
= density contrast across interface;
In the Shuey equation, R(0) is the reflection coefficient at normal incidence and is controlled by the contrast in acoustic impedances. G, often referred to as the AVO gradient, describes the variation of reflection amplitudes at intermediate offsets and the third term, F, describes the behaviour at large angles/far offsets that are close to the critical angle.
This equation can be further simplified by assuming that the angle of incidence is less than 30 degrees (i.e. the offset is relatively small), so the third term will tend to zero. This is the case in most seismic surveys and gives the "Shuey Approximation":
:
This was the final development needed before AVO analysis could become a commercial tool for the oil industry.
Use

Modern
seismic reflection surveys are designed and acquired in such a way that the same point on the subsurface is sampled multiple times, with each sample having a different source and receiver location. The seismic data is then carefully processed to preserve seismic amplitudes and accurately determine the spatial coordinates of each sample. This allows a geophysicist to construct a group of traces with a range of offsets that all sample the same subsurface location in order to perform AVO analysis. This is known as a Common Midpoint Gather (a midpoint being the area of the subsurface that a seismic wave reflects off before returning to the receiver) and in a typical seismic reflection processing workflow, the average amplitude would be calculated along the time sample, in a process known as "stacking". This process significantly reduces random noise but loses all information that could be used for AVO analysis.
[Young, R. & LoPiccolo, R. 2005. AVO analysis demystified. E&P. https://e-seis.com/wp-content/uploads/2014/11/AVO-Analysis-Demystified.pdf]
AVO crossplots
A CMP gather is constructed, the traces are conditioned so that they reference the same two-way travel time, sorted in order of increasing offset and the amplitude of each trace at a specific time horizon is extracted. Remembering the 2-term Shuey Approximation, the amplitude of each trace is plotted against sin^2 of its offset and the relationship becomes linear, as seen in the diagram. Using linear regression, a line of best fit can now be calculated that describes how the reflection amplitude varies with offset using just 2 parameters: the intersect, P, and the gradient, G.
As per the Shuey approximation, the intersect P corresponds to R(0), the reflection amplitude at zero-offset, and the gradient G describes the behaviour at non-normal offset, a value known as the AVO gradient. Plotting P (or R(0)) against G for every time sample in every CMP gather produces an AVO
crossplot and can be interpreted in a number of ways.
Interpretation
An AVO anomaly is most commonly expressed as increasing (rising) AVO in a sedimentary section, often where the hydrocarbon reservoir is "softer" (lower
acoustic impedance
Acoustic impedance and specific acoustic impedance are measures of the opposition that a system presents to the acoustic flow resulting from an acoustic pressure applied to the system. The International System of Units, SI unit of acoustic impeda ...
) than the surrounding shales. Typically amplitude decreases (falls) with offset due to geometrical spreading, attenuation and other factors. An AVO anomaly can also include examples where amplitude with offset falls at a lower rate than the surrounding reflective events.
Applications in the oil and gas industry
The most important application of AVO is the detection of hydrocarbon reservoirs. Increasing AVO is usually present in oil-bearing sediments with at least 10% gas saturation, but is especially pronounced in porous, low-density gas-bearing sediments with little to no oil. Particularly important examples are those seen in Middle Tertiary gas sands of the coastal counties of Southeast Texas,
turbidite
A turbidite is the geologic Deposition (geology), deposit of a turbidity current, which is a type of amalgamation of fluidal and sediment gravity flow responsible for distributing vast amounts of clastic sediment into the deep ocean.
Sequencing
...
sands such as the Late Tertiary deltaic sediments in the
Gulf of Mexico
The Gulf of Mexico () is an oceanic basin and a marginal sea of the Atlantic Ocean, mostly surrounded by the North American continent. It is bounded on the northeast, north, and northwest by the Gulf Coast of the United States; on the southw ...
(especially during the 1980s–1990s), West Africa, and other major
deltas
A river delta is a landform, wikt:archetype#Noun, archetypically triangular, created by the deposition (geology), deposition of the sediments that are carried by the waters of a river, where the river merges with a body of slow-moving water or ...
around the world. Most major companies use AVO routinely as a tool to "de-risk" exploration targets and to better define the extent and the composition of existing hydrocarbon reservoirs.
AVO is not fail-safe
An important caveat is that the existence of abnormally rising or falling amplitudes can sometimes be caused by other factors, such as alternative lithologies and residual hydrocarbons in a breached gas column. Not all oil and gas fields are associated with an obvious AVO anomaly (e.g. most of the oil found in the
Gulf of Mexico
The Gulf of Mexico () is an oceanic basin and a marginal sea of the Atlantic Ocean, mostly surrounded by the North American continent. It is bounded on the northeast, north, and northwest by the Gulf Coast of the United States; on the southw ...
in the last decade), and AVO analysis is by no means a panacea for gas and
oil exploration
Hydrocarbon exploration (or oil and gas exploration) is the search by petroleum geologists and geophysicists for hydrocarbon deposits, particularly petroleum and natural gas, in the Earth's crust using petroleum geology.
Exploration methods
V ...
.
References
{{reflist, colwidth=30em
External links
*http://sepwww.stanford.edu/public/docs/sep73/carlos2/paper_html/node5.html
Seismology measurement
Petroleum geology