Signal, noise and the unity of opposites


Marx and Engels both took a keen interest in the scientific developments of their time and wrote a number of articles on scientific topics. Marx himself produced a deep analysis of the foundations of differential and integral calculus, unpublished during his lifetime but available now on the web [i], in which he anticipated the developments in that subject that took place later in the 19th century. Engels in the "Dialectics of Nature" involved himself with some of the scientific controversies of the time, placing these in the context of the dialectical and materialist philosophy which he and Marx had developed. His article "On the part played by Labour in the Transition from Ape to Man", for example, is a major contribution to the subject and is recognised as such by some, if not all, modern anthropologists.

The involvement of Marx and Engels in the scientific and technological developments of their age was for them a very practical question. They saw the development of technology as one of the keys to ending the barbarism of class society. Through technology it would be possible to raise the productivity of human labour to the point where in Marx's famous phrase "from each according to his ability, to each according to their needs" could become the living reality for all of humanity. It is one of the deepest contradictions of capitalism, and one of the clearest indications that this system has completely outlived itself, that in private hands technical developments are now used to lower living standards, throwing millions out of work and leaving billions to face a continuing life of grinding poverty. Together with its military applications, new technology under capitalism now does not enhance life but instead destroys it.

There was also a theoretical side to Marx and Engels interest in science. Politics is mainly a battle of ideas, even if at critical points it can become a physical battle in the factories, or in the desert wadis. It is fundamental to the philosophy of dialectical materialism that ideas do not fall from the sky, but are rooted in physical reality. It was particularly in Engels writings on science that they were able to show that the same dialectical processes of change that exist in society, economics and politics also exist in natural processes. Quantitative changes, such as an increase in the temperature of a liquid, at a certain point become qualitative, when the liquid turns into a gas. Things that are thought to be opposites, a wave or a particle for example, can be identical, as in the "wave-particle" of quantum mechanics. What is cause can also be effect - a spring pushes but is also pushed. Processes repeat, not as a circle but as a spiral. A seed becomes a tree becomes a seed again, but with chance genetic changes that can lead to evolution and development. Marxism, dialectical materialism, is the application of these laws to society, economics and politics, and to nature.

This article looks at one small part of modern science - signal and noise in seismic sounding for oil exploration - and aims to show that the dialectical laws of motion can also be seen here as in other parts of nature. Even though this is a fairly specialist topic it is hoped that the article will be of interest not only to readers with a scientific background but also to anyone who has a general interest in science and in politics. Engels too wrote at times about very specialised topics; in chapter 4 of "Dialectics of Nature" for example there is a detailed discussion on the question of what should be used as a measure of motion - momentum or energy [ii]. This part of the book would have been difficult enough at the time it was written as it was dealing with ideas that were then relatively new, and is possibly even more difficult now many years later when the controversy is long past. Sometime, however, it is necessary to get close to the detail, even if it is not completely straightforward, in order to get close to the truth; simplification can lead to a lie.

The article concentrates on the technical aspects of seismic exploration for oil, and little is said about the political and social consequences of oil exploration. That would take many, many articles; some are available in the sections of this website on Iraq, Nigeria or Venezuela. Those scientists and technicians who work in the oil industry know very well the activities of the companies they work for and its effects on the countries they operate in. They also know the nature of the management in the oil industry - bureaucratic and corrupt, at best ineffectual, at worst brutal. But the pay and conditions that are given to scientists and engineers in the oil business mean that many choose to support the status quo - Western imperialism in its most predatory form - or to simply look the other way.

The Iraq war has caused at least a minority of these scientists and engineers to question the role they are playing, who they are working for, and what is being done with the product of their labour. There is just the beginning of a stirring of discontent. This article is mainly about scientific topics, and the intention is to show that there are general dialectical laws of motion which can be seen in nature. When those laws are applied to society - another complex and chaotic system - the conclusions are revolutionary. This article is particularly addressed to those honest scientists who wish to use their skills to better humankind and not to impoverish it. Read other articles on this site, familiarise yourself with the scientific study of economics, politics and society which is Marxism. Capitalism is incapable of taking society forward. It will drag humanity into the abyss if not stopped. You have the opportunity to play a role in preventing that, and to use your technical skills for the common good.

Signal and noise

In almost all areas of human activity it is difficult to obtain information that is free from noise. Effects that appear to be random can overwhelm the faint signals that a scientist is looking for - in the same way that noise hides the information that shows the reality of class society. By far the biggest practical concern of working scientists and engineers is how to deal with this problem - how to obtain reliable results, how to prevent noise overwhelming signal.

Important advances have been made in this topic in the last thirty years or so with the advent of modern computers and digital technology. A whole new area of science and engineering - signal processing - has developed that aims to understand the statistical and physical properties of noise and signal in different circumstances and from that learn how to separate one from the other. This is one of the great successes of digital technology - compare, for example, the quality of the television images that we can receive today from anywhere on the planet with the faint grainy pictures of the first transatlantic broadcasts.

Often noise can seem to be random, and this is an idea that can be used for noise removal. The grainy speckles of noise on a photographic image, for example, appear to be random compared to the structure and shape of the photographic subject itself. So a computer program can detect and remove the speckles by finding those parts of the image that are random compared to their surroundings.

But noise is never truly random. Nothing happens without cause - a point that supporters of the Big Bang theory should think hard about. Physical phenomena can be complex, with many interacting features, to the point that their behaviour becomes unpredictable. But unpredictability is not the same as lacking cause. A feather that is allowed to fall to the floor is moved by what are apparently random currents of air, so that it is impossible to say exactly when or where it will fall. At most it might be possible to describe the motion of the feather by its statistics (the average time taken to fall, the spread of positions on the floor) and little more. But there are still physical laws at work even when there is a complicated web of cause and effect. Modern science is just beginning to understand this type of behaviour - that complex systems, although determined by causal physical laws, can be unpredictable. Modern science has rediscovered in fact what Hegel brilliantly anticipated. Necessity is expressed through chance; physical law is expressed through apparently random events. Noise is not random; it may be difficult or even impossible to predict but physical laws are as much responsible for the noise as for the signal.

In the same way, signal and noise are usually thought of as polar opposites. The signal in a radio transmission contains the information, the noise obscures that information. The signal has been created deliberately, the noise is accidental. But on closer investigation the situation is less clear. For an atmospheric scientist the background noise heard on a radio might contain useful information about the state of the earth's upper atmosphere. What is noise for the radio listener is signal for the scientist; the radio transmission now gets in the way and is noise. There are cases where the signal and the noise are equivalent, where the noise is a form of signal and contains similar information to that in the signal. In a radar display, for example, the background "clutter" on the screen is a jumble of reflections that have been produced by the radar beam and which have been scattered back to the radar receiver. It is noise for the radar operator but is also a form of signal, transformed into noise, and in some circumstances might contain useful information. The distinction between signal and noise, like the distinction between cause and effect, is only relative and approximate.

Electronic systems and physical processes in general consist of many different but interacting parts. It is rarely enough to look at each part of the process in isolation from the other; this is useful when beginning to investigate what is happening but at best is an approximation. To go further it becomes necessary to look at the process as a whole, in terms of its connections and their contradictions. Often its characteristics can derive as much from the interaction between its different parts as from the details of the physical laws involved. "The whole is greater than the sum of its parts" is a familiar idea to many modern scientists. But the more general dialectical law which that statement is an example of, that quantitative changes at a certain point become qualitative, is unfortunately less well known. Only recently in the physical sciences, slightly less recently in the biological sciences, have scientists begun to study processes in their entirety, their change and their development, to see what unifies rather than what separates.

Seismic exploration for oil

Seismic surveys at sea use high-pressure sound sources to send pulses of sound into the earth. One of the areas where there has been a significant development of signal processing technology in the last 30 years has been in oil exploration, and in particular in seismic surveying. Seismic surveys generate images that are cross-sections through the structure of the earth, and oil company geologists use these images to decide the best place to drill a new well. The information from a seismic survey, together with other geological information, helps the geologist to discover the geological history of the region, how the rocks were laid down and subsequently distorted, where the oil might have formed from organic material, how it might have moved since then and what rocks might have trapped the oil to form a reservoir. It is ironical that many of the most confirmed opponents of evolution, the Christian right in America, are either part of or are close to the oil industry - Condoleeza Rice, past director of Chevron; Dick Cheney, past head of oil-field services company Halliburton; Bush elder and younger, many and varied oil interests. Where do these people think oil comes from, and how do they think it got there? It is impossible to find oil without taking an evolutionary and dynamical approach - i.e. a dialectical approach - to understanding the earth's geology.

A modern seismic survey is a large operation that requires a significant capital investment, and the oil companies usually contract the survey operations to specialist sub-contractors. At sea, a large survey boat tows an array of high-pressure hydraulic airguns, similar in design to pneumatic drills, and these are fired periodically and produce strong pulses of sound that are able to penetrate deep into the earth [iii]. The echoes are recorded by thousands of sensitive marine microphones (hydrophones) which are towed in long cables behind the boat, and the seismic source is fired at a dense grid of locations throughout the survey area.

Seismic surveys have been used since the 1930's to find oil, but the possibility of recording and processing seismic data digitally that became available during the 1960's has led to a dramatic improvement in the quality of seismic images, similar to the improvement in the quality of television images that was mentioned earlier. During the last 40 years the oil companies and the seismic contractors have invested heavily in seismic research and development, and there are now processing techniques available that can remove the serious distortions of seismic images that are caused by irregularities in the earth's layers, and which can remove many of the different types of noise that are present. The amount of data that is recorded during a typical survey has also increased dramatically since the 1960's as the cost of electronic hardware has declined. In order to process these large amounts of data the seismic contractors have become one of the main users of large high power computer systems, second only to government funded bodies such as the weather centres or the military. Some of the techniques developed for seismic imaging have in fact also had military applications; there has also been some limited application to medical imaging (ultrasound scans, for example) but this has occurred mainly in the private medical system in the United States.

Oil wells are expensive, and becoming more expensive as existing fields are depleted and oil companies are forced to explore in more difficult areas. An oil well in the North Sea, a difficult environment to work in but one where the sea is relatively shallow, might cost 10 to 15 million US dollars to drill. A well in deep water in the Gulf of Mexico, currently an active area of exploration, might cost as much as 50 million US dollars. (Drilling new wells on land, in the Middle East for example, is much cheaper - perhaps 1/10th of the cost of drilling at sea.) Technology that even marginally improves the quality of the seismic images used to locate the wells can be very cost effective, even if the end result is just one less dry well in ten or even a hundred. This is the principal reason for the significant research and development expenditure on signal processing that has taken place in the oil industry. The enormous financial resources that are available here have led perhaps to a greater degree of expenditure on that topic than in many other industries, with the exception of research for military applications.

Scattering of seismic waves

The information from a seismic survey that the oil company geologist needs is the sound from the seismic source that goes directly down into the earth, reflects from each rock layer, and comes directly back to the surface. But the earth's rocks are often very irregular and contain features that scatter and distort the sound waves. Seismic exploration is like looking through many twisted layers of frosted glass of different thicknesses; the image is distorted, is dim, and is hidden by numerous apparently random events. Only a small proportion of the sound that is recorded during a survey can be used to infer the geology. This is the signal, and the rest is the noise. The fact that it is still possible to obtain useable images that represent the earth's geology is one of the best examples there is of the power of modern digital technology.

Much of the sound from the seismic source never returns to the surface, and instead is scattered in all directions, bouncing around between the different irregularities in the rock layers. Ultimately, as the sound waves become more and more disorganised, they become completely random, like the ripples produced by rain on a pond. From being able to describe them by a causal physical process - wave propagation - we are reduced to a statistical description - the average amplitude, the amount of spatial variation, the degree of irregularity. The sound becomes chaotic in the sense of modern dynamics - an unpredictable but nonetheless deterministic process. At a further stage, the quantitative increase in the amount of scattering - the increase in the "order" of the scattering in the jargon - leads to a qualitative change. Instead of sound waves there is simply a random vibration of the atoms and molecules that make up the rocks; the sound has been transformed into heat.

The sound waves that do arrive back at the surface can be very complicated. They contain many apparently random features caused by the scattering of the scattering of the scattering. There is a slightly greater amount of consistency in some of the waves than others, and these are the "reflections" from the boundaries between the rocks. Seismic images show layers and boundaries, but the reality of exactly what in the earth has caused these is often not clear. Any cliff face shows that the rock layers in the earth can have many different thicknesses and contain many different features. All that can really be said is that the different rocks usually have some degree of spatial consistency, and a portion of the seismic waves detected back at the surface also have some degree of spatial consistency.

It has been known for many years in fact that isolated boundaries between rocks rarely produce reflections that are strong enough to be detected, and that the reflections that are actually seen are often a complicated sum over many weaker reflections [iv]. But this is a forbidden topic - no oil company exploration manager and no research manager in a seismic company would dare to mention it in public. Suggest that millions of dollars are being spent when the seismic reflections are not directly related to the rocks? Impossible. And it would be a brave researcher in a university who risked suggesting this as an area for study, when all the significant research groups are funded by industry. This is how bureaucratic corruption can hold back technical developments; a clearer understanding of the physical mechanism that produces the seismic reflection might lead to different and new ways of using the information in seismic data. But as far as the author is aware there is little current research in this topic [v].

Noise in marine seismic data

Seismic surveys at sea suffer a very strong and severe type of noise problem which has been a concern for marine seismic exploration from its beginning. There is still no complete solution to the problem and it remains an important area for research and development.

When sound echoes come back up from the earth they travel up to the surface of the sea - and are immediately reflected back down again. Because the sea surface is an almost perfect reflector, almost all of the sound energy that comes back up goes back down. It then produces more echoes, which come back up and are again reflected back down by the sea surface. This goes on repeatedly and leads to very complicated "multiple reflections" in the seismic images. Every echo has additional echoes; there are reflections of every reflection. The signal the geologist wants is the sound that has simply gone down and come back (these are called "primary" reflections). But the sound carries on repeatedly bouncing down into the earth and back again, producing multiple arrivals - noise - which can completely obscure the signal.

Over the last 30 years or more there have been numerous attempts to find ways of dealing with this type of noise, with varying degrees of success. Almost always the approach is to see the noise as a type of interference that must be subtracted from the seismic image. But this is noise, like the background clutter on a radar screen, that is a form of signal. Like the signal, it has been generated by the seismic source. Noise and signal are interconnected. And unlike the scattered noise mentioned above, this type of noise is not disorganised to the point that it is unpredictable. The sea-surface is smooth, or at least smooth enough at the scale of the seismic wave, and this gives some important and useful structure to the noise.

The signal, the primary reflections, is caused by sound from the seismic source that goes one trip down through the earth and back. The multiple reflections occur when this sound reflects at the sea-surface and goes back down. Imagine if it was possible somehow to arrange many sound sources at the sea surface and create exactly the same downgoing wave as when the signal, the one-trip sound, was reflected at the sea surface. This would then recreate exactly the situation that produces the multiple arrivals. If we could do that experiment then we would record only multiples - only the noise.

But we could describe the experiment from a different point of view. We could say that we are doing nothing different from what normally happens during a seismic survey, except that we have changed the seismic source and made it equal to the signal. Although this would be difficult to do in reality, if it was possible the result would be simply another version of the seismic record, containing both the primary and the multiple reflections as usual, but now with the signal itself as the seismic source. So we have the original seismic record but in some sense this has been "multiplied" by the signal [vi].

From the first description of the experiment we decided that we would obtain only the noise. But in the second description we are saying that we would obtain the seismic record multiplied by the signal. So the two must be equal:

Noise = Seismic record x Signal

This is an extremely powerful way of describing the physical process that generates the noise. It has been the subject of intense research and development over the last decade. It corresponds exactly to the dialectical view that noise and signal are inter-related, that there is a union of opposites, and that noise is a form of signal. And what predicts the noise is the seismic record itself; if we know the signal, and we have the seismic records, then multiplying them together gives - the noise.

At first sight this all seems very strange. The proof that we've just been through works because each time the sound goes down and comes back again it is weaker than before, and also because this happens repeatedly an infinite number of times. The proof wouldn't work if the sound arrived back at the surface only a finite number of times. The proof and the result feel strange because they contain one of the contradictions of infinity - an extra term added to an infinite series gives the same infinite series.

In practice we don't know the signal. All we have are the seismic records, which contain both signal and noise. But we could start with an initial guess for the signal - perhaps even guess initially that the signal is just equal to the seismic records. If we multiply this initial guess for the signal by the seismic records then we will get an initial guess for the noise. And we know that the seismic records are just signal plus noise - so subtract this guess for the noise from the records to get a new guess for the signal. We can carry on doing this, getting repeated new guesses for the signal and then using that to obtain a new guess for the noise, and so on.

Each time we obtain a new guess for the signal we will get closer to its true value, and eventually we will arrive exactly at the true value. But the true value for the signal is what the geologist wants to have - it's the noise-free seismic record. So by a process of successive approximations we are able to remove the noise from the seismic records.

This turns out to be a very powerful approach that can work even when the multiple reflections are very strong and the geology is complicated. It has the big advantage that unlike some of the other approaches that have been tried in the past it doesn't need any information other than that in the seismic data itself. It does, however, need a lot of computer processing to make it work, and it turns out to be quite expensive in practice. It has been used commercially during the last ten years or so, initially only in a relatively limited form, but has been extended as the cost of computer hardware has gone down. It is now used quite extensively when the multiple reflections are complicated and other less costly approaches are found to be unsuccessful.

But there is another and quite different possibility that comes from the insight that the noise is a form of signal. If the noise can be predicted from the signal, perhaps the signal can be predicted from the noise. This would be something very different from the signal processing that has been applied to seismic data in the last 30 years. There the noise has been viewed as an unwelcome problem that has to be removed. But perhaps instead it might be possible to convert the noise to signal and add it to what already exists in the seismic records. This could even increase the information obtained from the data, because the noise may have come from parts of the earth that were not recorded directly during the survey.

If the noise is the seismic record times the signal, then the seismic record is the noise divided by the signal:

Seismic record = Noise / Signal

This too is a very powerful result. It says that it is possible to create a new version of the seismic record from the noise. It opens up the possibility that the noise can be converted to signal, and that the seismic image can be improved not by subtracting the noise but by adding it, after conversion, to the signal we already have. Rather than simply removing the noise and throwing it away, perhaps it is possible to use it to obtain additional information about the earth's geology.

These are some of the research topics that are current in seismic signal processing. In every part of the subject the dialectical laws of motion are evident. Necessity is expressed through chance - as sound moves through the earth and is scattered, gaining an apparent randomness that is nonetheless a consequence of physical law. Quantity becomes quality - as the scattering increases and the sound turns to heat. There is a union and interpenetration of opposites - the severe noise in marine seismic records is also a form of signal. The noise is not separate and different from signal but is one part of a complex whole, and is related to the whole by the dynamics of wave propagation. And when the noise is converted to signal it can provide extra information - the signal becomes noise becomes signal, the process repeats, not as a circle but a spiral.

These are not metaphors or analogies but are a precise description of the geophysics, and come directly from the motion of the sound as it passes repeatedly through the earth. The dialectical laws and contradictions of motion are as clear and obvious here as they are elsewhere in nature, and in every other form of motion.

June 2006

[i] See

[ii] See Engels' conclusion was that energy was a better measure of motion than momentum because energy, not momentum, is conserved between different forms of motion - mechanical, electrical, heat, etc. This was also the position that was adopted eventually, after some initial controversy, by 19th century physicists. It was extended at the beginning of the 20th century by Einstein's famous equation E=mc2 which states that motion as measured by energy E is also equivalent to and can be obtained from mass m; c is the velocity of light.

[iii] There has been increasing concern that the high levels of sound produced by seismic sources can be damaging to marine life, particularly to marine mammals. There have been a number of well publicised incidents recently of whales that have become stranded on beaches and in rivers. Although denied by the authorities, these are likely to have been caused by sound from either seismic surveys or from military sonar.

[iv] See: "Reflections on amplitudes" by R. F. O'Doherty and N. A. Anstey, Geophysical Prospecting, 1971, vol. 19, pages 430-458.

[v] It has also been known for years that errors in processing seismic data (due to random and unavoidable software errors) mean that at a certain level the apparent detail in seismic images is unreliable. A study took place in the early 1990's, funded by an oil company, but the results were quietly shelved and are little known. See "Analysing the agreement between seismic data processing packages - The Enterprise seismic software calibration experiment" by L. Hatton and A. Roberts, abstracts of the 62nd meeting of the Society of Exploration Geophysics, 1992, pages 828-830.

[vi] For the mathematically interested: the noise is the time-space convolution of the signal with signal plus noise, together with correction terms for the properties of the seismic source, the surface reflection, and the seismic detector. A derivation is given in "Inverse data processing, a paradigm shift?" by A.J. Berkhout and D.J. Verschuur, abstracts of the 75th meeting of the Society of Exploration Geophysics, 2005, pages 2099-2102.

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