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In the Russian school, the total normalized gradient method belongs to the most wide‐spread of direct interpretation methods for potential field data. This method was also used and partly developed by many experts from abroad. The main advantage of the total normalized gradient method is its relative independence of parameters such as the expected differential density of interpreted structures. The method is built from a construction of a specially transformed field (total normalized gradient) on a section crossing the potential field sources. The special properties of this transformed field allow it to be used to detect the source positions. From the 1960s, the mathematical basis of the method underwent enormous development and several modifications of the method have been elaborated. The total normalized gradient operator itself represents a relatively complicated, non‐linear band‐pass filter in the spectral domain. The properties of this operator can be handled by means of several parameters that act to separate the information about field sources at different depth levels. In this contribution, we describe the development of the method from its very beginning (based mostly on qualitative interpretation of simple total normalized gradient sections) through to more recent numerical improvements to the method. These improvements include the quasi‐singular points method, which refines the filter properties of the total normalized gradient operator and defines an objective criteria (so called criterion ‘α’ and ‘Г') for the definition of source depths in the section. We end by describing possibilities for further development of the method in the future.

We reformulate the original model of Hatchell and Bourne and Roste, Stovas and Landro that couples fractional velocity change to subsurface strain via a fundamental constant R. The new model combines elastic compressibility of a dual-porosity system for a sand–shale mixture with horizontal planes of inter-granular weakness. The majority of observed R-factor magnitudes from post-stack 4D seismic data in both the reservoir and overburden can thus be explained. R is predicted to depend strongly on lithology and also initial strain state. The model is also extended to predict the observed angle-dependence of time-lapse time-shifts from pre-stack data. An expression for the gradient of time-shift with incidence angle is obtained in terms of the background VP/VS, and also the ratio of tangential to normal compliances BT/BN representing loss or creation of inter-granular coupling. If accurately estimated from data, this compliance ratio can be used as an additional parameter to assess the post-production state of the overburden. It is concluded that whilst R remains the over-arching parameter controlling the magnitude of time-shifts measured from 4D seismic data, BT/BN is a subtler parameter that may also prove of future value.

In Part I of this paper, we defined a focusing wave field as the time reversal of an observed point‐source response. We showed that emitting a time‐reversed field from a closed boundary yields a focal spot that acts as an isotropic virtual source. However, when emitting the field from an open boundary, the virtual source is highly directional and significant artefacts occur related to multiple scattering. The aim of this paper is to discuss a focusing wave field, which, when emitted into the medium from an open boundary, yields an isotropic virtual source and does not give rise to artefacts. We start the discussion from a horizontally layered medium and introduce the single‐sided focusing wave field in an intuitive way as an inverse filter. Next, we discuss single‐sided focusing in two‐dimensional and three‐dimensional inhomogeneous media and support the discussion with mathematical derivations. The focusing functions needed for single‐sided focusing can be retrieved from the single‐sided reflection response and an estimate of the direct arrivals between the focal point and the accessible boundary. The focal spot, obtained with this single‐sided data‐driven focusing method, acts as an isotropic virtual source, similar to that obtained by emitting a time‐reversed point‐source response from a closed boundary.

A review and analysis of post-stack time-lapse time-shifts has been carried out that covers published literature supplemented by in-house datasets available to the authors. Time-shift data are classified into those originating from geomechanical effects and those due to fluid saturation changes. From these data, conclusions are drawn regarding the effectiveness of post-stack time-shifts for overburden and reservoir monitoring purposes. A variety of field examples are shown that display the range and magnitude of variation for each class of application. The underlying physical mechanisms creating these time-shifts are then described, and linked to a series of generic and field-specific rock physics calculations that predict their magnitudes. These calculations serve as a guide for practitioners wishing to utilize this information on their own datasets. Conclusions are drawn regarding the reliability of this attribute for monitoring purposes, and the extent to which further development is required and how it should be reported by authors.

Igneous intrusions, notably carbonatitic–alkalic intrusions, peralkaline intrusions, and pegmatites, represent significant sources of rare-earth metals. Geophysical exploration for and of such intrusions has met with considerable success. Examples of the application of the gravity, magnetic, and radiometric methods in the search for rare metals are presented and described. Ground gravity surveys defining small positive gravity anomalies helped outline the shape and depth of the Nechalacho (formerly Lake) deposit within the Blatchford Lake alkaline complex, Northwest Territories, and of spodumene-rich mineralization associated with the Tanco deposit, Manitoba, within the hosting Tanco pegmatite. Based on density considerations, the bastnaesite-bearing main ore body within the Mountain Pass carbonatite, California, should produce a gravity high similar in amplitude to those associated with the Nechalacho and Tanco deposits. Gravity also has utility in modelling hosting carbonatite intrusions, such as the Mount Weld intrusion, Western Australia, and Elk Creek intrusion, Nebraska. The magnetic method is probably the most successful geophysical technique for locating carbonatitic–alkalic host intrusions, which are typically characterized by intense positive, circular to sub-circular, crescentic, or annular anomalies. Intrusions found by this technique include the Mount Weld carbonatite and the Misery Lake alkali complex, Quebec. Two potential carbonatitic–alkalic intrusions are proposed in the Grenville Province of Eastern Quebec, where application of an automatic technique to locate circular magnetic anomalies identified several examples. Two in particular displayed strong similarities in magnetic pattern to anomalies accompanying known carbonatitic or alkalic intrusions hosting rare-metal mineralization and are proposed to have a similar origin. Discovery of carbonatitic–alkalic hosts of rare metals has also been achieved by the radiometric method. The Thor Lake group of rare-earth metal deposits, which includes the Nechalacho deposit, were found by follow-up investigations of strong equivalent thorium and uranium peaks defined by an airborne survey. Prominent linear radiometric anomalies associated with glacial till in the Canadian Shield have provided vectors based on ice flow directions to source intrusions. The Allan Lake carbonatite in the Grenville Province of Ontario is one such intrusion found by this method. Although not discovered by its radiometric characteristics, the Strange Lake alkali intrusion on the Quebec–Labrador border is associated with prominent linear thorium and uranium anomalies extending at least 50 km down ice from the intrusion. Radiometric exploration of rare metals hosted by pegmatites is evaluated through examination of radiometric signatures of peraluminous pegmatitic granites in the area of the Tanco pegmatite.

The next generation of seismic imaging algorithms will use full wavefield migration, which regards multiple scattering as indispensable information. These algorithms will also include autonomous velocity-updating in the migration process, called joint migration inversion. Full wavefield migration and joint migration inversion address industrial requirements to improve the images of highly complex reservoirs as well as the industrial ambition to produce these images more automatically (automation in seismic processing). In these vision papers on seismic imaging, full wavefield migration and joint migration inversion are formulated in terms of a closed-loop, estimation algorithm that can be physically explained by an iterative double-focusing process (full wavefield Common Focus Point technology). A critical module in this formulation is forward modelling, allowing feedback from the migrated output to the unmigrated input (‘closing the loop’). For this purpose, a full wavefield modelling module has been developed, which uses an operator description of complex geology. Full wavefield modelling is pre-eminently suited to function in the feedback path of a closed-loop migration algorithm. ‘The Future of Seismic Imaging’ is presented as a coherent trilogy of papers that propose the migration framework of the future. In Part I, the theory of full wavefield modelling is explained, showing the fundamental distinction with the finite-difference approach. Full wavefield modelling allows the computation of complex shot records without the specification of velocity and density models. Instead, an operator description of the subsurface is used. The capability of full wavefield modelling is illustrated with examples. Finally, the theory of full wavefield modelling is extended to full wavefield reverse modelling (FWMod−1), which allows accurate estimation of (blended) source properties from (blended) shot records.

The next-generation seismic imaging algorithms will consider multiple scattering as indispensable information, being referred to as Full-WavefieldMigration. In addition,these algorithms will also include autonomous velocity updating in the migration process, being referred to as Joint Migration Inversion. Full-Wavefield Migration and Joint Migration Inversion address the industrial needs to improve images of very complex reservoirs as well as the industrial ambition to produce these images in a more automatic manner (automation in seismic processing). In this vision paper on seismic imaging, Full-Wavefield Migration and Joint Migration Inversion are formulated in terms of a closed-loop estimation algorithm that can be physically explained by an iterative double focusing process (full-wavefield common-focus-point technology). A critical module in this formulation is forward modelling, allowing feedback from migrated output to unmigrated input (closing the loop). For this purpose, a full-wavefield modelling module has been developed, which utilizes an operator description of complex geology. The full-wavefield modelling module is pre-eminently suited to function in the feedback path of a closed-loop migration algorithm. ‘The Future of Seismic Imaging’ is presented as a coherent trilogy, proposing the migration framework of the future in three consecutive parts. In Part I, it was shown that the proposed full-wavefield modelling module algorithm differs fundamentally from finite-difference modelling because velocities and densities need not be provided. Instead, an operator description of the subsurface is used. In addition, the concept of reverse modelling was introduced. In Part II, it is shown how the theory of Primary Wavefield Migration can be extended to Full-Wavefield Migration by correcting for angle-dependent transmission effects and by utilizing multiple scattering. The potential of the Full-Wavefield Migration algorithm is illustrated with numerical examples. A multidirectional migration strategy is proposed that navigates the Full- Wavefield Migration algorithm through the seismic data cube in different directions.

The next generation seismic imaging algorithms will consider multiple scattering as indispensable information, referred to as Full Wavefield Migration. In addition, these algorithms will also include autonomous velocity updating in the migration process, referred to as Joint Migration Inversion. Full wavefield migration and joint migration inversion address the industrial needs of improving images of very complex reservoirs as well as the industry ambition of producing these images in a more automatic manner (‘automation in seismic processing’). In this vision paper on seismic imaging, full wavefield migration and joint migration inversion are formulated in terms of a closed-loop, estimation algorithm that can be physically explained by an iterative double focusing process (full wavefield Common-Focus-Point technology). A critical module in this formulation is forward modelling, allowing feedback from migrated output to unmigrated input (‘closing the loop’). For this purpose a full wavefield modelling module has been developed that utilizes an operator description of complex geology. Full wavefield modelling module is pre-eminently suited to function in the feedback path of a closed-loop migration algorithm. ‘The Future of Seismic Imaging’ is presented as a coherent trilogy, proposing in three consecutive parts the migration framework of the future. In part I it was shown that the proposed full wavefield modelling module algorithm differs fundamentally from finite difference modelling, as velocities and densities need not be provided. Instead, full wavefield modelling module uses an operator description of the subsurface. In Part II it was shown how the theory of Primary Wavefield Migration can be extended to Full Wavefield Migration by correcting for elastic transmission effects and by utilizing multiple scattering. In Part III it is shown how the full wavefield migration technology can be extended to Joint Migration Inversion, allowing full wavefield migration of blended data without knowledge of the velocity. Velocities are part of the joint migration inversion output, being obtained by an operator-driven parametric inversion process. The potential of the proposed joint migration inversion algorithm is illustrated with numerical examples.

One hundred and fifty five years ago, Kelvin published the first part of a fundamental analysis of the elastic tensor, in which he proposed a coordinate-free representation through its eigensystem. His thoughts were apparently far ahead of his time, since it took 125 years before the paper elicited a positive reaction (it is now accessible through several modern reviews). Science not only lost track for 125 years of the original paper but also lost the ideas Kelvin might have proposed in the second part, a publication that was never put to paper, presumably in view of the lack of appreciation of the first part. In an attempt to establish what might have been on Kelvin's mind for a second part, one has to ‘forget’ the progress of mathematical physics in the intervening time and base all arguments strictly on the content of the first part and on the state of science in the second half of the 19thcentury. The theory of elasticity would certainly have developed faster, had Kelvin's paper peen appreciated by his ‘peers’. But a theory based on Kelvin's ideas would be fruitful even today.

We review and describe the electromagnetic transmitters and receivers used to carry out magnetotelluric and controlled source soundings in the marine environment. Academic studies using marine electromagnetic methods started in the 1970s but during the last decade these methods have been used extensively by the offshore hydrocarbon exploration industry. The principal sensors (magnetometers and nonpolarizing electrodes) are similar to those used on land but magnetotelluric field strengths are not only much smaller on the deep sea-floor but also fall off more rapidly with increasing frequency. As a result, magnetotelluric signals approach the noise floor of electric field and induction coil sensors (0.1 nV/m and 0.1 pT) at around 1 Hz in typical continental shelf environments. Fluxgate magnetometers have higher noise than induction coils at periods shorter than 500 s but can still be used to collect seafloor magnetotelluric data down to 40‐100 s. Controlled source transmitters using electric dipoles can be towed continuously through the seawater or on the sea-bed, achieving output currents of 1000 A or more, limited by the conductivity of seawater and the power that can be transmitted down the cables used to tow the devices behind a ship. The maximum source-receiver separation achieved in controlled source soundings depends on both the transmitter dipole moment and on the receiver noise floor and is typically around 10 km in continental shelf exploration environments. The position of both receivers and transmitters needs to be navigated using either long baseline or short baseline acoustic ranging, while sea-floor receivers need additional measurements of orientations from compasses and tiltmeters. All equipment has to be packaged to accommodate the high pressure (up to 40 MPa) and corrosive properties of seawater. Usually receiver instruments are self-contained, battery powered and have highly accurate clocks for timekeeping, even when towed on the sea-floor or in the water column behind a transmitter.

The efficient production of “Geophysical Prospecting” depends upon the co-operation of the individual authors and this paper serves as a guide for them. Some suggestions are also made on the presentation of papers at meetings in the hope of promoting successful discussions.

Parasnis' method of obtaining the gravity anomaly of circular laminae can in some cases lead to large errors. The use of the solid angle chart given by Nettleton (1942) is suggested instead.