I think that this one can actually work. It is my understanding that attempts to use electromagnetism to detect oil relate to the fact that the difference in the permittivity of oil and other materials is used to construct an image which would indicate where the oil is. A region with lower permittivity indicates oil. This basis of this principle is that there are particular constants associated with the propagation of electromagnetic waves that depend on the medium they are propagating through. These are permittivity and permeability. The former is a measure of the degree to which a region can permit an electric field. The higher the permittivity, the smaller the field strength at any particular region than if the medium had a lower permittivity. The other constant is permeability which measures the degree to which a magnetic field can permeate a region of space. Unlike permittivity, this one is directly proportional to magnetic field strength. By itself, there is nothing particularly pseudoscientific about such a principle since it is well known that different materials have different permittivity and permeability, but the meaningless term you used "electromagnetic field wave resonance" made me realize that people often use these terms (which they themselves probably don't know) to sell something absurd (alt medicine, etc.)

Do you remember that time when you pointed out that there is no "layman's guide to quantum mechanics", and as a result, anyone can bamboozle the gullible with QM and call it a day?

It's sort of the same with EM. Electromagnetism is one of the most complex topics in physics. To understand classical EM, you must be intimately familiar with vector calculus and field equations.

The term "electromagnetic field wave resonance" does not mean anything. Let's start decomposing this and understand what internal terms do make sense. I can use this topic to articulate terms that people often use carelessly. Terms like “field”, “wave”, “electromagnetism” and “resonance” all have the potential, for some reason, to induce pseudoscientific claims. Definition is important, so lets start with that.

Electromagnetic fields: Numerous pseudoscientific institutions and snake oil sellers love the term "field", and use it to justify a wide variety of nonsense. Virtually entirely, these people are unfamiliar with field equations and mechanics. Field theory arose to replace action-at-a-distance theories. Coulomb's Law, the Biot-Savart Law and Newton's Law of Gravitation are such examples. These are field equations which tell us the magnitude and direction of the field at the unprimed coordinates (called the field coordinates) as a function of the distance from the primed coordinates (source coordinates). According to these laws, any object which can feel a force in a region of space based on an action at a distance based on a source of that field will also exert an equal and opposite force on the source. The field generated by a particular source is therefore independent of other objects which can be affected by the field but the force that is exerted between two objects depends on both objects. Action at distance theories are problematic because they predict that the response of an object to a change in the field is instantaneous. But if a source were suddenly eliminated, or vanished, then an instantaneous response would imply that the rate of propagation of information is greater than c, violating Relativity. We could deny that the object responds immediately, but this means that Newton's Third Law is not true, because in the time between the object being removed and the information being transmitted, the object is still responding, so there is a reaction but no action. Field theory is employed to replace action at a distance theories. According to a field theory, the field is what transmits information between the source and the other object. The rate at which information is transmitted is finite, and the field can store energy. Even if the source were removed, the other object would still respond, and this response would not violate Relativity or Newton's Third Law.

Field: A field has a definition in mathematical physics that must be clarified. A function in n dimensions has an input in the form of an (n-1)-tupule. There is usually only one output value, but sometimes (like for holomorphic functions) there are more. Most functions have one output and that one output is (in n dimensions) a function of n-1 variables.  But a field in n-dimensions will always have components, each of which is a function of n variables. If it is a scalar field, then there is one component, if it is a vector field, then there are n components, and if it is a kth-rank tensor, then there are n^k components. So, for example a 2D scalar field would assign a scalar value to every point in the 2D region, whereas a function in 2D would take one input dimension and produce an output in the second dimension. In field equations, the dimensions are all input values. The output is a function of n variables. 

A comparison between a function in 2D (1 input axis, 1 output axis) and a field equation (specifically a vector field) with 2 input values defined at each ordered pair in the Cartesian space:

Wave: "Electromagnetic field wave" doesn't really mean anything. What we say is that there are wave-solutions to the Maxwell equations. The differential forms of the Maxwell equations are all source functions. According to them, there are two sources to an electric field (charges and changing magnetic fields), and there are two sources to a magnetic field (moving charges and changing electric fields). As a result, electric and magnetic fields are the result of each other, and are both fundamentally the result of a unified property called electromagnetism. A magnetic field is usually denoted B and an electric field E. These fields (remember, if one is present and changing, the other must be present) can propagate through space as plane waves.

 The wave solutions state that the d'lAmbertian operation over B and E fields is zero. Electromagnetic waves are plane propagations. The E and B fields are mutually perpendicular and perpendicular to the direction of propagation. The phase velocity of an electromagnetic propagation is a constant depending on the electric and magnetic constants for the medium. That's why Newton was wrong, by the way, since he predicts that velocity follows Galilean transforms. But magnetic and electric constants are invariant under coordinate transforms. The “Maxwell equations” are actually a bit of a misnomer. Two of them were formulated by Gauss, one by Ampere, and the other by Faraday, and the modern form with four equations in modern vector notation was formulated by Heaviside.

The primary contribution Maxwell made to the Maxwell equations was correcting Ampere’s Law to make it consistent with the continuity equation. But Maxwell’s primary contribution to our understanding of reality was to realize that there are wave solutions to these equations.

Resonance: Totally different thing. To understand resonance, it is necessary to understand that a wave propagates energy without the propagation of matter. For something like a water wave, we model this by saying that individual particles (which oscillate about fixed equilibrium points in phase with the other particles) are exhibiting simple harmonic motion. The nice thing about SHM is that the time period T for a system left to oscillate by itself (like a pendulum) depends only on one variable. That variable is the degree to which the medium allows the propagation of the wave. For a spring exhibiting SHM, one could change the mass and amplitude of the body oscillating and nothing would happen to T. The only way to change T would be to change k, a constant for a particular system that refers to the degree to which it is deformed by force being exerted on it. A wave whose particles oscillate with a particular speed in water would oscillate with a different speed in, say, syrup. Within any system, there is a natural frequency at which it oscillates which depends only on the constant for the medium. If you let a pendulum swing back and forth, it will tend to oscillate at that natural frequency determined only by its length (not by mass, angle of incline or amplitude).

Resonance is the principle by which the input of energy at a frequency which matches the natural frequency of the system causes the amplitude to increase in an arithmatic sequence (such as pushing a child on a swing set every time they swing back to you). In theory, in an undamped system would have an increase in amplitude up to infinity (or at least until, by the second law of thermodynamics, you ran out of useful energy). In reality, there is no such thing as an undamped system (which would violate the second law of thermodynamics). As you can see by observing the image, there is a rate function which gives the amplitude of a system without a driver where the amplitude A decays geometrically with n, the number of oscillations since t=0, meaning that:

A(t)=A₀e^-kn

Where c is a constant which will differ for the material in question and A₀ is the initial amplitude. This is an example of first order functions. The rate at which the amplitude dies away in an uncontrolled system depends purely on the number of oscillations that have occurred.Radioactive decay and First order chemical reactions work on the same principle.

Basically, what you should understand by familiarizing yourself with this is that when someone says they can “tap into electromagnetic field  wave resonance” they are seeing who they can impress when they stick random large words together.

The method ExxonMobile uses is based on the quasistatic approximation to Maxwell's equations; the permittivity is not a significant factor. The technique looks at contrasts in the electrical resistivity between highly-resistive oil-saturated formations, and highly-conductive saltwater-saturated formations or otherwise less resistive rocks and sediments. There are some secondary effects that are also of interest, but this is the primary indicator of the presence or absence of significant levels of petroleum and gas.