Can you please review these slides and comment?

SergioEspinosa1
SergioEspinosa1 Posts: 28 Fluorite Rank Badge
edited January 16 in Oasis montaj

Dear all,

as many of you perhaps know, I train geologists with a strong and genuine interest in Geophysics.

What can I still add to this set of slides? Check please attachment.

The geological meaning of this topic is another set of slides which I will be sharing later.

Regards

Sergio.-

Explaining the Gradient as a Vector.pdf

Comments

  • ElizabethBaranyi2
    ElizabethBaranyi2 Posts: 16 mod

    @Sergio reviewing your slides needs more context.

  • SergioEspinosa1
    SergioEspinosa1 Posts: 28 Fluorite Rank Badge
    edited March 28

    Dear Elisabeth,

    Here is for example more context.

    A vector V in the 3D space can be decomposed into the three orthogonal components Vx, Vy, and Vz.

    The magnitude (called mathematically modulus) of that vector is calculated as follow:

    SQRT of ( (Vx)^2 + (Vy)^2 + (Vy)^2 )

    Now, the spatial derivative of a scalar is called gradient, and gradient is a vector. 

    This means the gradient of the scalar TMI can be described as d(TMI) / dX, d(TMI) / dY, d(TMI) / dZ.

    Last is normally known as First Vertical Derivative.   

    The magnitude (called mathematically modulus) of that Gradient vector is calculated as follow:

    SQRT of ( (dTMI/dx)^2 + ( dTMI/dy)^2 + ( dTMI/dz )^2 )

    I have asked myself all my life since I started using Oasis montaj, why Geosoft calls that "Analytic Signal". That should be called Gradient Magnitude.

    Also, the ratio (Vertical Gradient) / (Magnitude of Horizontal Gradient) is a dimensionless amplitude-equalizing value. This means, it does not matter how deep or how shallow a source is. All sources will appear as coming from the same depth.

    When we apply the trigonometric function arctan to that ratio, the ratio becomes an angle. This is an amplitude-normalizing value. It does not matter whether the project is related to archaeology or to exploration in the Gulf of Mexico, the values will be normalized between -1.56 and +1.56 radians.

    I have asked myself all my life since I started using Oasis montaj, why Geosoft calls that "Tilt Derivative (TDR)". That should be called just Tilt. 

    And Tilt is an angle only when it is drawn on paper or only when we imagine the Gradient vector field in 3D space. But that angle has nothing to do with geological angles such as strikes, dips, and plunges.

    Naming all these parameters wrongly only confuses the non-geophysicists (and also some geophysicists). I read recently in a text that the physical unit of "nT/m" was given to a parameter called Tilt Angle Derivative. As said, Tilt is neither a derivative nor a (geological) angle. 

    Would this be more context?

    Thanks

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