Andrew,
Derivatives (or better said Gradients) are irrelevant? Not at all. They are
heart and soul.
First of all, the intensity of the field (be this Gravity, Magnetics,
Electrical, Thermal, etc) is the gradient of the potential.
In exploration, while Gradients ("Derivatives" in usual jargon) are used to
map geometries, whether horizontal extensions, vertical emplacements, or
both simultaneously, the Tilt is used to enhance or amplify the amplitude
of deeper buried bodies. At the end of the day, the Tilt acts like an
"amplitude equalizer" of the intensity.
Just think how
(1) the maximum intensity amplitude decreases with increasing depth of the
source;
(2) the flanks of the anomaly (or horizontal gradients) decrease with
increasing depth of the source;
(3) how the horizontal gradients reflect themselves again in the vertical
gradients.
Everything is explained in Laplace and Potential Theory. However, to make
it simple, the model I use to explain to the non-geophysicist is the "heat
radiator model".
I have lots of geological examples. I could dig out some public data to
show.
Without writing any single mathematical formula, everytime I explain this
to geologists using their own geological and geophysical data, they all
understand. The only "formula" I show to them is the general relation in
geophysical exploration as follows:
Intensity of the anomaly == (contrast of the rock physical value) * (volume
of the source) / (distance between sensor and source)
Newton's equation is only an example of this relation.
Regards
Sergio.-
On Thu, Oct 8, 2020 at 5:42 PM Andrew Long via SEGMIN <
[email protected]> wrote:
> Hi to all of you,
> On the question of geophysical data, and such refinements as Verduzco, or
> someone else, I would like to mention that depth of investigation is key.
> The problem becomes more simple with depth as a result of entropy. Henry's
> comment alludes to what we understand geologically. It all becomes more
> simple as you traverse the Earth's traditionally geophysical Earth concept.
> It's all about entropy and Einstein's concept of relativity. He was right
> about the gravity, and Newton's doubtful equations that you all use
> faithfully in exploration.
> Tilt, derivatives, etc all irrelevant. Sorry.
> Feel free to give me the full inquisition.
> Andrew
>
> On Thu, 8 Oct 2020, 5:04 pm , <[email protected]> wrote:
>
>>
>>
>>
>> Today's Topics:
>>
>> 1. Re: Tilt is not a derivative (S E Geoscience and Exploration)
>>
>>
>> ----------------------------------------------------------------------
>>
>> Message: 1
>> Date: Wed, 7 Oct 2020 16:13:26 -0400
>> From: S E Geoscience and Exploration
>> <[email protected]>
>> To: [email protected]
>> Subject: Re: [SEGMIN] Tilt is not a derivative
>> Message-ID:
>> <CAN2kzWJA_1+Bc6NAvZ411=U=
>> [email protected]>
>> Content-Type: text/plain; charset="utf-8"
>>
>> Henry,
>>
>> it is definitely not a trick. Those orthogonal gradients are
>> intertwined more than we think. The explanation is to be found in
>> Potential
>> Theory.
>>
>> Regards
>>
>> On Wed, Oct 7, 2020 at 4:03 PM Henry Lyatsky via SEGMIN <
>> [email protected]> wrote:
>>
>> > Personally, I am no fan of tricks that combine such dissimilar beasts as
>> > vertical and horizontal derivatives. Math is abstract and it can bear
>> > anything, but we should remain skeptical when it comes to mixing apples
>> and
>> > oranges. For this reason, I also dislike the total gradient (analytic
>> > signal).
>> >
>> > The mathematically simplest methods are best, combined with solid
>> > geological thinking.
>> >
>> > *Henry.........................................................*
>> > *Dr. Henry Lyatsky, P.Geoph., P.Geol.*
>> > *cell: 403/710-7490 [email protected] <[email protected]>*
>> > *Skype: henry.lyatsky*
>> > *www.linkedin.com/in/lyatsky/* <https://www.linkedin.com/in/lyatsky/>
>> >
>> > *?This message and any attachments are confidential. Any redistribution
>> > is strictly prohibited. If you are not an intended recipient, please
>> > notify the sender and delete this message and attachments from your
>> > system. Please check this message, links and attachments for viruses;
>> we
>> > accept no liability for any malware damage. Thank you.*
>> >
>> > ------------------------------
>> > *From:* SEGMIN <[email protected]> on behalf of S E
>> > Geoscience and Exploration via SEGMIN <[email protected]>
>> > *Sent:* Wednesday, October 7, 2020 1:43 PM
>> > *To:* [email protected] <[email protected]>
>> > *Cc:* S E Geoscience and Exploration <
>> > [email protected]>
>> > *Subject:* Re: [SEGMIN] Tilt is not a derivative
>> >
>> > Alan
>> >
>> > thank you for the comments.
>> >
>> > My point is that the term "Tilt Derivative" might be rather confusing
>> for
>> > non geophysicists, since they might tend to think that it is a
>> derivative,
>> > or a change of a parameter Y (e.g. Magnetic Induction B) in relation to
>> > parameter X (e.g., Depth Z or Time t), which is not.
>> >
>> > "Derivative Tilt" is certainly more appropriate. When I explain the
>> useful
>> > parameter to the geoscientist who is not knowledgeable in potential
>> > techniques, I tell them that it is a sort of "amplitude equalizer" in
>> order
>> > to enhance weaker and low frequency signals in order to see better in
>> areas
>> > with thick cover, so that they understand.
>> >
>> > Generally, I personally prefer to use the term "Gradient" instead of
>> > "Derivative", for obvious reasons. But I understand that technical
>> jargon
>> > is deeply rooted.
>> >
>> > Thanks
>> >
>> >
>> >
>> > On Wed, Oct 7, 2020 at 11:47 AM Alan Reid via SEGMIN <
>> > [email protected]> wrote:
>> >
>> > Folks,
>> >
>> > There?s a clear enough definition in the paper by Verduzco et al in The
>> > Meter Reader (TLE February 2004). I believe they coined the term, so
>> their
>> > definition should stand. TDR (Tilt Derivative) is effectively the tilt
>> of
>> > the derivatives, They also define the ?TDR_THDR? which is the total
>> > horizontal derivative of the TDR. I do not believe Verduzco et al were
>> > trying to suggest that Tilt is a derivative. Its clearly not.
>> >
>> > Given that they defined and published the term, perhaps we should
>> respect
>> > that and not go off with our own names for this entity? Nor go off with
>> > other definitions for the term?
>> >
>> > I confess that ?Derivative Tilt? might have been a more descriptive
>> name,
>> > but it somehow doesn?t have much of a ring, does it? Anyway, its useful
>> as
>> > described. And I teach it and use it in that form.
>> >
>> > I do not have any conflict of interest to declare, here.
>> >
>> > Regards
>> >
>> > Alan Reid
>> >
>> > On 6 Oct 2020, at 18:40, S E Geoscience and Exploration via SEGMIN <
>> > [email protected]> wrote:
>> >
>> > Thanks.
>> >
>> > I prefer to call it "Amplitude Equalizer", sort of.
>> >
>> > On Tue, Oct 6, 2020 at 1:35 PM Richard Smith via SEGMIN <
>> > [email protected]> wrote:
>> >
>> > Perhaps it is called tilt derivative as you have to calculate
>> derivatives
>> > to calculate it, as in the "tilt of the derivatives". Personally, I
>> > prefer the term, "local phase" (Thurston and Smith, 1997), but I have a
>> > conflict of interest!
>> >
>> > Regards
>> > Richard Smith
>> >
>> >
>> >
>> > -----Original Message-----
>> > From: S E Geoscience and Exploration via SEGMIN <
>> [email protected]>
>> > To: [email protected]
>> > Cc: S E Geoscience and Exploration <
>> > [email protected]>
>> > Sent: Tue, Oct 6, 2020 11:29 am
>> > Subject: [SEGMIN] Tilt is not a derivative
>> >
>> > Dear all,
>> >
>> > I am always so puzzled. Why do people call the Tilt in potential
>> > techniques a derivative? It is not.
>> >
>> > Regards
>> >
>> > --
>> > *Sergio Espinosa, Ph.D., P.Geo*
>> > Director, Geophysics
>> > *S E G*eoscience & *Ex*ploration
>> > -----------------------
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>> >
>> > --
>> > *Sergio Espinosa, Ph.D., P.Geo*
>> > Director, Geophysics
>> > *S E G*eoscience & *Ex*ploration
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>> >
>> > Alan B Reid PhD
>> > Reid Geophysics Ltd
>> > 7 Keymer House
>> > Michel Grove
>> > Eastbourne BN21 1JZ
>> > UK
>> >
>> > Phone: +44 (0) 1323 735520
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>> >
>> > --
>> > *Sergio Espinosa, Ph.D., P.Geo*
>> > Director, Geophysics
>> > *S E G*eoscience & *Ex*ploration
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>> --
>> *Sergio Espinosa, Ph.D., P.Geo*
>> Director, Geophysics
>> *S E G*eoscience & *Ex*ploration
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Director, Geophysics
*S E G*eoscience & *Ex*ploration
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