Hampson russell inversion
He then worked for Teknica and Veritas in Calgary before co-founding Hampson-Russell in 1987 with Dan Hampson. Or, take some quantitative industry training courses and see what the mathematics is really telling you about your data.īrian Russell started his career as an exploration geophysicist with Chevron in 1976, and worked for Chevron affiliates in both Calgary and Houston. Then, pick up a copy of Geophysics, or any geophysics textbook, and see how many of the equations can be expressed in the same way. On the other hand, if you are thinking: ‘why would I ever need to use those boring-looking equations,’ you are a tougher challenge! I would recommend starting with these equations and really trying to understand them (perhaps you will need to dust off your linear algebra, and I recommend the book by Gilbert Strang).
![hampson russell inversion hampson russell inversion](https://i.ytimg.com/vi/Gok8hTiqpa4/maxresdefault.jpg)
If you are thinking: ‘yes, I saw those equations once in a class, but haven’t thought about them for years,’ perhaps I can inspire you to look at them again.
![hampson russell inversion hampson russell inversion](https://d3i71xaburhd42.cloudfront.net/47aaecfe072c485d8e1f779e7dcfe3a48f2f6c62/5-Figure4-1.png)
If you are thinking: ‘what’s the big deal, I use those types of equations every day,’ you probably don’t need my advice. The way that you react to these equations tells me a lot about you as a geophysicist. So, what lesson should we take away from these equations? It is the basis of deconvolution, AVO attribute analysis, post- and pre-stack inversion, refraction and reflection statics, and so on. Again, this equation, sometimes called the Normal Equation, is ubiquitous in geophysics. $$ m = (G^\mathrm\) (and adding a little pre-whitening by multiplying the value λ by I, the k by k identity matrix), and h is the zero-lag cross-correlation vector, found by multiplying the transpose of the G matrix by the data vector. Since n is usually greater than k, the solution can be written: Solving the equation is a little more difficult. The simplicity of the way I have written the equation hides the fact that d is usually written as an n-dimensional vector, m as a k-dimensional vector, and G as an n row by k column matrix. This ubiquitous equation can be found in every area of geophysics, from seismology through potential fields to electromagnetic theory. Where d is our data, a set of n geophysical observations, m is our model, a set of k model parameters, and G is a linearized relationship that relates the observations to the parameters. Let me illustrate my point with two equations. However, I do think that an appreciation of some of the fundamental applied mathematical ideas in our profession can go a long way towards enhancing your enjoyment and appreciation of your day-to-day job. And I do not expect that every exploration geophysicist should be able to understand the latest implementation of Green’s functions in anisotropic depth imaging. Indeed, picking up a copy of Geophysics and trying to read every article is a daunting task. But once we were in the working world, especially if we became seismic interpreters, we tended to leave the details to the specialists.
![hampson russell inversion hampson russell inversion](https://media.springernature.com/original/springer-static/image/chp%3A10.1007%2F978-3-030-45662-7_3/MediaObjects/494518_1_En_3_Fig22_HTML.png)
We all struggled through tough math and physics classes at university to get our degrees. By that I mean that it is a science based on ‘hard’ facts, but also that it can be difficult. Neglect it and your muscles (intellectual or physical) fade away. Do a little bit every day and you stay in shape, either intellectually (in the case of math) or physically (in the case of exercising).