Welcome to my website!
Next to presenting my personal info, the purpose of my website is to distribute
some technical stuff and knowledge.
My curriculum vitae and some of my scientific papers about inversion can be
Some computer codes for Graham's algorithm, Cardano's method, Ferrari's method,
numerical dispersion analysis, and Cagniard-De Hoop technique are included.
Other technical topics and computer codes will be added later.
- Name: Mark Lam
- Nationality: Dutch
- E-mail: email@example.com
- Master of Science in Electrical Engineering (2003), Delft
University of Technology, Netherlands.
Graduation in applied electromagnetism and telecommunications: M.Sc. thesis.
- Bachelor of Science in Electrical Engineering (2001), Delft
University of Technology, Netherlands.
- Geophysical Exploration
Time-lapse seismic reservoir characterization with the aid of a regularized nonlinear inversion technique.
- Medical Imaging
Acoustic inversion with the aid of the scattering technique. Verification of theoretical
results and a comparison in the time and frequency domains.
Stabilization of inversion schemes using the nonlinear multiplicative
Applications in seismic signal processing, image processing and medical imaging.
- Cagniard-De Hoop technique
Analytical technique for 3D modelling of impulsive acoustic and electromagnetic waves in stratified media.
- Finite Volume Method
Numerical technique for solving partial differential equations governing the acoustic and electromagnetic waves on unstructured mesh grids.
- M. C. H. Lam,
"Time-lapse seismic reservoir monitoring with a local waveform inversion
Journal of Applied Geophysics, vol. 71, no. 4, pp. 99-108, Aug. 2010.
- A. T. de Hoop, C. H. Lam and B. J. Kooij,
"Parameterization of acoustic boundary absorption and dispersion properties
in time-domain source/receiver reflection measurement,"
The Journal of the Acoustical Society of America, vol. 118, pp. 654-660,
- C. H. Lam, B. J. Kooij and A. T. de Hoop,
"Impulsive sound reflection by an absorptive and dispersive planar
The Journal of the Acoustical Society of America, vol. 116, pp. 677-685,
- M. C. H. Lam (2010).
"On the macro velocity model in full-waveform inversion applied to
time-lapse seismic reservoir monitoring,"
Society of Exploration Geophysicists, SEG/Denver 2010, USA, pp. 2885-2889.
- M. C. H. Lam and M. D. Sacchi (2009).
"Seismic signal processing with automatic edge-preserving algorithms,"
Society of Exploration Geophysicists, SEG/Houston 2009, USA, pp. 2511-2515.
- C. H. Lam. P. M. van den Berg and D. Gisolf (2007).
"Nonlinear acoustic inversion of focused seismic data,"
Society of Exploration Geophysicists, SEG/San Antonio 2007, USA, pp.
- C. H. Lam. P. M. van den Berg and D. Gisolf (2007).
"Acoustic time-domain inversion of focused data,"
European Association of Geoscientists and Engineers, EAGE/London 2007, UK,
- C. H. Lam. P. M. van den Berg and D. Gisolf (2006).
"On the background model for nonlinear inversion of seismic data,"
Society of Exploration Geophysicists, SEG/New Orleans 2006, USA, pp.
- Lecture assistant Introduction to Electricity and Magnetism (2008,2007).
- Lecture assistant Introduction Electromagnetic Waves (2005,2004).
- Laboratory course assistant Signal Processing Laboratory Course
Algorithm implementation in MATLAB for speech signal processing and
BACKGROUND AND COURSES
- Electrical engineering: digital and statistical signal processing, array
signal processing, antennas, radar
- Physics: wave propagation and diffraction, waveguides, computational
- Mathematics: partial differential equations, finite-element method,
numerical analysis, functional analysis
- Geophysics: reservoir engineering, seismic data processing,
geo-statistics, fluid flow in porous media
The included computer codes are made available for students, and
not for commercial purposes nor scientific research.
TIME-DOMAIN WAVE REFLECTION
Transient Wave Reflection against a Planar Impedance Boundary
This book presents theoretical time-domain studies of both acoustic and
electromagnetic wave reflection against a planar impedance boundary.
The interest for investigating analytically the employment of the surface
impedance boundary approximation stems from the need of efficient wave
simulation tools to tackle large-scale transient wave modelling problems, also
called forward problems, in which approximations are desirably invoked for
reducing the required computational efforts to a minimum.
Presented analytical studies unveil the mathematical structure of the transient
acoustic and electromagnetic wave fields after reflection by an impedance plane,
about which general purpose wave simulation techniques such as the
finite-difference time-domain (FDTD) method and time-domain finite-element
method (TD-FEM) can only yield qualitative insights.
The first part of this book investigates impulsive acoustic wave reflection
against porous materials and viscous fluids, which are subjects of interest in
sound control and geophysical exploration, respectively.
The second part investigates transient electromagnetic wave reflection by
imperfectly conductive materials.
For these purposes, the elementary two-media configuration is considered, which
consists of a planar boundary that separates a simple medium from a complex
The reflected wave in the simple medium is of interest and the complex medium
is mathematically represented by an approximating impedance wall.
At the core of tackling the impedance boundary value problem corresponding to
the resulting half-space configuration is the derivation of the space-time
reflected-wave Green's function, to which end the extended Cagniard-De Hoop
method is invoked for the analytical transformation back to the time domain.
The main features of this time-domain method are the preservation of
causality by employing the unilateral Laplace transform and uniqueness of the
causal wave solution.
The analytically derived closed-form wave field expressions are fully discussed
in the main chapters to reveal the fundamental structure of the space-time
reflected wave fields in their dependence of the physical properties of the
Numerically computed time snaps of the reflected-wave Green's function and the
reflected-wave Green's tensors are illustrated to exhibit the spatial
distribution of the reflected wave fields in the near, intermediate and far
Furthermore, modelled time traces of the reflected wave fields are also
included in the main chapters to serve as benchmark results for general purpose
wave simulation software.
Time-lapse Seismic Reservoir Monitoring with a Local Waveform Inversion Technique
The characterization of changes in a producing hydrocarbon
reservoir is of importance for both fluid injection strategies and
an assessment of the reservoir.
In 4D seismic monitoring, a quantitative measure is obtained from
changes in the acoustic medium properties, of which the parameter
values are extracted from over time acquired seismic data.
In this paper, full-waveform inversion is applied to tackling a
class of 1.5D time-lapse seismic problems.
The local linear inversion concept is at the core of the applied
regularized iterative scheme, which aims at locally estimating
P-wave velocity parameters from seismic data, and requires a macro
velocity model that resembles the low-frequent representation of
the true P-wave velocity profile.
The comparative inversion results reveal substantial improvement
with regard to both kinematics and dynamics after performing three
For practical interest, the employment of updated and non-updated
background velocity models is addressed.
Two-Parameter Acoustic Waveform Inversion in the Local Born Approximation
using Inhomogeneous Background Models
A local Born inversion based regularized iterative scheme was
previously presented, which aims at retrieving only P-wave
velocity parameters from seismic data.
The additional estimation of mass density parameters is of
importance for a number of exploration and reservoir monitoring
applications, in which two-parameter full-waveform inversion is
desirable for high-resolution imaging of the subsurface.
In this abstract, an extension of the previous iterative scheme to
performing two-parameter acoustic inversion in the local Born
approximation is discussed.
Numerical results illustrate the capability of the inversion
scheme in simultaneously reconstructing measured borehole profiles
for the P-wave velocity and the mass density from noisy synthetic
data with SNR = 20 dB.
Inhomogeneous background models are employed in this 1.5D study,
which serves as a preliminary work to two-parameter inversion in
Fourier-Domain Extrapolation with Edge-Preserving Regularization
The Fourier-domain extrapolation property of edge-preserving
regularization (EPR) is proved in this paper with the aid of the
limiting Ewald circle from linear inverse scattering theory.
A tomographic imaging strategy based on a sequence of linear
inversions is first reviewed.
Comparative results obtained from linear inversion with and
without EPR are subsequently presented to verify the
spectral-domain reconstruction bounds and to illustrate correct
amplitude reconstruction exterior to the limiting Ewald disc.
The objective is to explain medical imaging results, which have a
resolution that is higher than what can be expected based on the
source signature's bandwidth if EPR-based linear inversion
techniques are employed.
Furthermore, super resolution obtained from EPR-based nonlinear
inversion methods is discussed in this theoretical study.
Edge-Preserving Multiplicative Regularization with Weighted Total Variation
An automatic inversion algorithm is presented, which targets at
edge restoration in low signal-to-noise (SNR) scenarios and is free from estimating
a regularization parameter.
The iterative scheme is based on the SNR-independent
multiplicative regularization technique and employs a weighted
total variation constraint.
Compared with standard total variation (TV) regularization, utilizing the weighted
strategy is first related to half-quadratic regularization, and
then shown to yield improvement in edge preservation for a range
of practical SNR values.
Furthermore, various deterministic regularization strategies are
compared in a deconvolution setting, in which weighted TV
regularization is shown to outperform weighted l2-norm
SCATTERING IN THE TIME AND FREQUENCY DOMAINS
Review of the Convergence Criterion for the Time-Domain Neumann
Series applied to Wave Scattering by Dispersive Metals
This article reviews the convergence criterion for the time-domain
Neumann series and presents novel numerical experiments.
In [De Hoop, J. Opt. Soc. Am. A, vol. 8, pp. 1256-1260, 1991],
fundamentally different convergence criteria for the time- and
frequency-domain Neumann series were derived and argued to be
caused by causality of wave motion, which is only preserved in the
For the class of dispersive metals, it was theoretically shown
that only the time-domain Neumann series is unconditionally
That result is in this study numerically supported by
investigating impulsive electromagnetic wave scattering in a
With experiments using different numerical implementations,
instability of any FFT-based implementation of the Neumann series
Note that though all codes have thorougly been checked, bugs might still be
Graham's Algorithm for 2D Convex Hull Construction
In computational geometry, which is heavily applied to Computer Aided Design
tools, a fast generation of the convex hull from a point set in a plane is given
by Graham's algorithm.
A pseudo code with complexity of O(N log N) is given for example by WIKIPEDIA.
Note the sorting algorithm for ordering the angles in the included code.
Furthermore, a more efficient implementation using data structures such as
linked lists instead of vectors is recommended.
Procedure in Convex Hull Construction
Cardano's Method for Solving Cubic Equations
In nonlinear optimization, solving cubic equations with real coefficient is
encountered for example if the multiplicative regularization technique is
Cardano's method provides a procedure for analytical computation of the three
roots of a cubic equation.
Many websites are devoted to this Cardano's technique, which outperforms numerical
search methods in solving for the roots of a third-order polynomial.
The mathematical derivations/procedures can be found in for example WIKIPEDIA.
Ferrari's Method for Solving Quartic Equations
In applications such as computer graphics, solving quartic equations with real
coefficients must be carried out with the highest efficiency.
Ferrari's method provides a procedure for solving for the roots of a
fourth-order polynomial by first turning the quartic equation into depressed
form and then invoking Cardano's method, e.g. WIKIPEDIA.
Numerical Dispersion in Finite-Difference Time-Domain Method
Numerical dispersion is a well-known phenomenon in grid based time-domain
forward modelling techniques such as the FDTD.
The included program compares the FDTD 1D technique (without Perfectly Matched
Layers) with an analytical solution in a two-media configuration.
The source domain is `well-sampled,' whereas the source-free domain is `under-sampled'
as a result of a higher mass density in the investigated seismic configuration.
This problem arises in general when costly, but necessary, local grid refinement
in spatial regions with a higher `index number' is ignored in practical FDTD
Numerical Dispersion Analysis:
Increasing Phase Lagging as Time evolves
Cagniard-De Hoop Method applied to Canonical Fluid/Solid Configuration
Analyzing transient acoustic wave reflection against a fluid/solid interface is
of interest in geophysical exploration, for example in borehole/well log
The included code is based on the Cagniard-De Hoop method, cf. JASA paper by
De Hoop and Van der Heijden (1983).
Two time traces of the 2D reflected-wave Green's function for the acoustic
pressure are depicted below.
Note the head-wave arrival due to the P-wave in the solid (first discontinuity)
and the Scholte wave (surface wave represented by the last lump).
The body-wave arrival and the effect of the S-wave in the solid are found in
between these two phenomena, with the order of occurrence being dependent on
the consideration of a fast or slow rock formation.
Cagniard-De Hoop Method (2D Fluid/Solid):
Acoustic Response of a Fast Rock Formation (left) and Slow Rock Formation
Delaunay Triangulation for 2D Mesh Generation
Delaunay triangulation method produces a 2D topology and is based on Watson's algorithm.
It is heavily used for unstructured mesh grid generation for the purpose of 2D finite-element analysis.
A more efficient implementation using data structures such as
linked lists instead of vectors is recommended.
Delaunay Triangulation Algorithm:
Procedure in 2D Mesh Generation